• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Tidal inlet hydraulics
 Inlet ebb shoals related to coastal...
 Management of sandy inlets: coastal...
 Understanding fluid mud in a dynamic...
 Laboratory studies on cohesive...






Group Title: Miscellaneous Publication - University of Florida. Coastal and Oceanographic Engineering Program ; 91/5
Title: Selected papers for a short course on coastal engineering
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00074649/00001
 Material Information
Title: Selected papers for a short course on coastal engineering
Series Title: Miscellaneous Publication - University of Florida. Coastal and Oceanographic Engineering Program ; 91/5
Physical Description: Book
Creator: Mehta, Ashish J.
Affiliation: University of Florida -- Gainesville -- College of Engineering -- Department of Civil and Coastal Engineering -- Coastal and Oceanographic Program
Publisher: Dept. of Coastal and Oceanographic Engineering, University of Florida
Publication Date: 1991
 Subjects
Subject: Coastal Engineering
University of Florida.   ( lcsh )
Spatial Coverage: North America -- United States of America -- Florida
 Notes
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00074649
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida

Table of Contents
    Front Cover
        Page 1
    Title Page
        Page 2
    Tidal inlet hydraulics
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Inlet ebb shoals related to coastal parameters
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
    Management of sandy inlets: coastal and environmental engineering imperatives
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
    Understanding fluid mud in a dynamic environment
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
    Laboratory studies on cohesive sediment deposition and erosion
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
Full Text




UFL/COEL-MP-91/5


SELECTED PAPERS FOR A SHORT COURSE ON
COASTAL ENGINEERING







by







Ashish J. Mehta


1991


L















SELECTED PAPERS FOR A SHORT COURSE ON

COASTAL ENGINEERING




by



Ashish J. Mehta

Professor, Coastal and Oceanographic Engineering

University of Florida

Gainesville, Florida, U.S.A.




for


Universidad del Norte

Barranquilla, Colombia


May, 1991


L










TIDAL INLET HYDRAULICS


By Ashish J. Mehta' and Prakash B. Joshi,2 Members, ASCE

ABSTRACT: The unique physiographic features of tidal inlets make it convenient
to treat inlet hydraulics in two parts, one pertaining to the channel through the land
barrier, and the other to the near-field region characterized by ebb and flood cir-
culations beyond the channel. Theoretical formulations for flow description in these
regions lead to approximate but useful analytic solutions in simple cases. For de-
tailed hydraulic description, physical and numerical modeling techniques are widely
employed. Limitations in predictive capabilities seem to arise mainly from a lack
of fuller understanding of hydromechanical processes. Such interactive phenomena
as the propagation of the buoyant jet through ambient sea waters during the ebbing
phase of tidal flow, and the influence of waves on the tidal flow regime, require
considerable additional scrutiny via field investigations. The complex nature of inlet
behavior necessitates the collection of site-specific prototype information as an es-
sential component of hydraulic analysis and interpretation.

INTRODUCTION

Inlets have long attracted the attention of hydraulic engineers (Brown 1928;
Brunn and Gerritsen 1960; Chapman 1923; Eads 1971; Escoffier 1940; Keu-
legen 1967; O'Brien 1931; Stevenson 1886; Watt 1905). In the-past few
decades, research interest has increased considerably as a result of various
engineering works and the ecological ramifications of enhanced human ac-
tivity along lands bordering inlets. Thus, for example, the role of inlets in
causing alteration of adjacent shorelines, trapping or expelling sediment, and
exchanging polluted bay or lagoon waters with the sea have become matters
of concern (Dean and Walton 1975; Mehta and Joshi 1984; Sorensen 1980;
Taylor and Dean 1974).
Fig. 1 shows a simple inlet-bay system. It consists of a tidal inlet con-
necting the bay (or lagoon) with the sea (or ocean). Tributary inflow leaves
the inlet as freshwater outflow. The bay may be a distinct physiographic
feature or, as in the case of many river mouths, it may constitute the seaward
end of the river influenced by tide. Most inlets have a rather well-defined
throat section, i.e., flow cross section of minimum area, which is analogous
to the vena contract of such flow-measuring devices as the Venturi meter.
Inlets. may therefore be "calibrated" by determining a coefficient that relates
the discharge to the tidal head difference between the sea and the bay.
As a result of the high degree of variability in inlet physiography, such
commonly used terms as channel, gorge, entrance, and mouth require clar-
ification. The term channel is considered here to include the entire inlet length
between the bayward and the seaward ends of the land barrier, including
jetties, where applicable. The gorge is the segment of the channel between
the throat and the bayward end of the channel. The entrance, or the mouth,
is the region seaward of the throat up to, and including, the outer bar or ebb
'Prof., Coast. and Oceanographic Engrg. Dept., Univ. of Florida, Gainesville, FL
32611.
2Prin. Res. Sci., Physical Sci. Inc., Andover, MA 01810.
Note. Discussion open until April 1, 1989. To extend the closing date one month,
a written request must be filed with the ASCE Manager of Journals. The manuscript
for this paper was submitted for review and possible publication on October 17, 1986.
This paper is part of the Journal of Hydraulic Engineering, Vol. 114, No. 11, No-
vember, 1988. ASCE, ISSN 0733-9429/88/0011-1321/$1.00 + $.15 per page.
Paper No. 22883.


1321


r --I








Inflow






-:' Bay
or
Lagoon .'

Throat
Barrier Barrier

Sea
or
Ocean

FIG. 1. Simple Inlet-Bay System with Tributary Inflow

shoal. Thus the channel segment seaward of the throat is a part of the mouth.
The term near-field will be interpreted as the region encompassing inlet-in-
fluenced waters in the bay and the sea, not including the channel.
Hydraulic information of typical interest includes temporal and spatial vari-
ations of currents and water level in the channel and vicinity. Depending
upon the degree of accuracy of the answer desired, several predictive ap-
proaches are available. Relatively simple analytical approaches, even though
approximate, yield quick answers and are used quite extensively. Channel
and near-field hydraulics are described in the sequel, with reference to an-
alytic solutions followed by physical and numerical modeling. This paper is
the outcome of effort by the writers as members of ASCE Task Committee
on Tidal Inlet Hydraulics. The goal of this committee was to assess and report
on the state-of-the-art understanding of long wave propagation through tidal
entrances.

CHANNEL HYDRAULICS

Governing Equations
An idealized inlet is considered to be a relatively short and geometrically
narrow, but hydraulically wide, open channel with mean cross-sectional area
Ac, mean depth he, and length L,. The sea tide represents the boundary con-
dition, or the forcing function, at one end of the channel. The bay, repre-
senting storage, imposes the boundary condition at the other end. The one-
dimensional, depth- and width-averaged shallow (long) water wave equation
for the channel is
au au a8q n2uul
+ u x ................... ............(1)
at ax ax h


1322









2
ken-2g
L Lc bu 2gn2Lc U2
_- 0g 't2 hC4/3 2g
Mean o ~ -- ... ,J__-kex- -
Water Level *

Sea u=O hc Channel Bay u=O

LC

FIG. 2. Contributions to Total Head Loss in Idealized Channel


where u(x, t) = the cross-section averaged flow velocity in the x-direction,
i.e., along the length of the channel; t = time, l-(x,t) = the tidal elevation
with respect to mean water level; and n = Manning's bed resistance coef-
ficient. The term n2u lu/h1/3 is the slope of the energy grade line in the chan-
nel.
Given no(t) and aqB(t) as the tidal elevations in the sea and in the bay,
respectively, Eq. 1 upon integration over length Lc yields

LZ Qu ( 2gn2L,\ ulul
o = ke,, + k, + 4/3 .......... ............ (2)
g at h4 I 2g

where u and -q now are functions of time only. The quantities k,, and kex are
the head loss coefficients associated with channel entrance and exit flows,
respectively. Three noteworthy assumptions inherent in Eq. 2 are: (1) Current
velocities in the bay and the sea are negligible compared to those in the
channel; (2) the tidal amplitude is small compared to the mean depth; and
(3) change of water volume in the channel due to tidal variation is negligible
compared to mean volume in the channel.
The total head, -qo qsB, is the sum of four contributions indicated by the
dashed lines in Fig. 2. These are: entrance loss, k,,u2/2g; distributed loss
due to bed friction, 2gn2Lc/h/3; head due to inertia, (Lc/g)au/at, and exit
loss, kexu2/2g. By analogy with steady-state electrical or acoustical problems,
the term within parentheses in Eq. 2 has been referred to as impedance, F
(O'Brien and Clark 1974).
Application of Eq. 2 additionally requires a continuity relationship for the
bay storage volume -V-, i.e., Q = Qf + d--/dt, where the channel discharge
Q is equal to uAc, and Qf = the freshwater discharge. At this point, an as-
sumption is introduced concerning the bay, which is considered to be rela-
tively small in surface area as well as deep, such that the tide propagates
rapidly through the bay waters. As a consequence, spatial gradients in the
bay water surface at any instant may be ignored. This condition has been
referred to as hydraulic filling (O'Brien and Clark 1974). Continuity may
therefore be expressed in terms of velocity u according to

Au + (3)
A, dt A,

where AB = the bay surface area. .


1323








Analytic Solutions
Solving the governing equations, Eqs. 2 and 3, analytically requires some
additional simplifying assumptions. The sea tide is usually considered to be
sinusoidal, i.e., 9o = ao sin (ot T), where ao = the tidal amplitude, a =
the tidal frequency; and T = the angular measure of the lag of slack water
in the channel after midtide in the sea. The parameters AB and Qf are assumed
to be independent of time. Then, by eliminating u between Eqs. 2 and 3,
the following is obtained:
d\B FAB (dqB Qf\ dB Q, gAc gAca .,
S+ FAB- + Q -+ + + B= -Aa sin (o-t ) ..... (4)
dt 2ACL,\ dt ABI dt AB LAB LAB
Solutions to Eqs. 3 and 4 that have appeared in the literature fall broadly
into two categories: (1) Those in which both the freshwater inflow Qf and
the inertia term d2%B/dt2 have been ignored; and (2) those in which the middle
term on the left-hand side of Eq. 4 is essentially linearized or simplified
'(Baines 1958; Brown 1928; Chapman 1923; Dean 1971; Escoffier 1940; Es-
coffier and Walton 1979; Goodwin 1974; Keulegan 1967; Kondo 1975; Mehta
and Ozsoy 1978; Mota Oliveira 1970).
As a consequence of their relative simplicity, the solutions of Keulegan
(1967) are commonly used, and it is worthwhile stating the assumptions un-
der which they are obtained. The assumptions are: (1) The inlet and bay
banks are vertical; (2) the range of tide is small compared with the depth of
water everywhere and, as a corollary, the time variation of water volume in
the channel is small compared to the mean channel volume; (3) the bay water
surface remains horizontal at all times; (4) the mean water level in the bay
equals that in the sea; (5) flow acceleration in the channel is negligible; (6)
there is no freshwater discharge; and (7) the tide in the sea is sinusoidal.
Thus the head difference, 9q, riB, is due to bed frictional dissipation plus
entrance and exit losses. Under these conditions, Eqs. 3 and 4 are simplified
and can be solved for the channel current and the bay tide, both of which
can be related uniquely to the dimensionless parameter, K = (Ac/orA)(2g/
Fao)1/2. This parameter is referred to as the coefficient of filling or repletion,
since bay filling increases with increasing K.
A definition sketch for the time-variations of -q,, jIB and u is shown in Fig.
3. Principal parameters that define these curves are ao, aB, T or E (lag of slack
water after high water or low water in the sea), and the maximum velocity
u,. A characteristic feature of Keulegan's result is that slack water (Ur = 0)
occurs when the bay elevation is at its maximum (or minimum) value, i.e.,
aB. Furthermore, as the lag E (= 0.5rr T) increases, the bay tide becomes
smaller until E approaches 900, when there is no tidal variation in the bay.
This limiting situation arises as K 0, which can occur, for example, when
Ac/AB -> 0, or when the impedance F becomes very large as the inlet cross
section diminishes. Another limiting situation occurs as K -> c, when E ->
0. This is the case of a very wide inlet with large Ac/AB or very small F. In
this case a, approaches ao, and the bay essentially becomes a part of the sea
without the constricting influence of the inlet. Finally, the maximum velocity
u, occurs when qo 'rB is a maximum at midtide in the bay.
Eqs. 3 and 4 can be solved in a different way without excluding the inertia
term, and without linearization of the equations themselves, but by ignoring
the generated higher harmonics in obtaining a first-order solution, as shown


1324












IHW in Bay
{ Slack Water in Channel


in Channel


KC--


FIG. 3. Sea Tide, Bay Tide, and Current through Channel as Functions of Di-
mensionless Time (radians)


0.05 0.
0.05 o.I


0.5 1.0
Dimensionless Frequency, a,


FIG. 4. Dimensionless Bay Tide Amplitude, d, or Channel Velocity a,, as Func-
tions of Dimensionless Frequency a,


1325











120I. -. ///_ _20/
W "-" Maximum Value of E 0
without Inertia

W; 60


5 1, 0.5

0.05 0.1 0.5 1.0 5.0
Dimensionless Frequency, xc

FIG. 5. Lag e..as Function of Dimensionless Frequency a,

by Ozsoy (Dilorenzo 1986; Mehta and Ozsoy 1978). This procedure, cou-
pled with a sinusoidal variation of the flow velocity u, leads to the results
plotted in Figs. 4 and 5. The following dimensionless quantities are repre-
sented: bay amplitude, d, = aB/ao; channel velocity, im = u,Ac/ao'AB; tidal
frequency, xa = cr(LcAB/gAc)'/2; and bed dissipation coefficient, 3 = aoFAB/
2LAc. Significant features (not predicted by Keulegan's results) are bay water
level amplification (d4 > 1) under a certain range of conditions specified by
a, and p (Fig. 4) and lag E greater than 900 (Fig. 5). Both features are
exhibited by several inlet-bay systems (Dorrestein 1961; Mehta and Ozsoy
1978; O'Brien and Clark 1974; Sorensen and Seelig 1976). Another con-
sequence of the retention of the inertia term is that unlike the Keulegan case,
the time of slack water does not necessarily coincide with high or low tide
in the bay. It can be easily shown that at slack, the bay and the sea tide
elevations differ by an amount equal to the contribution to the head from
flow inertia. If inertia is ignored, Ozsoy's solutions become similar in form
to those obtained by Brown (1928) and Dean (1971).
Eqs. 3 and 4 can be solved inclusive of freshwater discharge, as shown
by Escoffier and Walton (1979). This analytic solution is achieved by re-
placing the middle term on the left-hand side of Eq. 4 with a linear term and
then minimizing the integral of the difference between the linear and the
nonlinear terms over a tidal period. In the absence of freshwater discharge,
the resulting equations become identical to those given in Figs. 4 and 5.
Applications of Eqs. 3 (with Qf = 0) and 4 (usually in the linearized form)
to multiple inlet-bay systems by obtaining analytic solutions have been con-
sidered (Cotter 1974; Dean 1971; Dilorenzo 1986; Keulegan 1967; Mota
Oliveira 1970).

HYDRAULIC PARAMETERS

Tidal Amplitude in Sea
If National Ocean Service tide tables or similar documentation of coastal
tides is used, care should be exercised in selecting the tidal amplitude a,,
since any tidal record obtained near an inlet, e.g., at one of the jetties or at
a bridge spanning the channel, will be affected by numerous factors, in-


1326








cluding the draw-down of the water surface and the effects of freshwater
discharge. It is preferable to select ao, for example, by interpolating the tide
between outer coast values flanking the inlet (Mehta and Ozsoy 1978).
If measurements are required, the gage should be located at such a distance
from the inlet as to minimize the influence of inlet currents.

Equivalent Length and Throat
The equivalent length Lc of an ideal channel is a hypothetical quantity that
is related to the length Lr of a real channel by requiring that the head loss
due to bed friction be equal in the two cases. The introduction of this def-
inition of Lc essentially means that the channel can be conveniently consid-
ered to be prismatic, e.g., having a cross section equal to that at the throat.
The current velocity in the governing equations also therefore becomes equal
to that at the throat. These requirements lead to the following relationship
for Lc (Escoffier 1977):
i=mm AXi
L..A.3 ............................................ (5)
i=1 hi/3A
where hc = the depth at the throat. In using Eq. 5, the channel must be
subdivided into mm sections of lengths Axi, depths hi, and cross-sectional
areas A,. In deriving this equation, Manning's bed resistance coefficient has
been assumed to be constant throughout the channel. A similar expression
for Lc is obtained by assuming the Darcy friction factor to be constant (O'Brien
and Clark 1974). Keulegan (1967) obtained an equivalent cross-sectional area,
as opposed to Lc, for the idealized channel.
When inertia effects are significant, a small additional correction to L, in
the dimensionless frequency a, has been recommended. Such a correction
was first evaluated for the case of a frictionless cylindrical tube coupled to
a half-space, later used in the problem of harbor resonance due to a fric-
tionless channel, and subsequently applied to inlets (Mehta and Ozsoy 1978;
Sorensen and Seelig 1976).

Bed Resistance and Loss Coefficients
A major difference between bed resistance in an inlet channel and in a
river arises due to the oscillatory nature of flow in the former case. The flow
depth and the bed form vary with the stage of tide. Ripples, dunes, or a flat
bed can occur in succession over a single tidal cycle depending upon the
grain size and the Froude number. The situation is further complicated by
density-driven circulation as well as by wind-generated waves.
For many engineering purposes, it is sufficient to estimate the bed resis-
tance coefficient on a tide-averaged basis. Using the Ch6zy coefficient C,
Bruun and Gerritsen (1960) proposed an approximate empirical relationship:
C = a2 + a3 log Ac, which was based on measurements at many sandy inlets
in which the maximum velocity u, was on the order of 1 m/s. The suggested
representative values of a2 and a3 were 30 and 5, respectively, when Ac is
in m2 and C in ml/2/s.
Based upon data from a number of North American inlets, Graham and
Mehta (1981) obtained approximate empirical relationships of the form he =
pW1, between throat depth he and width We. Values of coefficients p and q
are given in Table 1. The aforementioned relationship between C and Ac can
be stated in terms of Mannings's n as


1327








TABLE 1. Values of Coefficients p and q

Number Width, W, < 150 m Width W, > 150 m
of jetties Coefficient p Coefficient q Coefficient p Coefficient q
(1) (2) (3) (4) (5)
0 0.038 0.87 1.164 0.19
1 or 2 0.082 0.80 1.661 0.20


h /6
n e= .................... ................ ........ (6)
a2 + a3 log Ac
Noting furthermore that Ac = hWc, Manning's n can therefore be roughly
estimated. For inlets ranging in width from 100-50,000 m, the resulting val-
ues of n range from 0.025-0.027 for inlets without jetties and from 0.026-
0.029 for inlets with jetties. These ranges of n are common at sandy inlets
(Mehta and Ozsoy 1978).
The flow issuing from a channel is similar to that of a separated jet ex-
panding from a narrow channel into a very large basin. Most of the energy
dissipation occurs in the expanding part of the flow due to turbulence. Since
the kinetic head is usually lost as the flow enters the basin, k, = 1. In some
cases, however, when flow inertia in the channel is significant, a part of the
head is retained so that k, < 1. In the case of flow entering the channel, the
energy loss is not very significant, particularly if the corners of the entrance
are naturally rounded. For such a case, ke, = 0.05 or less. However, values
up to 0.25 have been considered as well (Dean 1971). The latter value is
likely to be appropriate for inlets with exposed jetties where the flow must
bend sharply as it enters the channel.

Equivalent Bay Area
The condition of hydraulic filling of the bay is reasonably met only at
relatively small bays (O'Brien and Clark 1974). Spatial water surface gra-
dients due to inertia and bed friction in larger bays can be estimated using
a simple approach involving the continuity principle (Escoffier 1977). If these
gradients are not small in comparison with the bay tide amnplitude, Eq. 3 is
not applicable, unless "qB is considered to be the tide at the bayward end of
the inlet, and AB is redefined as an "equivalent" bay area corresponding to
this tide. This can be achieved, for example, from Fig. 4, in which A, is
treated as the unknown to be solved for, given all other parameters including
ai. The latter quantity must be obtained from measurements of the tidal am-
plitude aB at a site in the bay located in the proximity of the channel and
from ao. Another way to obtain an equivalent bay area is to divide the tidal
prism derived from discharge measurement at the throat by the range of tide
in the bay 2aB close to the channel.

Tidal Current and Prism
As a general rule, the cross-sectional average maximum velocity at the
throats of many sandy inlets is on the order of 1 m/s under a semidiurnal
tide, except when the inlet is very small, in which case the velocity is usually
found to be lower (Bruun and Gerritsen 1960; Bruun et al. 1978; Byrne et
al. 1980; O'Brien and Clark 1974). Inlets with rocky bottoms can have ve-


1328


I








locities well in excess of 1 m/s (Bruun et al. 1978). Flow cross sections are
seldom symmetric, and flood- and ebb-dominated channels are almost always
present. Slack water tends to occur later in deeper portions of the cross sec-
tion than in the shallower parts, due to greater effects of flow inertia asso-
ciated with larger depths. Likewise, inertia causes flow reversal to occur near
the bottom before it occurs in the surface layers. Secondary circulation cells
are set up in pockets along the banks, and the strength of flow varies meas-
urably across any cross section, as well as along the length of the channel.
Current measurements made with shallow drogues or floats do not, as a
rule, yield the depth-mean velocity. Surface current is affected by freshwater
discharge and other effects. Flood flow is usually dominant near the bottom
and ebb near the surface (O'Brien and Clark 1974; Yoshida and Kashiwa-
mura 1976). In situ measurement at several elevations across the flow section
using current meters is the preferred means for evaluating the flow field.
The tidal prism is the most commonly used measure of inlet size and in-
fluence in the near-field waters. It is the volume of water that is drawn into
the bay between low water slack and the following high water slack, i.e.,
during flood. Aperiodicity of the tide, freshwater discharge, and the presence
of other openings in the bay are some of the reasons why the prism is not
always equal to the volume of water that leaves during ebb. The latter is
sometimes referred to as the ebb prism, while the former is termed the flood
prism. The difference between the two has been referred to as skewness (Bruun
et al. 1978). In many cases, skewness is exaggerated due to erroneous current
data, as, for example, when surface current measurements are used to esti-
mate discharge. In the case of a single inlet-bay system with sinusoidal tide,
there is no skewness, and the prism (flood or ebb) is equal to 2Qm/lCK,
where Qm = umAc is the maximum discharge; and CK = a parameter that
varies with the repletion coefficient- K (Keulegan 1967). The value of CK
accounts for the nonlinearity in the variation of the discharge Q as a result
of the quadratic friction term in the governing equations. At K = 1, CK =
0.81, and at K = 4, CK = 1. For simple computations, an average value of
0.86 has been recommended (O'Brien and Clark 1974).

NEAR-FIELD HYDROMECHANICS

The role of the inlet as an interface between water bodies and its contri-
bution to flushing and water exchange has been well-demonstrated (Dean and
Taylor 1972; Stommel and Farmer 1952; Taylor and Dean 1974). Flushing
is a result of the unique features of flow in the neighborhood of the inlet.
The forcing mechanism is typically due to astronomical tide, but where tides
are small, low-frequency oscillations associated with meteorological events
can contribute measurably to bay flushing (Smith 1977). The domain of in-
fluence of near-field flow extends from the confined areas of the bay to the
open waters, and the presence of a narrow tidal entrance causes large-scale
circulation to be generated in both interior and exterior regions (Joshi and
Taylor 1983). This circulation has important influences on the water mass
distributions in the adjacent shallow seas (Rouse and Coleman 1976).
Near-field flow distribution is characteristic of the abrupt changes in the
geometrical dimensions at an inlet. During ebb, a boundary-separated, sur-
face-buoyant jet is issued into the sea. Shear and flow entrainment at the jet
boundaries induce circulation in the surrounding waters (Joshi 1982). On the


1329







bay side, streamlines converge radially towards the channel forming a sink
flow. During flood, the flow distribution is reversed, with a surface jet in
the confined bay waters and sink flow into the channel on the seaward side.
As water starts ebbing into the sea, the flow dynamics are dominated by
unsteady effects. Initially, a radially expanding source flow is issued from
the inlet. As the inlet velocity increases, the flow is separated from land
boundaries and is transformed into a jet. At the start of the motion, a vortex
pair is shed and moves offshore, forming the frontal portion of the jet. The
unsteady tidal jet has been analyzed analogous to a buoyant plume by ap-
proximating the jet as a composite of a steady turbulent jet with an unsteady
frontal region (Middleton 1975; Tsang 1970; Turner 1962). Offshore of this
momentum-dominated jet, the buoyancy effect detaches the jet from the bot-
tom, and turbulence is jet-generated rather than advected from the entrance.
An ebb jet plume issuing from Ponce de Leon Inlet, Florida, is shown in
Fig. 6.
The large roller in the frontal region shown in Fig. 6 is an area of active
mixing, the fluid from which is swept into the lee of the roller, where tur-
bulence tends to be damped via buoyancy stratification. Fig. 7 shows an
elevation view of an ebb jet descriptive of measurements at the Cut, an es-
tuarine entrance in Koombana Bay, Australia (Luketina and Imberger 1987).
Due to freshwater discharge, buoyancy effects are significant in this jet, which
lifts off the bottom and entrains the underlying water within a few hundred
meters from the channel. The surface centerline velocity at this site was found
to reduce with distance from the lift-off point to the one-half power. The
roller at the leading front had a well-defined rotating core, as shown by the
streamlines. Water at the surface moved towards the leading front, where it
plunged to a depth equal to about twice the thickness (depth) of the jet and
entrained the underlying ambient water, forming a mixing layer in the lee of
the roller immediately underneath the overflowing water.
In situations in which freshwater discharge is negligible, the lift-off point
can occur at a distance that is several inlet widths offshore. Ozsoy (1977)
investigated the near-field jet under these conditions, considering it to be
quasi-steady and nonbuoyant for purposes of analysis. This analysis, which
followed previous efforts (Borichansky and Mikhailov 1966; French 1960;
Taylor and Dean 1974), included the effects of bottom friction, offshore
bathymetric changes, turbulent mixing, and lateral entrainment. Starting with
depth- and time-averaged continuity and momentum equations within the
shallow water approximations, and invoking boundary layer approximations
typical of free turbulent shear flows, the following governing equations are
obtained for the motion of a steady tidal jet:

continuity:

a a
- (hu) + (hv) = 0 ............................................ (7)
ax ay

momentum:

Sn2 1
S(hu) + (huv) = -g + F ....................... (8)
ax ay h1/3 p ay


1330








0 1/2 1
II I
SScale (km)




^J1


FIG. 6. Ebb Jet Plume Issuing from Ponce de Leon
Joshi 1984)


-16L
0


600 1200 1800 2400
DISTANCE FROM CHANNEL (m)


Inlet, Florida (Mehta and


3000


FIG. 7. Elevation View of Buoyant Jet Representative of Measurements at Cut
in Koombana Bay, Australia; Streamlines Are in Frame of Reference Moving with
Plume Line (Luketina and Imberger 1987)

where h = depth, which for simplicity is assumed to vary only along the
offshore x-direction; u and v = the depth- and time-averaged offshore and
alongshore velocities, respectively; n = Manning's coefficient, p = fluid
density; and Fy = the depth-averaged turbulent shear stress acting laterally
on the jet.
In solving Eqs. 7 and 8, the velocity profiles u(x,y) are assumed to be
self-similar (Stolzenbach and Harleman 1971), and the entrainment hypoth-
esis for turbulent jet transport is employed. According to the self-similarity
assumption, the lateral velocity distribution, u(x,y/b)/uc, where b(x) = the


1331








5 I \ 1 I I \ I 0
4 -t---Shoal '
41
032
.0 2 Data -3 0
-- Prediction
1 -4
S-- Depth
0 1 1 11 I A 1 5
0 2 4 6 8 10
x/bo

FIG. 8. Jet Width Variation at Jupiter Inlet, Florida; Comparison between Data
and Prediction. Here h. = 3 m, b, = 50 m (Ozsoy 1977)

jet half-width and uc(x) = the jet centerline velocity, is considered to be
independent of the offshore distance x. According to the entrainment hy-
pothesis, the velocity of the laterally entrained flow at the nonbuoyant jet
boundary, at a given distance from the inlet opening, is assumed to be pro-
portional to the jet centerline velocity uc at that distance. The proportionality
factor a is referred to as the entrainment coefficient. Under these conditions,
general solutions for the jet centerline velocity and width are obtained. De-
pending upon assumptions concerning the nature of offshore depth-variation,
these solutions can be reduced further analytically, or solved numerically.
Fig. 8 shows an application for Jupiter Inlet on the Atlantic coast of south-
ern Florida. The numerical solution for the jet width 2b (normalized by the
width 2bo = 100 m at the mouth) is compared with data up to the dimen-
sionless offshore distance, x/bo = 8. After an initial rapid expansion due to
reduced depths over the ebb shoal or delta, the jet is observed to contract
due to the dominant effect of rapidly increasing depth offshore. The solution
for the jet centerline velocity (not shown) indicated a decay of this velocity
with distance characteristic of surface jets, past the core or zone of flow
establishment in which the centerline velocity uc was equal to u,, the initial
jet velocity. The offshore extent of this core decreases with increasing bottom
friction, and in many cases, as at Jupiter Inlet, important features of the jet
may be inferred without considering the core. For simulation purposes, the
entrainment coefficient a was selected to be 0.050 in the zone of established
flow past the core (Ozsoy 1977). In cases where depths do not increase sig-
nificantly, a high bottom friction effect can cause the jet to expand expo-
nentially as at Redfish Pass in Florida (Bruun et al. 1978).
The described characteristics of the tidal jet have been further formalized
by Joshi (1982), by demonstrating that the exponential variation of jet half-
width (and centerline velocity) decay is a necessary condition for the exis-
tence of self-similar solutions. The equations for width, growth, and velocity
decay have been derived without assuming a specific form of the similarity
function for velocity. This function is then determined using an eddy vis-
cosity model for turbulent transport.
Flow towards the inlet converges radially into the channel. A proof that
the flow can be assumed in this case to be irrotational (in addition to inviscid)


1332









under the approximation of gentle bottom slopes has been given elsewhere
(Ozsoy 1977). Such a flow is governed by Laplace's equation, and, in the
absence of other currents such as an alongshore flow, the velocity at any
radial distance is easily obtained, since the potential lines are semicircular
arcs (Ozsoy 1977). Measurements at a small inlet in Florida seem to cor-
roborate this description (Mehta and Zeh 1980). When the bottom slope is
steep, the uneven effect of bed friction can lead to selective withdrawal of
offshore waters relative to those closer to the shoreline (Wolanski and Im-
berger 1987).
Joshi and Taylor (1983) have developed analytic solutions for the offshore
and alongshore velocity components of the induced large-scale circulations
flanking nonbuoyant jet boundaries. These circulations are treated as poten-
tial motion, arising from flow entrainment due to the jet and bottom friction
in the jet region. The influence of jetties has also been considered. In par-
ticular, induced alongshore currents are found to be significantly affected by
the ratio of jetty length to inlet half-width.
Near-field flows are complicated by.bathymetric crosscurrents, the earth's
rotation, and incident wind-generated waves. Flows in bays are further com-
plicated due to confinement within land boundaries (Hwung et al. 1980; Ia-
mandi and Rouse 1969; Ismail 1980; Luketina and Imberger 1987; Mehta
and Zeh 1980; Ozsoy 1977; Purandare 1985; Savage and Sobey 1975; Tak-
ano 1955; Wolanski and Imberger 1987; Yoshida and Kashiwamura 1976).

PHYSICAL AND NUMERICAL MODELING

Fixed-bed models are commonly used for simulating complexities asso-
ciated with inlet hydraulics. Model scales can be so chosen as to allow the
inclusion of relatively detailed features of inlet physiography (Bruun et al.
1966; Sager and Seaberg 1977). Movable-bed models require careful inter-
pretation of test results, owing to problems associated with scaling the sed-
iment (Jain 1982;,Mayor-Mora 1973). It is advantageous to use both physical
and numerical models concurrently, since this allows for an internal com-
parison of results (McAnally and Stewart 1982). A well-documented study
of this nature was conducted for Masonboro Inlet, North Carolina (Harris
and Bodine 1977).
For channel hydraulics, numerical solutions fall broadly into two cate-
gories. The first involves solutions of Eqs. 3 and 4 with all terms included,
when necessary. The main constraint associated with this approach is that
spatial variations of u and lB cannot be considered. On the other hand, vari-
ations-of inlet cross-sectional area Ac and bay area AB with the stage of tide
can be easily accounted for. Furthermore, where tides are mixed and it is
desired to determine inlet behavior over several tidal cycles, appropriate time
variation of qno may be used, since the solution is not constrained by the
sinusoidal tide approximation (King 1974; Mayor-Mora 1973; Seelig et al.
1977; Shemdin and Forney 1970; van de Kreeke 1967).
A second category of modeling involves the solution of one-dimensional
(e.g., Eq. 1 together with the corresponding equation of continuity) or two-
dimensional shallow water wave equations with appropriate initial and boundary
conditions. The problem is one of estuarine tidal wave propagation.and is
not restricted to inlets, although when inlets with long or multiple channels
or bays are involved, numerical modeling of this nature becomes essential


1333








(Speer and Aubrey 1985). Some models combine shallow water equations
for bays with the inlet equations (Eqs. 3 and 4) (Dean 1973; van de Kreeke
1972).
Near-field modeling is generally more complex than for the channel as a
consequence of the open nature of the flow domain, and at present it is
restricted by the lack of adequate knowledge on frontal dynamics. Confining
influences of bay boundaries tend to induce complicated circulation patterns.
Numerical models of varying degrees of complexity have been developed to
predict circulation in bays (Dean and Taylor 1972; Wang and Connor 1975).

CONCLUDING REMARKS

The collection of a minimal amount of field information is essential for
developing a general understanding of hydraulics and for verifying models.
Valuable information concerning the anticipated long-term behavioral changes
at inlets can be derived from analyses of past records. Aerial and satellite
images of near-field waters can be very helpful in understanding the physics
of induced circulations and the spatial extent of inlet influence.
Channel hydraulics prediction can be improved by advancing the present-
day knowledge concerning the relationship between flow, time-dependent
bed forms, and bed resistance. Further field-oriented studies are required,
particularly for a better understanding of near-field frontal dynamics. The
influence of waves in near-field circulation, including that in the inlet mouth,
requires better quantification.

ACKNOWLEDGEMENTS

The assistance provided by Task Committee members C. Linwood Vin-
cent and R. Bruce Taylor is appreciated.

APPENDIX I. REFERENCES

Baines, W. D. (1958). "Tidal currents in constricted inlets." Proc. Sixth Coastal
Engineering Conf., Council on Wave Research, Engineering Foundation, Gaines-
ville, Fla., 545-561.
Borichansky, L. S., and Mikhailov, V. N. (1966). "Introduction of river and sea-
water in the absence of tides." Proc. Symp. Scientific Problems of the Humid
Tropical Zone Deltas and Their Implications, UNESCO, Dacca, Pakistan, 175-
180.
Brown, E. I. (1928). "Inlets on sandy coasts." Proc., ASCE, 54, Feb., 505-553.
Bruun, P., Gerritsen, F. (1960). Stability of coastal inlets. North Holland Publishing
Co., Amsterdam, The Netherlands.
Bruun, P. M., et al. (1966). "Coastal engineering model studies of three Florida
coastal inlets." Engineering Progress at the University of Florida, Bull. No. 122,
XX(6), College of Engineering, University of Florida, Gainesville, Fla., 1-68.
Bruun, P., Mehta, A. J., and Jonsson, I. G. (1978). Stability of tidal inlets: theory
and engineering. Elsevier Scientific Publishing Co., Amsterdam, The Netherlands.
Byrne, R. J., Gammisch, R. A., and Thomas, G. R. (1980). "Tidal prism-inlet area
relations for small tidal inlets." Proc. 17th Coastal Engineering Conf., ASCE,
Sydney, Australia, Vol. III, 23-28.
Chapman, S. (1923). "A note on the fluctuation of water-level in a tidal-power res-
ervoir." Philosoph. Mag. J. Sci., XLVI, Sixth Series, Dec., 101-108.
Cotter, D. C. (1974). "Tide-induced net discharge in lagoon-inlet systems." Tech.
Report UM-RSMAS No. 743031, Rosenstiel School of Marine and Atmospheric


1334









Sciences, University of Miami, Miami, Fla.
Dean, R. G. (1971). "Hydraulics of inlets." UFL/COEL-71/019, Coastal and Ocean-
ographic Engineering Department, University of Florida, Gainesville, Fla.
Dean, R. G. (1973). "Coastal engineering study of proposed Navarre pass." UFL/
COEL-73/006, Coastal and Oceanographic Engineering Laboratory, University of
Florida, Gainesville, Fla.
Dean, R. G., and Taylor, R. B. (1972). "Numerical modeling of constituent transport
in bay systems." Proc. Thirteenth Coastal Engineering Conference, ASCE, Van-
couver, B.C., Canada, Vol. 4, 2217-2240.
Dean, R. G., and Walton, T. L. (1975). "Sediment transport processes in the vicinity
of inlets with special reference to sand trapping." Estuarine research, L. E. Cronin,
ed., Vol. II, Academic Press, Inc., New York, N.Y., 129-149.
Dilorenzo, J. L. (1986). "The override and filtering response of inlet/bay systems,"
thesis presented to the State University of New York, at Stony Brook, N.Y., in
partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Dorrestein, R. (1961). "Amplification of long waves in bays." Engineering Progress
at the University of Florida, Tech. Paper No. 213, XV(12), College of Engineer-
ing, University of Florida, Gainesville, Fla.
Eads, J. B. (1971). "Improvement at the mouth of the St. Johns River." Memoran-
dum regarding James B. Eads' contribution to the design of tidal inlets, by M. P.
O'Brien, HEL-24-6, Appendix B, Hydraulic Engineering Laboratory, University
of California, Berkeley, Calif., 6-28.
Escoffier, F. F. (1940). "The stability of tidal inlets." Shore and Beach, 8(4), 114-
115.
Escoffier, F. F. (1977). "Hydraulics and stability of tidal inlets." G.I.T.I. Report 13,
U.S. Army Corps of Engineers Coastal Engineering Research Center, Fort Belvoir,
Virginia.
Escoffier, F. F., and Walton, T. L. (1979). "Inlet stability solutions for tributary
inflow." J. Wtrwy., Port, Coast., and Oc. Div., ASCE, 105(WW4), 341-355.
French, J. L. (1960). "Tidal flow in entrances." Technical Bulletin No. 3, U.S. Army
Corps of Engineers, Waterways Experiment Station, Committee on Tidal Hydraul-
ics, Vicksburg, Miss.
Goodwin, C. (1974). "Physical parameters which control propagation of tidal waves
in estuaries, verified for three significantly different Oregon estuaries." Proc. Fourth
Annual Tech. Conf. on Estuaries of the Pacific Northwest, Oregon State University
Engineering Experiment Station Circular No. 40, Corvalis, Oreg., 37-49.
Graham, D. S., and Mehta, A. J. (1981). "Burial design criteria for tidal flow cross-
ings." J. Transp. Engrg. Div., ASCE, 107(TE2), 227-242.
Harris, D. L., and Bodine, B. R. (1977). "Comparison of numerical and physical
hydraulic models, Masonboro Inlet, North Carolina." G.I.T.I. Report 14, U.S.
Army Corps of Engineers Coastal Engineering Research Center, Fort Belvoir, Va.
Hwung, H. H., Tang, F. L. W., and Chen, Y. Y.-(1980). "Studies of the turbulent
plane jet interacting with wave motion." Proc. Fourth Conf. on Ocean Engineer-
ing, Taipei, Taiwan, 185-193.
Iamandi, C., and Rouse, H. (1969). "Jet-induced circulation and diffusion." J. Hydr.
Div., ASCE, 95(HY2), 589-601.
Ismail, N. M. (1980). "Wave-current interaction." HEL-27-7, Hydraulic and Coastal
Engineering Laboratory, University of California, Berkeley, Calif.
Jain, S. C. (1982). "Movable-bed tidal inlet model." J. Wtrwy., Port, Coast., and
Oc. Div., ASCE, 108(WW3), 326-342.
Joshi, P. B. (1982). "Hydromechanics of tidal jets." J. Wtrwy., Port, Coast. and
Oc. Div., ASCE, 108(WW3), 239-253.
Joshi, P. B., and Taylor, R. B. (1983). "Circulation induced by tidal jets." J. Wtrwy.,
Port, Coast. and Oc. Engrg., ASCE, 109(4), 445-464.
Keulegan, G. H. (1967). "Tidal flow in entrances: water level fluctuations of basins
in communication with seas." Technical Bulletin No. 14; U.S. Army Engineer
Waterways Experiment Station, Committee on Tidal Hydraulics, Vicksburg, Miss.
King, D. B. (1974). "The dynamics of inlets and bays." Tech. Report No. 22, Coastal
and Oceanographic Engineering Laboratory, University of Florida, Gainesville, Fla.

1335


I IL









Kondo, H. (1975). "Depth of maximum velocity and minimum flow area of tidal
entrances." Coastal Eng. Japan, 18, 167-183.
Luketina, D. A., and Imberger, J. (1987). "Characteristics of a surface buoyant jet."
J. Geophys. Res., 92(C5), 5435-5447.
Mayor-Mora, R. E. (1973). "Hydraulics of tidal inlets on sandy coasts." HEL-24-
16, Hydraulic Engineering Laboratory, University of California, Berkeley, Calif.
McAnally, W. H., and Stewart, J. P. (1982). "Hybrid modeling of Columbia River
mouth." Proc. Conf. on Applying Research to Hydraulic Practice, ASCE, Jackson,
Miss., 408-417.
Mehta, A. J., and Ozsoy, E. (1978). "Inlet hydraulics: flow dynamics and nearshore
transport." Stability of tidal inlets: theory and engineering, P. Bruun, ed., Elsevier
Scientific Publishing Co., Amsterdam, The Netherlands, 83-161.
Mehta, A. J., and Joshi, P. B. (1984). "Review of tidal inlet hydraulics." UFL/
COEL-TR/054, Coastal and Oceanographic Engineering Department, University
of Florida, Gainesville, Fla.
Mehta, A. J., and Zeh, T. A. (1980). "Influence of a small inlet in a large bay."
Coastal Engrg., 4(2), 157-176.
Middleton, J. H. (1975). "The asymptotic behavior of a starting plume." J. Fluid
Mech., 72(4), Dec., 753-771.
Mota Oliveira, I. B. (1970). "Natural flushing ability in tidal inlets." Proc. Twelfth
Coastal Engineering Conference, ASCE, Washington, D.C., Vol. 3, 1827-1845.
O'Brien, M. P. (1931). "Estuary tidal prisms related to entrance areas." Civ. Engrg.,
ASCE, 1(8), 738-739.
O'Brien, M. P., and Clark, R. R. (1974). "Hydraulic constants of tidal entrances."
Proc. Fourteenth Coastal Engineering Conf., ASCE, Copenhagen, Denmark, Vol.
2, 1546-1565.
Ozsoy, E. (1977). "Flow and mass transport in the vicinity of tidal inlets." Technical
Report No. TR-306, Coastal and Oceanographic Engineering Laboratory, Univer-
sity of Florida, Gainesville, Fla.
Purandare, U. V. (1985). "Laboratory study of tidal ebb flow jets." UFL/COEL/
MP-85/001, Coastal and Oceanographic Engineering Department, University of
Florida, Gainesville, Fla.
Rouse, L. J., and Coleman, J. M. (1976). "Circulation Observations in the Louisiana
Bight Using LANDSAT Imagery, Remote Sens. Environ., 5(1), 55-66.
Sager, R. A., and Seaberg, W. C. (1977). "Physical model simulation of the hy-
draulics of Masonboro Inlet, North Carolina." G.I.T.I. Report 15, U.S. Army Corps
of Engineers Coastal Engineering Research Center, Fort Belvoir, Va.
Savage, S. B., and Sobey, R. J. (1975). "Horizontal momentum jets in rotating ba-
sins." J. Fluid Mech., 71(4), Oct., 755-768.
Seelig, W. N., Harris, D. L., and Herchenroder, B. E. (1977). "A spatially integrated
numerical model of inlet hydraulics." G.I.T.I. Report 14, U.S. Army Corps of
Engineers Coastal Engineering Research Center, Fort Belvoir, Va.
Shemdin, O. H., and Forney, R. M. (1970). "Tidal motion in bays." Proc. Twelfth
Coastal Engineering Conf., ASCE, Washington, D.C., Vol. 3, 2225-2242.
Smith, N. P. (1977). "Meteorological and tidal exchanges between Corpus Christi
Bay, Texas, and northwestern Gulf of Mexico." Estuarine, Coastal Marine Sci.,
5(4), 511-520.
Sorensen, R. M. (1980). "The Corps of Engineer's general investigation of tidal in-
lets." Proc. Seventeenth Coastal Engineering Conf., ASCE, Sydney, Australia,
Vol. III, 2565-2580.
Sorensen, R. M., and Seelig, W. N. (1976). "Hydraulics of Great Lakes inlet-harbor
systems." Proc. Fifteenth Coastal Engineering Conf., ASCE, Honolulu, Hawaii,
Vol. 2, 1646-1665.
Speer, P. E., and Aubrey, D. G. (1985). "A study of non-linear tidal propagation in
shallow inlet/estuarine systems. Part II: Theory." Estuarine Coastal Shelf Sci.,
21(2), 207-224.
Stevenson, T. (1886). The design and construction of harbours: a treatise on mar-
itime engineering, 3rd Ed., A & C Black, Edinburgh, U.K.


1336


-L









Stolzenbach, K. D., and Harleman, D. R. F. (1971). "An analytical and experimental
investigation of surface discharges of heated water." Report No. 135, Ralph M.
Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts In-
stitute of Technology, Cambridge, Mass.
Stommel, H., and Farmer, H. G. (1952). "On the nature of estuarine circulation."
Reference Nos. 52-51, 52-63, 52-88, Woods Hole Oceanographic Institute, Woods
Hole, Mass.
Takano, K. (1955). "A complementary note on the diffusion of the seaward flow off
the mouth of a river." J. Oceanogr. Soc. Japan, Vol. 11, 1-3.
Taylor, R. B., and Dean, R. G. (1974). "Exchange characteristics of tidal inlets."
Proc. Fourteenth Coastal Engineering Conf., ASCE, Copenhagen, Denmark, Vol.
3, 2268-2289.
Tsang, G. (1970). "Laboratory study of two-dimensional starting plumes." Atmos.
Environ., 4, Sept., 519-544.
Turner, J. G. (1962). "The starting plume in neutral surroundings." J. Fluid Mech.,
13(2), July, 356-368.
van de Kreeke, J. (1967). "Water level fluctuations and flows in tidal inlets." J.
Wtrwy., Harb., and Coast. Engrg. Div., ASCE, 93(WW4), 97-106.
van de Kreeke, J. (1972). "A numerical model for the hydromechanics of lagoons."
Proc. Thirteenth Coastal Engineering Conf., ASCE, Vancouver, B.C., Canada,
Vol. 3, 2241-2254.
Wang, J. D., and Connor, J. J. (1975). "Mathematical modeling of near-coastal cir-
culation." Report No. 200, Ralph M. Parsons Laboratory for Water Resources and
Hydrodynamics, Massachusetts Institute of Technology, Cambridge, Mass.
Watt, D. A. (1905). "Notes on the improvement of river and harbor outlets in the
United States." Trans., ASCE, LV, Dec., 288-305.
Wolanski, E., and Imberger, J. (1987). "Friction-controlled selective withdrawal near
inlets." Estuarine Coastal Shelf Sci., 24(3), 327-333.
Wright, L. D., and Sonu, C. J. "Processes of sediment transport and tidal delta de-
velopment in a stratified tidal inlet." Estuarine research. L. E. Cronin, ed., Vol.
2, Academic Press, New York, N.Y., 63-76.
Yoshida, S., and Kashiwamura, M. (1976). "Tidal response of two-layer flow at a
river mouth." Proc. Fifteenth Coastal Engineering Conf., ASCE, Honolulu, Ha-
waii, Vol. 4, 3189-3207.

APPENDIX II. NOTATION

The following symbols are used in this paper:

As = bay surface area;
A, = inlet throat area;
Ai = cross-sectional area of ith channel segment;
aB = bay tide amplitude;
dB = dimensionless bay tide amplitude;
ao = sea tide amplitude;
b = jet half-width;
b, = inlet half-width at point of jet initiation;
C = Ch6zy bed resistance coefficient;
CK = coefficient accounting for nonsinusoidal variation of current;
F = impedance;
F, = depth-averaged turbulent shear stress acting laterally on jet;
g = acceleration due to gravity;
h = mean water depth or offshore water depth;
h, = depth at inlet throat as well as depth of equivalent channel;
hi = depth of ith channel segment;
h, = inlet depth at point of jet initiation;


1337









.i =. inlet channel segment number, varying from 1-mm;
K = coefficient of repletion;
ke, = entrance loss coefficient;
kex = exit loss coefficient;
Le = equivalent length of channel;
Lr = actual channel length;
mm = total number of channel segments;
n = Manning's bed resistance coefficient;
p = coefficient in channel width-depth relationship;
Q = discharge through channel;
Qf = freshwater discharge;
Qm = maximum discharge through channel;
q = exponent in channel width-depth relationship;
t = time;
u = velocity in channel, or depth- and time-averaged longitudinal ve-
lofity in jet, or offshore circulation velocity;
u, = jet center-line velocity;
um = maximum current velbcity in channel;
a,m = dimensionless maximum current velocity in channel;
uo = mean velocity of inlet at point of jet initiation;
V- = bay storage volume;
We = width at inlet throat as well as width of equivalent channel;
x = coordinate along channel or bay or along jet axis;
y = coordinate perpendicular to jet axis;
a = entrainment coefficient;
a, = dimensionless tidal frequency;
a2, a3 = coefficients in relationship between C and A,;
3 = dimensionless dissipation term;
Axi = length of ith channel segment;
e = lag of slack water after high water or low water in sea;
-q = instantaneous water surface elevation relative to mean water level;
TqB = instantaneous water surface elevation in bay;
nTo = instantaneous tidal elevation in sea;
p -= fluid or water density;
a = tidal frequency; and
T = angular measure of lag of slack water after midtide in sea.


1338


I










Reprinted from "Coastal Sediments '87"
WWDiv./ASCE, New Orleans, LA, May 12-14 1987





INLET EBB SHOALS RELATED TO COASTAL PARAMETERS

by

James N. Marino1, M., ASCE and Ashish J. Mehta2, M., ASCE

ABSTRACT

Tidal inlets impact significantly on the local coastal sedimen-
tary budget. The general nature of inlet ebb shoal development was
examined through a case study of St. Augustine Inlet on the east
coast of Florida. Next, the ebb shoal volumes of the eighteen inlet
systems on the east coast of Florida were estimated. Finally, the
degree to which various coastal physical parameters influence the ebb
shoal volume was investigated. There is a general trend of decreas-
ing ebb shoal volume from north to south. A total of 420 million
cubic meters of sediment are found to reside in the ebb shoals of the
eighteen inlet systems. Of that total, 83% resides in four northern-
most inlet systems. The ebb shoal volume, V, is found to depend on
the spring tidal prism, P, the inlet width/depth ratio, W/D, the flow
cross-sectional area, A and the tidal amplitude, ao. The effect of
the width/depth ratio on the ebb shoal volume signifies the role of
both inlet current and waves in influencing ebb shoal development, as
observed previously by Walton and Adams.

INTRODUCTION

Tidal inlets impact significantly on the local coastal environ-
ment. The inlet provides access to sheltered harbors from strong
ocean currents and waves, to both the commercial and recreational
user. The ebb tidal shoal is one of the most dominant features of a
coastal inlet.

The ebb shoal occurs at an inlet when sediment is trapped off-
shore of the mouth due to various coastal physical processes. The
sediment is removed from the littoral drift and deposited typically
in a crescent- or kidney-shaped formation. Once the shoal has devel-
oped, it can serve as a bridge of sorts, transporting material from
the updrift beach to the downdrift side, when conditions permit.
Since the shoal is typically a much shallower area than its surround-
ing region, it also serves as an energy dissipator. As ocean waves


Research and Development Coordinator, Coastal Engineering Research
Center, USAE Waterways Experiment Station, Vicksburg, MS, formerly at
University of Florida, Gainesville, FL.

Associate Professor, Coastal and Oceanographic Engineering Depart-
ment, University of Florida, Gainesville, FL.


1608


P










INLET EBB SHOALS


approach the shore, they break and dissipate their energies in the
shallow water regions. If the shoal causes these waves to break
offshore, then the local beach or coastline is in effect sheltered
from the erosional impact of these waves.

If the shoal is significantly large, it is a possible source of
sediment for beach nourishment. Several factors impact on the feasi-
bility of using this material in beach renourishment projects. One
must consider the relative amounts of material needed and that which
is available. Ideally, the material used for the fill should be of
the same or greater coarseness than that of the native material.
After the factors have been considered, the accessibility of the area
needs to be taken into account. Whereas, flood or bay shoals may have
been ruled out because of possible detrimental environmental effects
and distant offshore troughs ruled out because of the lack of quantity
or quality of material and transport problems, the ebb shoals can pose
a different kind of problem. The dredge or. device used to collect the
material from the shoal may very likely be subject to extreme breaking
wave conditions. An additional consideration before determining
whether or not the ebb shoal should be used for renourishment is the
effect that its removal will have on the local wave climate. If the
shoal had been sheltering the coast, how will its removal change the
erosional patterns? Should only part of the shoal be removed? How
will its removal impact on navigation? These are some of ?he
questions which must be considered in determining the best course of
action to be taken with regard to ebb shoals.

Each of the eighteen inlet systems is unique in its own way.
Although an "ideal" ebb shoal can be drawn graphically or developed in
a laboratory, rarely can one be found in nature. This holds true for
the east coast of Florida. The origins of all eighteen systems are
summarized by Marino and Mehta (1986). That report details the origin
of each inlet, whether natural or manmade, the year in which it was
opened and when jetties were constructed, if any.

This study investigated the following parameters and their rela-
tionship to ebb shoal volume, V, spring tidal prism, P, inlet cross-
sectional area, Ac, inlet width, W, inlet depth, D, spring tide
amplitude, ao. Several other physical parameters characterize the ebb
shoal; however, only these more significant ones are examined in this
study. Each of the parameters has been studied at one time or another
by other investigators, but never collectively. Relevant previous
work is utilized and presented in this study. A dimensional analysis
approach is used to determine which parameters best explain trends and
relationships that are found with respect to the inlet ebb shoals on
Florida's east coast.

GENERAL PHYSICAL ENVIRONMENT

The general physical environmental condition along the east coast
of Florida would serve as useful background information prior to
examining the possible relationships between the various selected
parameters and -the ebb shoal volumes. The wave energy, shelf width,
tide range, and net littoral drift rate versus the longshore distance


1609











COASTAL SEDIMENTS '87


of the east coast of Florida were investigated. The wave energy data
are taken from Jensen (1983). The shelf width data are obtained from
National Ocean Survey (NOS) nautical charts. The tide range data are
the spring tide values taken from the National Ocean Survey (NOS) Tide
Tables. The littoral drift rate data are taken from the U.S. Army
Corps of Engineers (1967).

A somewhat higher wave energy, defined as Hs2Tw2, where Hs is the
significant wave height and Tw is the wave period, is found in the
northern eleven inlet systems. The wave energy parameter, Hs2T 2
decreases most noticeably between Jupiter Inlet and Lake Worth Inlet.
The shadow effect caused by the Bahama Islands may be the most signif-
icant factor in that respect.

The shelf width is constantly narrowing from north to south. The
shelf width remains nearly constant from Lake Worth Inlet to the
south. The spring tide range in the northern inlets is somewhat
higher than in those from Sebastian Inlet to the south. The net lit-
toral drift rate generally, although not uniformally, decreases from
north to south.

The data presented subsequently in this study are derived
primarily from charts and survey maps of the National Ocean Survey,
the U.S. Army Corps of Engineers and from reports of the University of
Florida. Aerial photographs supplemented the information from these
sources. No field measurements or observations were made as a part of
this study. Personal visits were made to each of the inlets and their
respective controlling agencies, in an effort to gain the most recent
information.

EVOLUTION OF EBB TIDAL SHOALS

To trace the evolution of an inlet ebb shoal, a time history of
the inlet must be studied. The inlet of St. Augustine was selected as
a case study. This inlet has a unique history and helps in explaining
differences in evolutionary trends as well as difficulties which are
typically encountered in precisely determining the shoal volume at any
particular point in time. The effects of jetties, dredging and
longshore sediment transport become evident in the investigation.

St. Augustine Inlet was cut 4 kilometers north of an existing
inlet in 1941. Figure 1 depicts both the previously (1937) existing
shoreline and shoal patterns with that of the present (1975) for St.
Augustine Inlet (U.S. Army Corps of Engineers, 1977). Locations A and
B on the figure represent the areas through which the old, natural
inlet meandered, prior to the new inlet opening at location C, in
1940. The shoal contour lines delineate significant levels of
sediment deposition above the ideal beach profile, in meters. The
ideal profile is defined as the natural beach profile in that local
area, as if the inlet were not present. The exact volumes and methods
used in determining those volumes are covered in following sections.
It can be seen in Figure 1 that as a result of the opening of a new
inlet, the previously existing ebb shoal was caused to migrate. The
old shoal formation moved both westward, to form what is now known as


1610










INLET EBB SHOALS


S1 New Shoreline
1 / -.- Old Shoreline

i '-- New Shoal Contours
A AI // ---- Old Shoal Contours
/ /
-2 /
S/ 0 1200m



Figure 1. St. Augustine Inlet

Conch Island, and northward to the new inlet. The old inlet, which
was located at location B in 1937, was completely closed by 1957. The
present shoal is rather elongated as opposed to crescent-shaped. This
is believed to be due to the presence of a predominant longshore
current to the south. The narrowest part of the shoal seen directly
east of the inlet is evidence of the dredging done by sidecast dredges
through the shoal area since 1940. The large bulge adjacent to the
scut' jetty is a direct result of the jetty being constructed in 1957.
The shoreline since construction has moved eastward approximately 750
meters adjacent to the jetty. This is evidence of jetty sand-trapping
during periodic seasonal reversals of the littoral drift.

This inlet is a mere example of how ebb shoals form and how the
coastline reacts and adjusts due to the formation of an inlet. It can
be seen that by constructing jetties of sufficient length to stabilize
an inlet, as was done at St. Augustine, the shoals are maintained a
significant distance away from the inlet. It can also be observed
that dredging significantly affects the shape of the shoal. The
shoals are divided into two distinct lobes, where there is a channel
dredged, rather than one large mass as is the case with other inlets,
such as Boca Raton, where there is no dredged channel. The great
majority of the shoal area is located to the southeast of the inlet


I -1


1611











COASTAL SEDIMENTS '87


mouth. This is apparently due to the effect of the predominant
longshore current along the coast from north to south.

Each of the eighteen inlet systems identified have their own
unique features. The remainder of this study deals with estimating
the ebb shoal volumes associated with those inlets and in explaining
how the various physical parameters are related to those volumes.

METHODOLOGY

One approach to determine which parameters are important in
characterizing the ebb shoal volume is through appropriate non-
dimensional governing variables, using the procedure of dimensional
analysis. The process is started by identifying those variables that
are significant to the problem. In the most general sense, the fol-
lowing variables may be selected as having a bearing upon the ebb
shoal volume: the (maximum) inlet current velocity, Vmax, inlet width,
W, inlet depth, D, tidal range or amplitude, ao, tidal period, T, wave
height, Hg, wave period, Tw, alongshore current, ua, offshore bottom
slope, s, acceleration due to gravity, g, density of saltwater, p, and
sediment settling velocity, ws. Considering, however, the Florida
east coast environment (as described previously) and practical limits
imposed by the availability and accuracy of data used, only the more
significant of these variables could be considered; these may be
combined to form a functional relationship which can be written as

f(V,P,W,D,EwEt,a2,s) = 0 (1)

where V is the ebb shoal volume, P is the spring tidal prism, W is the
inlet width at the throat, D is the inlet depth, Ew is the wave energy,
Et is the tidal energy, ao is the spring tide amplitude, and s is the
offshore bottom slope. The slope, s, may be excluded in the deriva-
tion of dimensionless parameters. The slope, s, was obtained by
measuring the perpendicular distance offshore to the 10 meter depth
contour and dividing that distance by the depth. This was done in all
but the northern three inlets, where the 6 meter contour was used due
to the complex nature of the offshore bathymetry in the area. The
slope was eliminated from further discussion since all the values lie
in a very narrow range, between 0.3 and 1.0 degrees. Furthermore, the
ratio of the standard deviation to the mean was found to be signifi-
cantly small (0.34).

Thu-, the functional relationship is reduced to

f(V,P,W,D,Ew,Et,ao2) = 0 (2)

with seven physical quantities. The resulting Pi-terms from the
dimensional analysis are: Pil = V/W3, Pi2 = P/W3, Pi3 = W/D, Pi4 =
Ac/ao2, and Pi5 = Ew/Et. Thus, the following functional relationship
exists


1612










INLET EBB SHOALS


f(V/W3,P/W3,W/D,,A/ao 2,Ew/Et) 0 (3)

The fifth Pi-term can be eliminated from further consideration
for the reason that follows. The wave energy, E,, values lie in the
same range as defined by Walton and Adams (1976). Walton and Adams
state that if the values of the wave energy parameter Hs2TW2 are
between approximately 3 and 30 m2sec2, then the wave energy climate is
considered to be "moderate" (as opposed to "high" for values greater
than 30 m2sec2 and "low" for values less than 3 m2sec2). The wave
energy values for the east coast of Florida all fall within that
range. This study compares the ebb shoal volume to prism relationship
with that presented by Walton and Adams (1976). Since Walton and
Adams related that V/P ratio to the Ew parameter solely, and- not the
Ew/Et ratio, it is essential that this study rely on the same criteria
for comparison. The Ew-term can be considered as being predominant in
this ratio, because it is more widely varying. Since the wave ener-
gies all lie within the moderate range, the energy parameter, Ew/Et,
is eliminated from further consideration. An alternate explanation of
the elimination of the energy parameter is given by Marino (1986).
There it is shown that within the "moderate" energy band, Florida's
east coast inlet shoal volumes showed no identifiable relationship to
the ratio of wave energy to tidal energy.

This leaves the following functional relationship to be further
examined for significant trends.

V/W3 = f(p/W3,W/D,Ac/ao2) (4)

These parameters are related to the kinematic aspects of the tidal
inlets. A dynamic analysis involves the consideration of forces
acting on the fluid particles in motion with respect to one another.
The shear stresses involved and their effects are examined in detail,
in sections to follow. Additional dynamic aspects are considered in
Marino (1986), where the energy parameter, Ew/Et, is compared relative
to V, P and W/D. Thus the ebb shoal volume V, is seen to be dependent
on the spring tidal prism, P, the inlet aspect ratio (width to depth),
W/D, and the ratio Ac/ao2. This last parameter has been used by other
researchers for characterizing inlet-bay hydraulics, particularly as
it relates to the size of the inlet-bay system, and the manner in
which bay filling through tide occurs. The next step is to determine
the actual values of the parameters involved.

The ebb shoals include most of the stored sediment at an inlet.
The inlets under consideration presented several different problems in
the details of analysis, but in every case, the basic technique
applied for ebb shoal volume estimation was that developed by Dean and
Walton (1973), for differentiating between the sands making up the ebb
shoal and those of the coast proper. The technique is explained in
detail in that reference. This technique worked well in most
instances; however some adjustments had to be made in cases where
conditions were less than "ideal". Two significant problems were the
existence of offshore reefs in southern Florida and the existence of


1 1









COASTAL SEDIMENTS '87


large, natural offshore shoals between St. Marys Entrance and St.
Johns River Inlet. In their simplest description, the offshore
contour lines updrift and downdrift of the inlet would be shore-
parallel, and represent the idealized no-inlet condition. In the case
of Nassau Sound, there were no parallel contour lines which appeared
to fit the idealized description. Hence, the value of the ebb shoal
volume used was taken from Dean and Walton (1973). In the case of the
southern inlets, from Ft. Pierce to Government Cut, consideration had
to be given to reef formations. As an example, the contour lines at
Ft. Pierce updrift and downdrift of the inlet were not at the same
distance from the shoreline. The idealized contours were therefore
drawn by interpolation between the updrift and downdrift sides. In
the case of three inlets, Hillsboro, Pt. Everglades, and Government
Cut, the presence of offshore reefs and associated shoals made the
estimation of the ebb shoal volumes too complex. The inlets were,
therefore, eliminated from further consideration. Chronological
development at these inlets is presented in Marino (1986).

Another problem to be worked out was in determining how inlets,
which were very wide or had significant offsets, were to be dealt
with. Where the updrift and downdrift sides of the inlet were offset
(or imbalanced) with respect to each other, special consideration had
to be given in determining which grid pattern would be used. The best
solution was to reduce the size of the grid overlay from 305 meter
square to 152 or 76 meter square. By using a smaller grid less detail
was lost in the vicinity of the inlet.

Once the idealized contours and the appropriate grid size were
selected, they were superimposed on the charts. The depth differences
between the actual and idealized no-inlet contours were calculated to
the nearest 0.3 meters at the intersection of grid lines. Depth
differences were then averaged for each grid square. These values
were added to give the total volume difference between the actual and
the idealized condition. The results are presented in Table 1.

The values selected for prism on the spring range of tide were
taken from published sources with the exception of two inlets, South
Lake Worth and Boca Raton. The prisms for these two inlets were
calculated by the author using the Hydraulic Prism Method. Three
techniques were found to have been used in literature for the estima-
tion of tidal prism. The techniques are the Hydraulic Prism Method,
the Cubature Method, and the Volumetric Prism Method (see Marino,
1986).

The cross-sectional area, width and depth values were obtained
from previous studies. The sources for these sets of data are
enumerated in Marino (1986). It should be noted that cross-sectional
area was measured at the inlet throat or the narrowest point. The
width and depth values were taken from previous studies for each
inlet.

Wave energy is defined by Walton and Adams (1976) in terms of the
parameter, Hs2Tw2, where Hs is the wave height and Tw is the wave
period. This parameter is derived from fundamental Airy Wave Theory.


1614













Table 1. Ebb Shoal Volumes


Inlet


INLET EBB SHOALS



Volume x 10-6
(cu. m.)


Survey Year


St. Marys
Nassau Sound
Ft. George/St. Johns
St. Augustine
Matanzas
Ponce de Leon
Port Canaveral
Sebastian
Ft. Pierce
St. Lucie
Jupiter
Lake Worth
South Lake Worth
Boca Raton
Hillsboro
Port Everglades
Bakers Haulover
Government Cut


95.1
40.5
131.3
83.3
4.8
17.0


22.2
16.4


1975
1954
1978
1979
1978
1974
1979
1974
1975
1964
1978
1967
1979
1981
1961
1978
1969
1978


-0.3


The tidal energy parameter, ao2T2, can be derived in
fashion. Here, ao is the tidal amplitude and T the period.


a similar


Jensen (1983) presents hindcast, shallow-water, significant wave
information covering a 20-year period. The data are available for
each of the east coast inlets. These data are presented in Marino
(1986). The values derived from the hindcast data are then analyzed
to determine which energy range they fit into, as defined by Walton
and Adams (1976). The ranges chosen to describe mildly exposed, mod-
erately exposed, and heavily exposed were 0.0-3.0, 3.0-30.0, and
>30.0, respectively (in m2sec2). The results are provided in Marino
(1986).

The ebb shoal volume versus spring tidal prism relationship
presented by Walton and Adams (1976) was used as the focus of this
study's analysis. That study concluded that there is a strong
correlation between the volume of sand stored in the ebb shoals of
inlets with their respective tidal prisms (and cross-sectional areas).
The wave energy parameter was used to explain the differences in the
correlation of these parameters. Of the three ranges of energy,









COASTAL SEDIMENTS '87


previously described, the mildly exposed coast contained the largest
volumes, while the heavily exposed coasts had the smallest volumes.
Walton and Adams (1976) found the volume/prism ratio to be a function
of inlet cross-sectional area and wave energy. A linear regression
analysis is conducted to determine a comparable volume/prism relation-
ship based on this study's data. The volume/prism relationship
derived from this analysis is then compared to that presented by
Walton and Adams (1976). The correlation coefficient for each set of
data is determined and compared for relative accuracy (scatter).

This study takes that conclusion one step further to determine
which parameters explain the scatter of data within the same relative
wave energy range. The dimensional analysis, previously discussed,
revealed that the volume is likely to be dependent upon the prism, the
cross-sectional area/tidal amplitude (squared) ratio and the
width/depth ratio when the wave energy is invariant, as shown in
equation (4). These parameters are used to determine what physical
trends exist and their degree of correlation.

RESULTS

Estimated and compiled values of each of the parameters, V, P,
Ac, W, D, ao, s, Hs, Tw, and Hs2T 2, are presented in tables in Marino
(1986). Each of those tables represents the fifteen individual iniecs
under consideration. The data are selected based on their appropriate-
ness in time, relative to the volume estimates. It may be noted here
that the sediment grain sizes range from 0.12 mm to 0.52 mm along the
coast. Thus the sediment is in the range of fine- to medium-sized
sand.

The ebb shoal volume estimates obtained in this study and those
values from the corresponding inlets in Walton and Adams (1976) have
been compared. This comparison was made to ascertain whether the
values for each inlet obtained from two different sources were close
enough to permit further comparison of related parameters. An inspec-
tion of the data reveals that the values are relatively close to each
other. All of the values have a relative error of 11% or less, except
for the two smallest values, i.e. those for Jupiter and Bakers
Haulover inlets. These values have relative errors exceeding 30%.
This is explained by the fact that these volumes are so small (less
than 500,000 cubic meters) than even a relatively small deviation
yields a large percentage error.

Correlations were made of the inlets examined in this study with
the equation


V = bPm (5)

where V is the ebb shoal volume in cubic meters, P is the spring tidal
prism in cubic meters, and b and m are coefficients to be determined
through linear regression. The regression analysis yields the
following


1616









INLET EBB SHOALS


V = 5.59x1O-4p1.39 (6)

This equation is plotted on Figure 2, along with the equation from
Walton and Adams (1976) for a moderate energy environment. The indi-
cated data points are those from this study. Correlation coefficients
for both sets of data were computed to determine the relative
accuracy.

An examination of Figure 2 reveals a considerable spread of
values. Although the data from Walton and Adams (1976) are not plot-
ted on this figure, a similar spread of data exists. For prism values
which are approximately equal there is considerable scatter, even
within the same wave energy environment range as is presented here.

The correlation coefficient for data from this study is 0.75 and
for Walton and Adams (1976) it is 0.80. These values may be consid-
ered to be rather low, indicating unsatisfactory correlation between
the values. These somewhat poor correlations suggest the possibility
of examining the influence of other parameters as expressed in
equation (4).

The dimensional analysis, presented previously, yielded the fol-
lowing relationship to be examined for trends:

V/W3 = f(P/w3,W/D,Ac/ao2) (4)

Since V and P are both a function of W3, they will be combined to form
the ratio V/P for the discussion (although it is noted that V and P
are not linearly related). The values of the three dimensionless
parameters are contained in Table 2.

It should be noted that since the cross-sectional area is not
directly related to the W/D ratio, two inlets with identical areas can
have widely different aspect ratios. This situation is portrayed by
comparing St. Lucie and Lake Worth Inlets. In this case, their cross-
sectional areas are relatively equal, 13,900 square meters and 13,500
square meters, respectively. However, their W/D ratios are 211 and
74, respectively.

The parameters are plotted in Figure 3. An examination of Figure
3 reveals a somewhat significant trend with respect to the aspect
ratio, W/D. Two zones can be determined as is depicted by the dashed
line. This line is represented by the equation:

V/P = 0.0033 W/D + 1 (7)

This line, although clearly somewhat arbitrarily chosen, divides the
domain into two distinct zones with respect to the values of Ac/ao2.
V/P ratios will be greater than predicted by equation (7) when Ac/ao2
is greater than 1000. Likewise, V/P will be less than predicted by
equation (7) when Ac/ao2 is less than 1000. This relationship holds


I I


1617











COASTAL SEDIMENTS '87


0.5 1.0 5 10 50 100
EBB SHOAL VOLUMES (x 0l6ri-)


Figure 2. Linear Regression Analysis Results


x(1.7)


Note: Numbers in Parentheses ( )
Represent Ac Values xl03O
ao2


X(1.2)
(20)
X0(1.8) X Y
-L= x =-0.0033 -+1

S(2.8)
E =-1o W*


0.5r


x(O.I)
x(0.s) x(23)
x(o4, (o0.6) 1


50 100


x(1.2)


x(1.9)


AC ./


X (0.4) a 02

--<(LO)
S 00


150 200 250 300 350
W/D


Figure 3. Plot of V/P vs. W/D with Respect to Ac/ao2


I I I I I I
-- V= 559 x 104 P 9(Present Study)
V=6.08x 10 P '2(Walton and Adams)

St Marys/x
/X
x St. Augustine
.,Nassau x Ft.George/
/ Sound St.Johns
Lake Worth x /
/ L x Ft. Pierce
Bakers Haulover /- Ponce De Leon
x Matanzas
Sebostian x
Boca RFton
Jupiter
x x South Lake Worth
/ x Pt. Canaveral

I I I I


500 K000


2.0 H


X(1.6)


1


u ~


U


i I I | |


b5- I


--


1618









INLET EBB SHOALS


Table 2. Dimensionless Parameters

A/a/2((10-3)
Inlet V/P W/D c o

St. Marys 0.62 133 2.8
Nassau Sound 0.65 320 1.9
Ft. George/St. Johns 2.18 61 1.7
St. Augustine 1.02 25 1.8
Matanzas 0.34 123 0.4
Ponce de Leon 1.04 75 2.0
Port Canaveral 1.72 19 1.6
Sebastian 0.01 55 0.6
Ft. Pierce 1.28 64 1.2
St. Lucie 1.00 211 1.2
Jupiter 0.10 35 0.5
Lake Worth 0.10 74 2.3
South Lake Worth 0.35 11 0.1
Boca Raton 0.15 16 0.2
Bakers Haulover 0.05 31 0.5

in 14 of 15 cases examined. In the case of Lake Worth Inlet, for
which the relationship does not hold, the V/P ratio is a low 0.10.
From equation (7), a value of not less than 0.75 should be expected
for the V/P ratio.

Equation (7) should be used mainly as an expedient means of
estimating the maximum or minimum volume stored in the ebb shoals.
The width and depth can be easily measured in most field environments.
The cross-sectinal area can be estimated from the width and depth.
The tide range can be found locally or derived from Tide Tables. The
prism can be estimated from the Prism Area Relationship, as
presented for example by O'Brien (1969)

Ac = 2.0x10-5 P (8)

With these parameters now known, the maximum or minimum volume of sand
stored in the shoals can be estimated within the bounds of the two
zones defined. For example, assume the width of the inlet is 500
meters and the depth is 10 meters. The cross-sectional area is then
5000 square meters. Assume the tide range squared is 3.0 square
meters. The Ac/ao2 value is 1666 which is greater than 1000. The
prism is estimated, using equation (8), to be 2.5x108 cubic meters.
From equation (7), we know that the V/P value must be greater than
0.84. Therefore, the minimum volume estimated to be stored in the ebb
shoal is 2.1x108 cubic meters.


1619











COASTAL SEDIMENTS '87


Results of Figure 3 imply that if the wave energy and prism (and
therefore cross-sectional area via O'Brien (1969) are kept constant,
then a greater W/D ratio will yield a smaller volume and vice versa.
This can be seen on a relative basis by using Matanzas, Ponce de Leon
and Ft. Pierce as examples. These inlets have prism values of
14.2x106m3, 16.3x106m3, and 17.3x106m3, respectively. Their cross-
sectional areas are 910m2, 1170m2, and 980m2, respectively. These
values may be considered as being essentially constant for the present
purpose. It can be seen from Table 3 that as the W/D ratio decreases
from Matanzas to Ft. Pierce, the volume increases, lending credibility
to the hypothesis that volume is in fact a function of not only prism
(or cross-sectional area), but also the aspect ratio, W/D.


Table 3. W/D versus V Comparison

Inlet W/D V(m3)

Matanzas 123 4.8x106
Ponce de Leon 75 17.0x106
Ft. Pierce 64 22.2xl06

DISCUSSION

It would be difficult to find an ideal case in nature where the
wave energy, prism, area and tide are all constant. However, this
requirement may be further examined through mathematical or physical
modeling. Using a relatively simple approach, the effect of varying
W/D ratios on the ebb shoal volume may be best realized by examining
the influence of the bed shear stress. The critical shear stress is
that value of the bed shear stress that is exerted at the point of
incipient motion. When the actual .bed shear stress exceeds the
critical shear stress, the bed material is put into motion.

Jonsson (1966) finds that the wave friction factor, f,, is
significantly larger than the current friction factor, fc. The
equations representing the shear stress due current, Tc, and waves,
Tw are

T = 0.5 Pfcuc2 (9)

and "

Tw = 0.5 pfwuw2 (10)

respectively, where p is the density of seawater, uc is the water
velocity due to current and uw is the water velocity due to waves near
the bed.


T 7


1620










INLET EBB SHOALS


For the problem at hand, it is sufficient to consider two inlets
of the same cross-section, Ac, but having different aspect ratios,
W/D. Let inlet #1 be 3 meters deep by 400 meters wide, and inlet #2
be 6 meters deep by 200 meters wide. Thus both inlets have a cross-
sectional area of 1200 m2, but the corresponding aspect ratios are 133
and 33, respectively. It can be shown that by virtue of the Hydraulic
Prism equation and equation (8), the maximum ebb velocity through both
the inlets will be the same. Let us assume that the velocity, uc,
over the ebb shoal will as well be the same in both cases, in spite of
the differences in the flow depth over the bar. Let uc be 0.3 m/sec,
a representative value. Select further, a representative wave height
of 1 m and a wave period of 7 sec applicable to ebb shoals at both
inlets. For current, a typical value of 4.1x10-3 may be selected
for fc. The magnitude of fw depends on the relative bottom roughness,
i.e. the maximum water particle displacement near the bed, Ab,
divided by the bed roughness, ds. fw was estimated by using calcu-
lated Reynolds Numbers of 2.85x106 and 1.33x106 and corresponding
Ab/ds values of 2264 and 1586 for inlets #1 and #2, respectively.
The f, values are estimated to be 8.0x10-3 and 9.0x10-3 for inlets #1
and #2, respectively.

In Table 4, the current shear stress, Tc, and wave shear stress,
Tw, are given for the two inlets. It is observed that in the case of
both inlets, the wave shear stress is dominant. Hence the precise
selection of the magnitude of uc for the inlets is not a matter of
critical importance, so long as reasonable values are selected. Since
the shear stress is greater in the shallower inlet, it is more likely
that the critical shear stress will be exceeded there more often than
in the deeper inlet. As the sand is put into motion, it is moved by
the longshore current and wave forces back towards the shore. This
movement of sand, therefore, occurs more significantly in shallower
inlets than in deeper inlets, allowing the shoals of deeper inlets to
grow to greater volumes than those of shallow inlets. This reasoning
is in agreement with the conclusion of Walton and Adams (1976). They
state that more material is stored in the shoals of low wave energy
coasts than in high wave energy coasts. This is because there is more
energy available to drive the sand back to shore in high energy
environment after being deposited as a shoal. In the present study,
the same relative wave energy environment was considered, and the
local effect of the shear stress caused by incoming waves has been
examined. The role of the aspect ratio in determining the ebb shoal
volume is thus shown to be significant, along with the tidal prism and
cross-sectional area.


Table 4. Shear Stress Comparison

D(m) c (N/m) (N/m2)

Inlet #1 3 0.18 3.23


Inlet #2


6 0.18


1.62









COASTAL SEDIMENTS '87


CONCLUSIONS

A few important conclusions with respect to Florida's east coast
inlets are in order.

1. There is a general (but not uniform) trend of decreasing ebb
shoal volume from St. Marys Entrance (95x106 cubic meters) south to
Bakers Haulover Inlet (0.5x106 cubic meters).

2. The total amount of material stored in the ebb shoals of all
eighteen inlet systems is 420x106 cubic meters. Of that amount,
approximately 83% resides in the ebb shoals of the four northernmost
inlet systems--St. Marys, Nassau Sound, Ft. George/St. Johns and St.
Augustine. None of the other inlets account for more than 5% of the
total volume, individually.

3. The east coast inlets of Florida all reside within the
moderate wave energy range as defined in Walton and Adams (1976).

4. The volume of material found in the ebb shoals appears to be
a function of spring tidal prism, P, inlet area, Ac, amplitude of
tide, ao, and the inlet width to depth ratio, W/D.

5. The influence of the W/D ratio appears to arise as a result
of the differing effect of wave-induced sand transport at different
depths over the ebb shoal.

6. Two distinct regions are defined by relating V/P to W/D and
Ac/ao2. For values of Ac/ao2 greater than 1000, the V/P value will be
greater than that predicted by the equation V/P = 0.0033 W/D + 1, in
most instances. For values of Ac/ao2 less than 1000, the V/P value
will be less than that predicted by equation (23).

REFERENCES

Dean, R.G., and Walton, T.L., Jr., "Sediment Transport Processes in
the Vicinity of Inlets with Special Reference to Sand Trapping,"
in Estuarine Research, Vol. II (Geology and Engineering), Academic
Press, New York, 1973, pp. 129-149.

Jensen, R.E., "Atlantic Coast Hindcast, Shallow-Water, Significant
Wave Information," WES Wave Information Studies No. 9' U.S. Army
Engineer Waterways Experiment Station, Vicksburg, Mississippi,
1983.

Jonsson, I.G., "Wave Boundary Layers and Friction Factors," in
Proceedings of the Tenth Conference on Coastal Engineering, Vol.
1, American Society of Civil Engineers, New York, September, 1966,
pp. 127-148.

Marino, J.N., "Inlet Ebb Shoal Volumes Related to Coastal Physical
Parameters," UFL/COEL-86/0177 Coastal and Oceanographic
Engineering Department, University of Florida, Gainesville,
Florida, December, 1986.


1622









INLET EBB SHOALS


Marino, J.N., and Mehta, A.J., "Sediment Volumes Around Florida's East
Coast Tidal Inlets," UFL/COEL-86/009, Coastal and Oceanographic
Engineering Department, University of Florida, Gainesville,
Florida, July, 1986.

O'Brien, M.P., "Equilibrium Flow Areas of Inlets on Sandy Coasts,"
Journal of the Waterways and Harbors Division, Vol. 95, No. WW1,
Americal Society of Civil Engineers, New York, February, 1969, pp.
43-52.

U.S. Army Corps of Engineers, Jacksonville District, "Beach Erosion
Control Study on Brevard County, Florida," Jacksonville, Florida,
1967.

U.S. Army Corps of Engineers, Jacksonville District, "Feasibility
Report for Beach Erosion Control, St. John's County, Florida,"
Vols. 1 and 2, Jacksonville, Florida, 1977.

Walton, T.L., Jr., and Adams, Wm.D., "Capacity of Inlet Outer Bars to
Store Sand," in Proceedings of the Fifteenth Conference on Coastal
Engineering, Vol. 2, American Society of Civil Engineers, New
York, July, 1976, pp. 1919-1937.


1623




















Management of Sandy Inlets: Coastal and
Environmental Engineering Imperatives

Ashish J. Mehta and Clay L. Montague1

Abstract

Management of sandy tidal inlets is required for
maintenance of navigable channels and control of beach
erosion. Management elements essentially entail
"resharing" of sand by alteration of natural sediment
pathways, while preventing ecological damage. Although
technology for understanding sediment movement near inlets
has made strides in recent years, considerable effort is
required in developing efficient systems for bypassing
sand. Inlet design criteria are identified for the
management of critical habitats. These criteria are then
applied qualitatively to the issue of rising sea level.
Refinements in the criteria should result from their use
in inlet design and management decisions, which we
encourage.

Introduction

Management of a sandy tidal inlet for maintaining a
navigable channel has been an issue to contend with since
the early days-of waterborne commerce. In recent years
this issue has taken on new dimensions as a result of the
problem of recession of the contiguous shorelines, and
ecological damage that may accrue from corrective
measures. In consonance with the nature of the problem
for example along Florida's sandy shoreline, the focus
here will be on Florida inlets. In what follows a
perspective based on coastal processes and environmental
imperatives is developed (Mehta et al., 1990).






Professor and Associate Professor, respectively,
College of Engineering, University of Florida,
Gainesville, FL 32611.


Mehta












Shoaling due to Littoral Sand


Two relevant questions are: 1) what is specifically
meant by tidal inlet management?, and 2) why is it
required? In these contexts it is worth reviewing the
general nature of sand transport and budget along a
relatively straight barrier shoreline punctuated by tidal
inlets, say every 15 to 30 km, as shown in Fig. 1.
Consider a micro- or mesotidal environment having a
dominant direction of wave approach and associated
alongshore sand transport over a relatively narrow
nearshore column of water bounded by the shoreline and the
depth of closure, say on the order of 9 m. This alongshore
transport, coupled with shore-normal sand transport within
the water column leads to the development of a longshore
sand bar whose configuration is modified near each inlet.
This modification primarily amounts to the occurrence of
the ebb shoal, while in the interior tidal waterway flood
shoals occur.

Consider the net rate of littoral drift (equal to the
difference between the gross rates of drifts in the two
directions shown by arrows) applicable to barrier segments
of the shoreline. Reported values of the net drift rates
obtained from accumulations at the updrift jetties of
inlets tend to decrease, in many instances, from segment
to segment in the downdrift direction. With respect to the
difference in the net drifts between two adjacent
shoreline segments, say A and B, i.e. 10 6x10 = 4x10
m /yr, it follows that the mass of sediment corresponding
to this volume difference must deposit each year either in
the nearshore waters of barrier segment B, or inside the
inlet between segments A and B. Assume barrier B to be 20
km long having a width of 200 m between the shoreline and
the depth of closure The area available for sand
deposition will-be 4x10 m Let the inlet channel between
barriers A and B be 100 m wide and 0.5 km long.2 Thus the
deposition area of the channel will be 0.5x10 m Further
assume that only 0 % of the depositing littoral drift
sand, i.e. 4,000 m settles in the inlet each year. Then,
say over a 10 year period, the depth in the inlet will
decrease by 80 cm which is measurable, while the beach
bottom, assuming sand deposition to be uniform over it,
will rise by only 9 cm, which is comparatively small. This
simple illustration shows why shoaling of inlets can
become a problem for navigation, while deposition of a
much greater total quantity of sand over the beach bottom
may remain undetected.

Since the ingress of sand into the inlet channel is
a manifestation of littoral sand drift it follows that,
inasmuch as the role of each inlet in influencing the
regional inventory of sand goes well beyond the beaches in


L


















(Net Drift, 10 5 mlyr)







(Net Drift, 6 x 104m3/yr)
'^


Flood


Fig. 1. Barrier shoreline with sandy
littoral sand transport.


Likely Shoreline .
in Absence of Inlet-
Updrift Accretion
or Fillet
.''""-"".' : ' : : '. ,


Net Longsh
Littoral Dr

Beglnni
of


Influx Inlet Channel


S-~" W r. \Nearfield
SDowndrift Erosion \
S:or Deficit


tidal inlets




ore
ift

ng of Influence
Ebb Shoal

Point (A) of Pathway
Separation


SEbb Shoal Bypassing
Sediment Pathway













Point (C) of Pathway
SReattachment


Fig. 2. Interception and modification of the littoral sand
'pathway by an inlet.


AR-. ,4 -


and


1












the proximity of the inlet, a regional management approach
based on morphologically identifiable segments of the
shoreline is far more desirable than one based on physical
limits dictated by institutional constraints.

Elements in Inlet Management

Consider the sediment pathways near an inlet as shown
in Fig. 2. The updrift and downdrift shorelines have been
modified by the presence of the inlet as well as its
training by jetties. The updrift accretion or fillet, may
or may not be balanced by downdrift loss of sand depending
upon a-number of controlling physical parameters. Even in
cases where it is balanced, accretion is usually localized
over some distance updrift which depends on the jetty
length, wave intensity and approach direction etc., while
the effect of erosion is often felt over much longer
distances downdrift, occasionally over most of the
downdrift barrier beach. About 85 % of beach erosion in
Florida over the past century has been attributed to
effect of this type (Dean, 1988).

Of the two natural sediment pathways based on the net
drift concept shown in Fig. 2, one characterizes (net)
sand bypassing which occurs over the ebb shoal, while the
second indicates (net) sand influx. At point A the two
pathways diverge, while at point C the first pathway
reattaches itself to the shore-parallel sand bar. The
region of primary concern is between points B and C, the
main area of sand deficit. The cause of this deficit is
insufficient net supply rate of sand in relation to its
rate of depletion by local waves and currents. A
navigation channel cut through the ebb shoal may
measurably intercept the first pathway thus exacerbating
the deficit, while at the same time this channel may
experience significant shoaling in the interior as a
result of the second pathway.

The need to alter natural sediment pathways to
maintain adequate channel depths and minimize downdrift
erosion leads to the following three elements in inlet
management: 1) Maintenance of the navigation channel to
allow safe passage of vessels under non-extreme climatic
conditions, 2) restoration of the sand flow to mitigate
the downdrift deficit, and 3) maintenance of ecological
balance while fulfilling the requirements of the first two
elements.

Elements 1 and 2 can pose competing requirements,
since the ideal solution for meeting the second
requirement would be to close the inlet, and this has been
done in cases where the need of maintaining shoreline
stability is overwhelming. In general however, it is












essential that technology be provided to address the
issues of navigation and erosion simultaneously, without
damaging the environment in the process.

Creation of Artificial Pathways

Simultaneous fulfillment of the first two, coastal
engineering elements is conventionally achieved by
creating artificial pathways shown in Fig. 3, in order to
alter sand "sharing" at the inlet. Consider first the
natural pathways. Pathway 1 is the same as that in Fig. 2,
while pathway 2 is now considered to represent the total
influx of sand. Pathway 3 implies transport of sand to the
so-called passive part of the ebb shoal from which, by
definition, the deposited sand does not return to merge
with pathway 1. Pathway 4 is that portion of the sand
which is also transported out to the passive part of the
shoal by ebb currents.

Inherent to the described role of pathways 3 and 4 is
the assumption that the ebb shoal, at least the passive
portion, is in a state of growth, however small the growth
rate might be. This can only be the case if the bathymetry
surrounding the inlet has not attained equilibrium with
the ambient hydrodynamic environment. Consider for example
navigable inlets along the east coast of Florida, most of
which have been "newly" opened or trained by jetties in
the last 100 years. New inlets develop ebb shoals which
are previously absent, while training causes stronger
currents to push existing ebb shoals into deeper offshore
waters. Since however the controlling depth over the shoal
is determined largely by wave action, the shoal grows in
planform. The rate of growth is rapid in the initial
years, but steadily decreases as the shoal size approaches
equilibrium. Many of the ebb shoals along the east coast
of Florida are.known to be growing presently albeit at
slow rates, decades after new inlets have been opened or
natural ones trained.

While natural pathways operate over time-scales of
tides and are episodically influenced by wave action due
to storms and hurricanes, the time-scales of artificial
pathways vary widely, dependent as they are on the
technology used. Pathway 5 is the most common means of
"resharing" sand for example by hydraulic dredging of the
interior channel. Pathway 5' includes cases in which the
flood shoal is dredged independently of the navigation
channel, e.g. at Sebastian Inlet. Pathway 6 is typically
instituted by use of sand transfer plants, e.g. at Palm
Beach Inlet, or by related systems that essentially
achieve the same purpose. Pathway 7 involves dredging of
the offshore channel, which for example is customary in
Federally maintained navigation channels. In those cases


Mehta
























Channel


-- Natural Pathways
-----Artflllcal Pathways


Fig. 3. Natural and artificial sediment pathways in the
inlet nearfield and channel.


\ Depth of Closure


Zero Flux


Uttoral Drift
Boundary (1)


Offshore Edge
of Ebb Shoal


Passive
Ebb Shoal


Zero Flux
Boundary (2)


Uttoral Drift
Boundary (3)


Fig. 4. Control water area identifying the passive ebb
shoal.


i


~~ t
,a----












in which the dredged material is found to be compatible,
it is transported to the beach. Alternatively the ebb
shoal may be mined for sand through an operation not
related to navigation (pathway 7'), and the material
transported to the downdrift beach, as at Redfish Pass.

Given these artificial pathways, and having the
technology to utilize them as and when needed for purposes
of continuous or near continuous transport, thus amounting
to 100 % sand bypassing, the two coastal engineering
management elements can be fulfilled simultaneously.

Inherent to the development of artificial pathways is
the need to establish a sand budget based on the natural
pathways within a control region. In Fig. 4 such a region
is shown, whose designation requires the determination of
the different flux boundaries, i.e. boundaries with zero
net flux, or boundaries through which the fluxes are
known. The last condition occurs at the shore-normal
boundaries 1 and 3, given the littoral drift rates. Zero
flux boundary 4 can be established up estuary provided no
sediment arrives by river. If it does, there is the
likelihood that the riparian sediment is of different
composition than the marine material crossing the boundary
upstream. In the latter case fluxes in both the directions
must be considered.

In the absence of the inlet, the depth of closure
would practically suffice as the zero flux boundary 2,
especially over comparatively short term time-scales e.g.
on the order of 25 year design life of a sand sharing
project, during which shore-normal transport may be
negligible. In the area of the ebb shoal however, the
depth of closure typically diverges from the boundary
delineating the offshore extent of the shoal. Between
these two boundaries lies the passive ebb shoal. The zero
flux boundary in this area is therefore defined by the
offshore edge of the passive ebb shoal. The points at
which the two boundaries merge essentially defines the
extents of upstream and downstream influences of the ebb
shoal, and therefore boundaries 1 and 3.

In a hydrographic investigation for determination of
natural sediment pathways, shoal boundaries and sand
budget it is technically advantageous to follow a "hybrid"
approach involving a combination of a field study to
measure the governing parameters in situ, a laboratory
study with the help of a physical model to reinforce and
extend the results from the field, and a mathematical
study which, together with field data and physical model
results, can assist in developing management options. The
hydrographic investigation should sequentially focus on:
1) the nature of bottom topography, and the composition


V I












and stratigraphy of the bottom material within the control
region, 2) inlet nearfield and channel hydrodynamics
including the wave-current interaction, 3) effect of
changing water density between the interior and the
exterior water bodies on the flood and ebb flow
distributions, and interaction between river discharge and
salt water ingress up the channel, and 4) location of
sediment pathways, shoal boundaries and sand budget for
the control region. Once the sediment budget is developed,
selection of appropriate technology for the creation of
artificial pathways becomes feasible. For example if the
ebb shoal is to be dredged for beach sand, it is essential
to identify the passive part of the ebb shoal, since any
extensive dredging of the ebb shoal that is not passive
can lead to potentially serious problems for the stability
of the beaches due to increased wave penetration and
reduced sand bypassing.

Effective Bypassing

The requirements to achieve 100 % bypassing of sand
by artificial means, commensurate with the maintenance of
a navigation channel and control of downdrift erosion, are
contingent upon the availability of resources and
dedicated technology. Problems occur in implementing
bypassing technology in most cases due to inadequacies
associated with these two factors. Additional constraints
can arise if the sediment required to be bypassed is
either unsuitable for beach placement, or if there are
possibilities of damage to benthic habitats.

Effective bypassing solutions can be "passive" or
"active" or, as commonly the case, a combination of these
two modes. Passive solutions are based on construction of
structures including jetties, sometimes extended linearly
and sometimes with a certain curvature, or in some cases
having non-parallel orientation to control sand influx,
while attempting to minimize the blockage of sand transfer
from the updrift to the downdrift side.

Long jetties were constructed at St Mary's Entrance
and St John's River Entrance to cut off sand influx
completely, but given the concern for downdrift beach
erosion that this may cause, such an option may be
precluded from consideration. Curving one, (usually the
updrift) jetty, such as at South Lake Worth Inlet, can
actually serve two purposes. First, it allows a somewhat
smoother pathway for natural sand transfer from the
updrift to the downdrift side. Secondly, it provides a
certain degree of protection to vessels against beam waves
as they enter the inlet. Non-parallel jetties converging
towards the sea, such as at East Pass, are meant to
accentuate the difference between inlet nearfield ebb and


Mehta











flood flow patterns. The ebb jet is separated from land
boundaries and is flanked by induced flow eddies which
tend to transport beach sediment towards the inlet. The
jet interacts with the wave-induced cross flow via lateral
entrainment and mixing. On the other hand flood flow
"sinks" into the inlet without any drastic boundary
separation. By causing the converging jetties to "shoot"
the flow seaward, the ebb shoal is formed in deeper waters
than under weaker ebb currents, thus requiring lesser
amount of dredging for the offshore channel than for
parallel jetties. On the other hand, sand entering the
channel during flood is likely to settle out quickly once
inside-the entrance, since flow expansion there causes the
velocity to drop. The material can therefore be trapped in
a designated borrow pit, from which it can be transferred
to the downdrift beach. Providing a weir section in the
updrift jetty such as at Ponce de Leon Inlet, thus
deliberately allowing the jetty to "leak", accomplishes a
similar sand trapping purpose.

Active solutions would ideally consist of continuous
mechanical transfer of sand in order to mitigate downdrift
erosion by the placement of sand from the updrift,
nearfield or the interior areas. With respect to bypassing
by dredging the nearfield (e.g. offshore navigation
channel or the passive part of the ebb shoal), practical
considerations dictate that dredging be carried out on an
"as needed" basis. The same can be said of bypassing of
material in the interior, where vessel traffic and
shifting shoal patterns as well may preclude continuous
bypassing. Hence the question of continuous bypassing at
desired (variable) rates typically arises mainly in
transferring sand from the updrift to the downdrift beach.
This question deserves fuller examination, because of the
need to feed sand to the deficit area on a more continuous
and efficient basis than at present.

In selecting a sand bypassing system, four criteria
must be evaluated: 1) proven long-term, field tested
ability to transfer the desired amount of sand in the type
of physical environment for which the system is needed, 2)
commercial availability of the system including terms for
maintenance and repair, 3) capital and maintenance costs,
and 4) availability of necessary physical infrastructure
for operation and repair. At present there are real
constraints in all four areas, which makes the issue of
sand transfer one that requires considerable additional
technical development.

Environmental Considerations

Inlet management protocols today must consider a
broad suite of environmental consequences. Alterations


Mehta












to improve navigational safety may affect critical
habitats in the vicinity of an inlet. These effects not
only include the historically recognized problem of
downdrift beach erosion, but also impacts on habitats near
the ebb shoal and inside the inlet. The opportunity has
arisen to develop criteria for management both of nearby
ecosystems and of species of special concern. These
criteria can be used not only to minimize impact, but also
to restore or create critical habitats, thereby enhancing
the survival of particular animals and plants that may be
threatened with extinction, or be fundamental to the
continuation of a productive fishery.

The inlet as a passageway. Many animals migrate
through inlets. Most adult fishes of commercial and
recreational importance spawn offshore, yet the juveniles
of most species are found in estuarine nursery grounds.
Inlets are the pathways both by which larvae pass into
estuaries and later by which adults leave to spawn. Some
fish, such as striped bass (Morone saxatilis) and salmon
(Oncorhynchus spp), migrate from the ocean to freshwater
to spawn. Freshwater eels (family Anguillidae) migrate
from rivers to the ocean to spawn. In Florida, a mammal
-- the endangered West Indian manatee (Trichechus manatus)
-- is a frequent user of inlets. It migrates northward in
summer and southward in winter passing through inlets to
feed on submersed vegetation in estuaries along the coast.
An artificial inlet that has been stabilized for many
years may have become an important migration pathway for
many animals.

Rocky outcroppings. Critical habitats outside of an
inlet include rocky outcroppings near the ebb shoal and
near both updrift and downdrift beaches. Submerged rocks
develop a living surface consisting of rich and sometimes
very diverse communities of attached plants and
invertebrate animals. Offshore rocky outcroppings are
habitat for both spawning and non-spawning fishes. If
exposed to repeated scour or burial by sand, the attached
biological community will develop poorly if at all. Such
perturbations are a natural consequence of close proximity
to beaches or shoals. The time required for maximum
community development on unperturbed rock is perhaps years
to decades, though considerable development may take place
within a year. Manipulation of inlets may reposition
shoals and alter the pattern of sand accumulation along
beaches. Nearby rocks with well-developed biological
communities may be buried or scoured with greater
frequency. Conversely, rocks used in jetty construction
are also well-utilized by fishes and develop rich
biological communities within a period of one or two years
(Hay and Sutherland, 1988).












Beach habitats: sea turtle nesting. Some beaches
and dunes are habitat for species threatened with
extinction. The beaches of the Atlantic coast of Florida,
for example, are among the most heavily used in the world
by nesting loggerhead sea turtles, Caretta caretta (Ross,
1982). During the main nesting period (March through
November), more than 200 nests are laid per km in many
stretches of beach, along with nests of other sea turtles.
Because of the Federal listing of these species as
threatened or endangered, beach nourishment activities are
heavily restricted. Female sea turtles are easily
discouraged when they come ashore searching for a nest
site. -Lights, noises, and many unknown factors discourage
them. Beach construction activities are not allowed
during the nesting season. Eggs deposited during or prior
to construction activities would likely be destroyed
before hatching so they must be relocated to safer sites.

Although the criteria for developing a successful
nesting beach are not completely understood, good nesting
beaches are characterized by a gentle profile without
steep scarps, a wide (perhaps 20 m), wet-sand intertidal
zone, and a gently-sloping, drier berm of compaction less
than 350 t/m to a depth of one meter (Nelson, 1985; Nelson
and Dickerson 1988). Sea turtles will not dig nests in
sand that is too compact. Some constructed beaches are
initially suitable, but later become too compressed or
erode during the nesting season. Incubating eggs exposed
by erosion do not survive and new nests will likely not be
laid on eroded beaches. Maintaining a suitable profile
may require continual sand pumping or repositioning of
jetties. Selection of dredge material of a grain size
distribution similar to that found on nearby natural
beaches prevents compaction.

Inside the inlet: critical estuarine habitats.
Inlet alterations may subtly affect intertidal and
submersed vegetation inside the inlet. Changes in inlet
width or depth can alter tidal amplitude, mean water
level, patterns of circulation, transport of salt and
sediment, and turbidity. These factors can affect
salinity intrusion into freshwater supplies and habitats
and determine the extent and productivity of intertidal
and subtidal estuarine ecosystems. Intertidal and
submersed vegetation traps and stabilizes sediment.
Vegetative detritus comprises the main food for estuarine
food chains and provides cover for numerous estuarine
animals, including the juvenile stages of commercially
valuable fish and invertebrates (Montague and Wiegert,
1990). Moreover, submersed vegetation is eaten directly
as a main component of the diet of the green sea turtle,
Chelonia mydas, and the West-Indian manatee, Trichechus
manatus (Zieman, 1982).












Intertidal habitats. Intertidal vegetation occupies
the low wave-energy, intertidal zones of estuaries and
lagoons (Montague and Wiegert, 1990). Gentle slopes and
higher tidal ranges increase the extent of the intertidal
zone and therefore the area suitable for growth. Rises in
mean water level will shift the position of the intertidal
zone landward, falls will shift it toward the center of
channels. Since slopes may increase toward channels,
falls in water level may result in smaller intertidal
zones. Intertidal vegetation traps suspended sediments,
which can cause expansion or vertical growth of the
intertidal zone. If sediment supplies are large, sediment
trapping could eventually offset any decreases in width
caused by altered water level.

Submersed vegetation. Management of submersed
vegetation is more complex because it involves a variety
of plant species each with particular responses to changes
in salinity, temperature, nutrients, light, current, and
other factors (Zieman 1982; Fonseca and Kenworthy, 1987).
Inlet modifications may alter water level, tidal range,
bathymetric slope, currents, wave energy, and water
clarity. Where currents are sufficiently low to allow bed
development (probably less than 150 cm/s), submersed
vegetation will likely occur between the limits of
exposure to air on the shallow side of the bed and lack of
light on the deep side. The bathymetric slope between
these extremes is then the major determinant of the size
of the bed. Gentle slopes and continually high water-
clarity should allow extensive coverage of subtidal areas
by submersed vegetation. Growth increases as current
increases from 2 cm/s to perhaps 50 cm/s or more and as
light increases from 5% to 70% or more of surface
irradiance. A minimum average light for habitat
development is perhaps 15%.

A complex positive feedback loop exists among
available light, submersed vegetation, current, and
suspended sediment. As beds develop, drag increases,
current slows, and suspended sediments are trapped and
held by the vegetation, thereby decreasing turbidity
(Fonseca and Fisher, 1986). Beds can then expand both
into deeper waters and into areas formerly with higher
currents. Removal of the beds can upset this loop and
make it "snowball" in the other direction: sediment
destabilizes, turbidity increases, and submersed
vegetation at the edges of remaining beds both erodes away
and dies from lack of light. Control of this feedback
loop is a significant management challenge.


I -












Sea Level Rise Effects


The relative sea level rise during the years 1940-80
in Florida has ranged from 1.2 to 1.9 mm/yr (Marine Board,
1987). Studies have shown that during this period the
effect of this rise on the shoreline, if any, has been
masked by effects of inlet modifications (Dean, 1988). The
exception perhaps is the entrance to Nassau Sound, which
is in its natural state. Here, in keeping with sea level
rise, the volume of the ebb shoal increased by 6.3x100 m
during 1871-1970, since there the controlling depth over
the shoal has been primarily determined by wave action
which most likely remained unchanged in the mean over this
period (Mehta and Cushman, 1989).

In a scenario with a relative sea level rise that is,
say, ten times greater than in Florida, as has been the
case in recent years along coastal Louisiana, inlets,
particularly those backed by shallow bays and extensive
wetlands, may be significantly modified. This is because
the increased water storage volume in the bay will widen
the channel to accommodate the increased tidal prism.
Furthermore, enhanced entrapment of sand by the ebb shoals
may accelerate the rate of beach erosion. Also, jetties
could become less effective, but in most cases they can be
modified easily to counter.inundation. It is likely that
more serious consequences will actually be encountered in
the interior areas having low relief. In many parts of
Florida for instance interior banks are fronted by homes
with land elevations that are less than say one meter at
Spring high tides. Storm damage at higher than present
water levels and associated wave action in such areas is
indeed a matter of potential concern. Interestingly
enough, in shallow areas in which the effect of bottom
friction on the flow is strong, a higher water level will
reduce the friction effect thereby reducing the naturally
occurring head difference (superelevation) between the sea
and the interior waters (Mehta, 1990). This reduction
would counter the effect of sea level rise to some extent.

Some of the habitat criteria outlined above can be
applied to an understanding of the effects of a rise in
sea level. Beaches, for example, will lose dunes and
nesting habitat for terns and sea turtles as a result of
increased beach erosion. Residential and commercial
developments are likely to be protected by revetments that
will exacerbate these losses. Likewise inside the inlet,
rising water levels will shift vegetated intertidal zones
toward steeper land or revetments, reducing intertidal
area, unless sediment supplies allow intertidal vegetation
to grow vertically to keep up with rising water levels.
If not, subtidal habitats may expand into the former
lower-intertidal zone. Water on the deep sides of











submersed vegetation beds will become even deeper,
however, so vegetation there will die from lack of light,
releasing any trapped sediments and perhaps beginning the
"snowball" effect described earlier. Saltwater intrusion
into freshwater supplies and habitats will also increase,
requiring relocation of pumps and wells, and killing or
dislocating freshwater animals and plants. Saltwater
intrusion may eliminate all the freshwater wetlands within
small, low relief, coastal-plain watersheds. Some of
these contain unique or endangered freshwater biota.
These wetlands would be replaced by saltwater wetlands,
thereby reducing the diversity of coastal zone wildlife.

Concluding Comments

While our knowledge and understanding of coastal
processes in the vicinity of sandy tidal inlets has been
gaining ground, technology for bypassing sand must be
developed further to allow for flexibility in terms of
locations of sand catchment, control over the timing and
rate of bypassing, and installation, operation and
maintenance requirements.

Environmental protection and habitat restoration can
and should be incorporated into the design or redesign of
inlets. Design criteria that are focused on critical
habitats are presently crude compared to other engineering
criteria. Nevertheless they can now be used and improved
as needed. As is true of all management of natural and
living systems, the most relevant information needs will
be more efficiently identified and researched through
attempts to use the criteria. Environmentally improved
inlet designs will then be forthcoming.

Acknowledgement

Sponsorship of this paper by the Environmental
Sciences Division of the Oak Ridge National Laboratory,
Oak Ridge, TN, and support from the Jupiter Inlet
District, Jupiter, FL are acknowledged.

References

Dean R.G. (1988). Sediment interaction at modified inlets.
In: Hydrodynamics and Sediment Dynamics of Tidal Inlets,
D.G. Aubrey and L. Weishar eds., Springer-Verlag, New
York, 412-439.

Fonseca M.S. and Fisher J.S. (1986). A comparison of
canopy friction and sediment movement between four species
of seagrass with reference to their ecology and
restoration. Mar. Ecol. Prog. Ser., 29, 15-22.












Fonseca M.S. and Kenworthy W.J. (1987). Effects of current
on photosynthesis and distribution of seagrasses. Aquat.
Bot., 27, 57-78.

Hay M.E. and Sutherland J.P. (1988). The ecology of rubble
structures of the South Atlantic Bight: a community
profile. Biological Report 85(7.20), U.S. Fish and
Wildlife Ser., Washington, DC.

Marine Board (1987). Responding to Changes in Sea Level:
Engineering Implications, Nat. Acad. Press, Washington,
DC.

Mehta A.J. (1990). Significance of bay superelevation in
measurement of sea level change. J.Coast. Res., 6(4), 803-
813.

Mehta A.J. and Cushman R.M. eds. (1989). Workshop on sea
level rise and coastal processes. Rept. DOE/NBB-0086, U.S.
Dept. of Energy, Washington, DC.

Mehta A.J., Montague C.L. and Parchure T.M. (1990). Tidal
inlet management at Jupiter Inlet, Florida. Rept.
UFL/COEL-90/005, Coast. and Ocean. Engrg. Dept., U. Fla.,
Gainesville, FL.

Montague C.L. and Wiegert R.G. (1990). Salt marshes. In:
Ecosystems of Florida. R. Myers and J. Ewel eds., U.
Central Fla. Press, Orlando, FL, 418-516.

Nelson W.G. (1985). Guidelines for beach restoration.
Part I. Biological guidelines. Rept. 76, Fla. Sea Grant
Coll., Gainesville.

Nelson D.A. and Dickerson D. (1988). Effects of beach
nourishment on- sea turtles. In: Beach Preservation
Technology 88: Problems and Advancements in Beach
Nourishment. L.S. Tait ed., Fla. Shore and Beach Preser.
Assoc., Tallahassee, FL, 285-294.

Ross J.P. (1982). Historical decline in loggerhead,
ridley, and leatherback sea turtles. In: Biology and
Conservation of Sea Turtles. K.A. Bjorndahl ed.,
Smithsonian Inst. Press, Washington, DC, 189-195.

Zieman J.C. (1982). The ecology of the sea grasses of
south Florida: a community profile. Rept. FWS/OBS-82/25,
U.S. Fish and Wildlife Ser., Washington DC.












UNDERSTANDING FLUID MUD IN A DYNAMIC ENVIRONMENT


By

Ashish J. Mehta

Coastal and Oceanographic Engineering Department
University of Florida, Gainesville, Florida, U.S.A.


ABSTRACT
The generation, transportability and dewatering of fluid mud under current-
and wave-induced forcing is a multi-variate problem that requires knowledge not
only of mud density and composition, but also of rheology which ultimately

characterizes mud dissipative properties. It is therefore self-evident that the
predictive accuracy of mathematical modeling, which undoubtedly is a powerful

tool for simulating mud dynamics, will depend strongly on the reliability of
theological description. Defining the state of mud solely in terms of density,
as is done commonly, only leads to ambiguities in quantifying the rates of
transport of fluid mud.


INTRODUCTION

The significance of fluidized mud relative its transportability in coastal
and estuarine sedimentation zones has been considered for decades beginning with
the issue of mud underflows in quiescent waters, followed by transport due to
current- and wave-induced forcing (Einstein, 1941; Inglis and Allen, 1957 ;
Krone, 1962; Owen, 1976; Nichols, 1984-1985). For operational convenience it is
common to define the fluid state of mud in terms of a density range alone, while

tacitly recognizing that the coupling between the state of mud and the fluid
forces makes density an ambiguous descriptor of this state. In that context it
is not surprising therefore that the lower density limit proposed for fluid mud
has varied from 1.003 to 1.12 g/cm3, and the upper one from 1.11 to 1.30 g/cm3
(Ross et al., 1987). Inherent as well to this variability in the density range

is the additional influence of the composition of mud. In order to highlight
these matters, the effect of hydrodynamic forcing on the nature of fluid mud
response is here revisited, followed by reference to some tentative conclusions
based on recent observations on the effects of mud composition.


h L












MUD-WATER INTERACTION
Since the dynamic behavior of a given sediment-water mixture is contingent
upon the flow regime and the suspension concentration, the transition from
particulate behavior in dilute, low concentration suspensions under turbulent
flows to soil mechanical behavior in hyperconcentrated, viscous flows occurs
through wide ranges of flows and concentrations (Fig. l(a)). In reference to
these ranges, noted here only in the qualitative sense, the distinctly non-

Newtonian behavior of fluid mud occurs over comparatively high concentrations
under flows in which turbulence is damped to varying degrees. The mixed
particulate and fluid (continuum) behavior occurs over concentrations that may
be considered to be moderate, and poses challenging problems in modeling the
horizontal transport of sediment over the water column (Owen, 1976).
The layering of sediment-water mixture, that occurs by virtue of the phase
transitions (Fig. l(a)) and the character of flow, identifies the fluid mud layer

in terms of the water depth as shown in Fig. l(b), wherein fluid mud is
designated as a mobile hyperpycnal layer (Wright et al., 1988); mobility here
implying horizontal motion. The upper bound of this layer is characterized by
the suspension-induced pycnocline or lutocline, and the strong flow shear zone
that is associated with the rapid change in concentration that occurs over a
comparatively short vertical distance. Shear production is often associated with
interfacial instabilities and mixing that occur in this layer, but by-and-large
the lutocline itself is stabilized by the hindered nature of settling below the
lutocline (Ross and Mehta, 1989a). The lower bound of the hyperpycnal layer is
specified by the level at which the horizontal flow velocity becomes zero; hence
the mud below this layer is stationary in the horizontal sense of movement.
The difference between stationary mud and the cohesive bed below is that

the latter is characterized by the occurrence of a measurable effective stress,
while in the stationary mud this stress is zero; hence both the mobile and
stationary hyperpycnal layers have been correctly called "fluid-supported
particle assemblages" or slurries (Kirby, 1986; Parker, 1989). On an
instantaneous basis, stationary mud that has, for example, distinct Bingham
plastic character, and one which has not dewatered sufficiently to form a fully
"particle-supported assemblage", or matrix, will offer measurable resistance to

deformation; hence it may neither be a fluid nor a cohesive bed. Since however
it is not mobile, it does not contribute to instantaneous horizontal sediment
transport.


r











It is evident that for calculation of the horizontal transport rate of
sediment mass, the boundary between mobile and stationary hyperpycnal layers must
be identified on an instantaneous basis. In that connection it is noteworthy
that, at relatively low velocities at which there is little vertical mass
transport due to erosion or deposition, the horizontal flux of fluid mud can be
quite large. Fig. 2(a) shows measured instantaneous concentration and velocity
profiles below the lutocline (turbid layer surface) in the Avon River estuary,
England (Kendrick and Derbyshire, 1985), and Fig. 2(b) shows the corresponding
sediment mass flux. The total rate of transport was 0.7 kg/m/s per unit width
which is not negligible, particularly because at the time of measurement, about
one-half hour before low water, erosion of the turbid surface or its growth by
deposition from settling sediment were not significant. Ross and Mehta (1989b)
simulated the velocity profile of Fig. 2(a) using the principle of momentum
diffusion into the turbid layer by an applied stress at the surface (lutocline)
of this layer. It was found that a stress of only 0.02 Pa was necessary to cause
the measured velocity profile within -20 min of the application of stress. It
was further found that mud viscosity and its variation with sediment
concentration critically controlled the velocity magnitude.


GROWTH AND PERSISTENCE OF FLUID MUD
Since the thickness of the fluid mud layer and its relative elevation
respond continuously to hydrodynamic forcing, tracking this response through time
requires an understanding of the phase transitions that lead to changes in the
thicknesses of the various layers mentioned. In that context, the behavior of
the fluid mud is evidently easier to examine under purely depositional or purely
erosional conditions, particularly the former, as in that case the upper bound
is specified by the maximum rate of the settling sediment flux, as exemplified
in Fig. 3. In this figure, the settling flux, Fs, is plotted against suspension
concentration, C, for sediment from Lake Okeechobee, Florida (Hwang, 1989). The
region to the right of the peak value of Fs (4.5 g/m2/s) is characterized by
hindered settling, hence in terms of the vertical concentration profile, the
value of C = 4.4 g/l associated with the peak flux corresponds to the depth at
which fluid mud is first encountered. Hence this depth represents the approximate
level at which the lutocline occurs.
The transition from a hyperpycnal layer to a cohesive bed is revealed in
settling column experiments in which the effective stress is profiled vertically












at various times by measuring the corresponding profiles of total and pore
pressures. An example of instantaneous profiles during settlement of an estuarine
silty clay is shown in Figs. 4(a) and 4(b), 4.75 hr after test initiation
starting with a uniformly mixed suspension having a density of 1.09 g/cm3 (Sills
and Elder, 1986). The level dividing the suspension from the bed can be

considered to be practically at 60 cm, which is close to, but does not uniquely
correspond to the-instantaneous elevation of the lutocline. This level rose to
about 80 cm at the end of the test several hours later. It is interesting to note
however that, during this settling process no unique relationship between the
onset of effective stress and mud density was found, and that the transition
from suspension to structured phase occurred gradually over the density range
of 1.09 to 1.13 g/cm3.

Under wave action for instance, the reverse process of transition from a
bed to fluid mud can be documented in the same way as during settlement. This
process is essentially one of resuspension, since the fluidized mud becomes
amenable to horizontal transport if and when a steady flow is superimposed on
wave oscillation. Fig 5 shows the gradual dissipation of effective stress in an

estuarine mud bed subject to wave action in a flume. The 1 Hz waves were 6 cm
high in 12 cm deep water column above the bed. A relevant observation associated
with this process was that while the fluid mud thickness increased with depth,
no significant change in bottom mud density took place (Ross and Mehta, 1989a).
This in turn means that in general mud fluidization by wave action can not be
parameterized uniquely by density.

In general when erosion and deposition occur simultaneously, comprehension

of the vertical and the horizontal motions of fluid mud is significantly
facilitated by mathematical modeling, even though it may be relatively simple.
Fig. 6(a) for example shows measured tidal variation of the lutocline shear
layer, i.e. the layer within which the suspension concentration changes rapidly
with depth, in the macrotidal Severn Estuary, England (Kirby, 1886). Fig. 5(b)

shows the same layer approximately simulated by a simple one-dimensional model
(Ross and Mehta, 1989a). Observe that the layer rises and falls over an elevation
on the order of 6-8 m but, in spite of the 7 m tidal variation that occurred
during the measurement period, this layer is quite persistent owing to the strong
buoyancy stabilization imparted by the relatively high density of mud.


i












INFLUENCE OF SEDIMENT COMPOSITION
While the effect of sediment composition on the behavior of mud is
generally well known, the case of Lake Okeechobee in the south-central part of
Florida is noteworthy, particularly since the mud there contains about 40 % by
weight of organic matter of floral origin. It appears that the presence of such
a large fraction of organic material leads to the occurrence of an open structure
in the top 10-20 cm layer of the bottom mud which fluidizes quite readily and,
once fluidized, does not dewater easily as a result of the strength provided by

the organic matrix itself. A further consequence is that this layer possesses
a uniform bulk strength which, when exceeded by the applied stress, results in
structural failure and an almost instantaneous fluidization of the bed layer.
Thus for example, at a density of 1.12 g/cm3, the bed became fluidized when the
applied stress exceeded 0.75 Pa in laboratory flume experiments (Hwang, 1989).
The easily fluidizable nature of mud has rather obvious implications for
the dynamics of Lake Okeechobee which experiences seasonally high trophic levels
due to episodic release of phosphorus and other nutrients associated with the
bottom sediment. The diffusion of nutrients into the water column is also an
important mechanism of phosphorus loading in this lake, particularly during
intra-storm calms when the wave action is quite mild. It was therefore a matter
of interest to determine whether the top layer of bottom mud, with its very weak

structure, in a practically fluidized state even at low wave-induced stresses,
moves measurably and thereby conceivably increases the rate of nutrient
diffusion.
An example of the surface wave energy spectrum obtained under moderate
breeze conditions (20 km/hr) in the shallow margin of the southeastern part of
the lake is shown in Fig. 7(a). The still water depth at the test site was
1.43 m. The spectrum corresponds to a significant wave height of about 8 cm at
a dominant frequency of 0.42 Hz. Fig. 7(b) shows the corresponding spectrum of
the horizontal, wave-induced mud acceleration. The measurements were obtained
with a biaxial accelerometer embedded 20 cm below the mud-water interface, where
mud density was 1.18 g/cm3. Comparing this spectrum with the one in Fig. 7(a)
indicates the wave-coherent nature of the mud oscillation which amounted to a
maximum horizontal displacement of about 2 mm (Jiang and Mehta, 1990). The data
are compared with results from a simple, shallow water wave model which assumed
the water layer to be inviscid and mud to be a viscous fluid. Agreement between
the data and model calculated spectrum is only marginal, partly because the model











could not fully account for the occurrence of non-shallow water frequencies
above the dominant one (0.42 Hz). It is believed that an important additional
cause of error in simulation may have been the overly simplified constitutive
behavior of the mud as a fully fluid-supported slurry at a density as high as
1.18 g/cm3, even under the influence of continued wave action.
Notwithstanding these sources of error however, the data and calculation
in Fig. 7(b) demonstrate that under mild wave action which is persistent in the
lake, fluid-like bottom mud tends to undergo measurable oscillations. The impact
of these oscillations requires further examination, not only in relation to
nutrient exchange, but also for the generation and release of gas bubbles, which
occur most commonly in this lake, thereby presumably contributing as well to lake
nutrient dynamics.


CONCLUDING REMARKS
Inherent to understanding the behavior of fluid mud is knowledge not only
of the density and the composition of the material, but also of the nature of
granular packing including the state of flocculation, as related to mud
theological properties. A brief review of mathematical models dealing, for
example, with wave-mud interaction (Maa and Mehta, 1989) reveals that modelers
have chosen a range of constitutive relationships to characterize mud rheology
in terms of its elastic and dissipative properties. Furthermore, model
applications clearly show that the results are strongly contingent upon the
selected relationship. It is concluded therefore, that since appropriately
representing theology is demonstrably of critical importance in understanding
mud behavior, efforts must be directed towards improved understanding of mud
rheology and instrumentation for its characterization, in order to reliably
quantify the rate of transport of fluid mud under wide ranging dynamical
conditions.


ACKNOWLEDGEMENT
Support provided by the U.S. Army Engineer Waterways Experiment Station,
Vicksburg, MS (through Contract DACW39-89-M-4639), and the South Florida Water
Management District, West Palm Beach (through the Lake Okeechobee Phosphorus
Dynamics Study), is acknowledged.












REFERENCES
Einstein H.A. (1941). The viscosity of highly concentrated underflows and its
influence on mixing. Transactions of the Twenty-Second Annual Meeting of the
American Geophysical Union, Part I, Section of Hydrology Papers, National
Research Council, Washington, DC, 597-603.

Hwang K.-N. (1989). Erodibility of fine sediment in wave-dominated environments.
M.S. Thesis, University of Florida, Gainesville, 156p.

Inglis C.C. and Allen F.H. (1957). The regimen of the Thames estuary as affected
by currents, salinities and river flow. Proceedings of the Institution of Civil
Engineers, 7, London, 827-868.

Jiang F. and Mehta A.J. (1990). Some field observations on bottom mud motion due
to waves. Report UFL/COEL-90/008, Coastal and Oceanographic Engineering
Department, University of Florida, Gainesville, 85p.

Kendrick M.P. and Derbyshire B.V. (1985). Monitoring of a near-bed turbid layer.
Report SR44, Hydraulics Research Ltd., Wallingford, United Kingdom, 19p.

Kirby R. (1986). Suspended fine cohesive sediment in the Severn Estuary and Inner
Bristol Channel, U.K. Report ETSU-STP-4042, Atomic Energy Authority, Harwell
United Kingdom, 249p.

Krone R.B. (1962). Flume studies of the transport of sediment in estuarial
shoaling processes. Final Report, Hydraulic Engineering Laboratory and Sanitary
Engineering Research Laboratory, University of California, Berkeley, CA, 118p.

Maa P.-Y. and Mehta A.J. (1989). Considerations on soft mud response to waves.
In: Estuarine Circulation, B.J. Neilson, A. Kuo and J. Brubaker eds., Humana
Press, Clifton, NJ, 309-336.

Nichols M.M. (1984-1985). Fluid mud accumulation processes in an estuary. Geo-
Marine Letters, 4, 171-176.

Owen M.W. (1976). Problems in the modeling of transport, erosion, and deposition
of cohesive sediments. -In: The Sea, Volume 6, E.D. Goldberg, I.N. McCave, J.J.
O'Brien and J.H. Steele eds., Wiley, New York, 515-537.

Parker W.R. (1989). Definition and determination of the bed in high concentration
fine sediment regimes. Journal of Coastal Research, SI(5), 175-184.

Ross M.A., Lin C.-P. and Mehta A.J. (1987). On the definition of fluid mud.
Proceedings of the National Conference on Hydraulic Engineering, American Society
of Civil Engineers, New York, 231-236.

Ross M.A. and Mehta A.J. (1989a). On the mechanics of lutoclines and fluid mud.
Journal of Coastal research, SI(5), 51-61.

Ross M.A. and Mehta A.J. (1989b). On the transport of estuarine high
concentration suspension. In: Flocculation and Dewatering, B.M. Moudgil and B.J.
Scheider eds., Engineering Foundation, New York, 529-538.













Sills G.C. and Elder D. McG. (1986). The transition from sediment suspension to
settling bed. In: Estuarine Cohesive Sediment Dynamics, A.J. Mehta ed., Springer-
Verlag, Berlin, 192-205.

Wright L.D., Wiseman W.J., Bornhold, B.D., Prior D.B. Suhayda J.N., Keller G.H.,
Yang Z.S. and Fan Y.B. (1988). Marine dispersal and deposition of Yellow River
silts by gravity driven underflows. Nature, 332(6164), 629-632.


i L










Concentration


Turbulent










Viscous


Low


Particulate
Behavior

\


Moderate


High


- ,---


Particulate
+
Fluid Behavior


Non-
Newtonian
Fluid
Behavior


Hvyer


Soil Mechanical
Behavior


Fig. l(a). Qualitative plot showing transitions between particulate behavior and
soil mechanical behavior associated with sediment concentration and flow regime.


CONCENTRATION


Suspension
(No Effective Stress)






Bed (Measureable
Effective Stress)


Fig. l(b). Horizontal layering of the vertical sediment concentration profile.
The concentration axis should be considered to indicate the logarithm of
concentration, implying a rapid change of concentration with depth.









CONCENTRATION, C (g/1)
100 200 300 400


0.04 -o u -
u-

0 0.08 \-
0 o/ ,






o 0.16 \
-Uj
wI o\
m 0.18 -

I0
LJ 0.24 I I1
0 0.1 0.2 0.3 0.4 0.5

VELOCITY, u (m/s)
Fig. 2(a). Concentration and velocity pro-
files below lutocline in the Avon River,
England (after Kendrick and Derbyshire,
1985).


Lu.
0





in
U-
mUJ







00
CL
0


Fig. 2(b).


0.18 1 I I I I I
0 1 2 3 4 5 6 7

MASS FLUX, F (kg/m2/s)


Horizontal sediment mass flux
corresponding to Fig. 2(a).


1



0.1



0.01



0.001


0.0001 LI
0.01


0.1 1 10


100


CONCENTRATION, C (g/I)

Fig. 3. Settling flux as a function of sediment concentration for mud from Lake
Okeechobee, Florida.


500












120


01
1.0


1.1
DENSITY (g/cm3)


PRI


Fig. 4(a). Instantaneous density profile Fig. 4(b). Total
during settling of a silty clay in tap corresponding to
water (after Sills and Elder, 1986).


0--
E


LU





LU
0
O













LU
.J
LU


5I I 1 I t 1
0 2 4 6 8


ASSURE (kPa)

and pore water profiles
Fig. 4(a).


EFFECTIVE STRESS (Pa)


Fig. 5. Dissipation of effective stress with time in an
subjected to wave action in a laboratory flume.


estuarine mud bed














LU
0

M,




-uJ
w
Z w *


10

8

6

4

2

0
0


80 120 180 240 300 380 420 480 540


TIME AFTER LOW WATER SLACK (min)



Fig. 6(a). Measured tidal variation of the lutocline shear layer in the Severn
Estuary, England (after Kirby, 1986). The mean water depth was 21 m.


U1
0
W-.

00



-1


80 120 180 240 300 380 420 480 540


TIME AFTER LOW WATER SLACK (min)




Fig. 6(b). Numerical simulation of the layer shown in Fig. 5(a) using data
obtained at only five instances during the measurement period.












SI40







S 20


S10


0
0 0.2 0.4 0.6 0.8 1.0
FREQUENCY (Hz)

Fig. 7(a). Measured surface wave energy spectrum in Lake Okeechobee, Florida.


0.30 j


C1, 0.24 -

EI

U)Z 0.18 Calculated I


0< Measured i
<: 0.12
..CJ

u I i
C < 0.06

0J/ I I)
0 0.2 0.4 0.6 0.8 1.0
FREQUENCY (Hz)


Fig. 7(b). Measured and calculated horizontal mud acceleration spectra
corresponding to the surface condition in Fig. 7(a).










Laboratory Studies on Cohesive Sediment Deposition
and Erosion

A.J. MEHTA1





Contents
1 Introduction .......................................................... 427
2 Laboratory Studies on Deposition and Erosion .............................. 429
3 Deposition ................................................. ... ........... 429
3.1 Rate of Deposition ............................ ......... .. ............... 429
3.2 Sediment Sorting .......................... ............. ............. 431
4 Erosion ................................................................. 435
4.1 Modes of Erosion ................... ...... ................................. 435
4.2 Erosion Due to Current ................................................ 436
4.2.1 Soft Beds ................................................................. 436
4.2.2 Dense Beds .............................................................. 437
4.3 Bed Structure .......................................................... 438
4.4 Shear Strength Estimation .......................... ....... ........... 439
4.5 Erosion Due to Waves .................................... ............... 440
5 Concluding Remarks ........................................................ 443
Appendix ................................................................... 444
References .................................................................... 444


Abstract

Processes of erosion and deposition of fine-grained, cohesive sediment are review-
ed with reference to laboratory results generally applicable to low to moderate
energy estuarial environments. Under steady turbulent flows, the rate of deposi-
tion depends not only on the flow condition and the concentration regime, but
also on the degree of cohesion and the uniformity of the sediment. Weakly
cohesive sediment characteristically exhibits sorting during deposition. Particle
size gradients can thereby result, as for example in river deltas. The rate of erosion
is controlled by the bed shear strength and its variation with depth. Consequently,
under steady flows, soft, partially consolidated beds erode in a different manner
than dense, settled beds. Waves tend to weaken the bed due to oscillatory loading.
Wave-induced erosion can result in the generation of a high density, near-bed fluid
mud layer, which can be easily transported to areas prone to sedimentation.


1 Introduction

Deposition and erosion, coupled with consolidation of the deposit and advective
transport of the eroded material, are the key processes which govern cohesive sedi-


1 Coastal and Oceanographic Engineering Department, University of Florida, 336 Weil Hall, Gaines-
ville, Florida, USA







Table 1. Regime classification for estuarial cohesive sediment transport

Characteristic factors Regime

1 2 3

"Energy" Low Moderate High
Tidal range (m) <1 1-3 >3
Forcing factors Current/waves/wind Current/waves Current
Concentration (mg I) < 103 103 104 > 104


ment movement in estuarial waters. These processes are interlinked in a fairly
complex manner, such that any effort to classify the hydrodynamic and the
sedimentary regimes and the linkage between them, in a rational manner, is at best
a difficult task. Nevertheless, it is instructive to focus attention on estuarial
regime classification, even perhaps in an approximate manner, prior to examining
deposition and erosion in further detail.
Regime classification can be made in several different ways, one of which is
attempted in Table 1. Three regimes, 1, 2 and 3, have been categorized in terms
of four characteristic factors. The first is "energy", which has been used common-
ly in the literature in a rather subjective manner without quantifying its
magnitude, e.g., in the fluid mechanical sense. The categories in this respect are
defined as low, moderate, and high. One may correspondingly associate, in a very
approximate way, tidal ranges of magnitudes less than 1 m, between 1 and 3 m
and greater than 3 m, respectively, with the three regimes. It is noteworthy that
even though current velocity is a better indicator of the influence of tide on the
sedimentary regime, classification by range is preferable merely because it is more
easily and commonly measured than current.
Hydrodynamic forcing is typically due to tidal current, wind-generated waves
and wind-induced current. The smaller the influence of astronomical tide, the
greater is the significance of episodic phenomena including storms and associated
wind and waves. With increasing tidal range, the dominance of tidal current
becomes apparent. With reference to the influence of waves, only shallow- and
intermediate-water depth waves generate bottom velocities and thereby contribute
to resuspension. Finally, wind effect is contingent upon physiographic factors
besides, of course, the wind speed. Water depth is thus a critical parameter in
determining the influences of both waves and wind relative to tidal current.
The sedimentary regime is more difficult to characterize than the hydrodyna-
mic regime. The temporal and spatial variability of suspended sediment mass is
such as to result in measurable concentrations ranging in order from 101 to
10' mg 1-'. For reasons to be cited later, however, it may be appropriate to divide
the concentration into three ranges: less than 103 mg 1-1, between 103 and 104 mg
1-1, and greater than 10 mg 1-1. The concentration profile is oftentimes highly
stratified over depth, with near-bed concentrations that may be as much as two
to three orders greater than those near the water surface. Identification of a
representative concentration becomes difficult; hence, the concentration ranges
given in Table 1 may be associated with the corresponding hydrodynamic factors
in a loose, qualitative manner.








Laboratory Studies on Cohesive Sediment Deposition and Erosion


The above background is an attempt to place the processes of deposition and
erosion in a perspective that enables recognition of the rather wide ranges of
estuarial conditions under which these processes must be understood. Physical
aspects related to the rates of deposition and erosion must consequently be viewed
within the same general framework.


2 Laboratory Studies on Deposition and Erosion

It is important to recognize that the scope of most studies on erosion and deposi-
tion, to date, has been dictated mainly by two constraints: (1) the complexity of
the natural processes, and (2) specific needs related to mathematical modeling for
the prediction of estuarial sedimentation/scour rates. As a consequence of the
first constraint, the majority of investigations have been laboratory oriented,
wherein the interactions between physical and physicochemical conditions can be
usually understood better than in nature. In fact, in nature it is often difficult to
identify distinct phases of deposition from those consisting solely of erosion, as
a consequence of the time dependence of the flow field.
Most early mathematical modeling, usually essential for estuarial cohesive
sediment transport prediction, was based on depth-averaged transport equations.
In present modeling practice this approach is often retained as a result of the
usual limitations associated with scarce prototype data. Consequently, laboratory
studies have typically been concerned with providing deposition and erosion rate
expressions on a depth-averaged basis, with less than adequate emphasis placed,
in some cases, on the evolution of the vertical structure of the suspension as ob-
served in nature. Nevertheless, model results indicate that for many engineering
applications, depth averaging does not always critically limit predictive capability.
In the following discussion, the approach taken is one of describing salient
physical and physicochemical aspects related to deposition and erosion, with the
tacit understanding that since the natural physical phenomena are quite complex,
and further scope for improving upon the present-day knowledge clearly exists.
With some exceptions, the discussion is focused on those low to moderate energy
regimes in which the role of high concentration fluid transport is not critical.


3 Deposition

3.1 Rate of Deposition

The time rate of decrease of sediment mass per unit bed area, m, under steady,
turbulent flows is given by:
dm
=-p WC (1)
dt
where p [0,1] is defined as the probability of deposition, Ws is the settling veloci-
ty and C is the depth-averaged suspended sediment concentration. The product,







A.J. Mehta


p Ws = W, is the apparent settling velocity, and W'C is the flux of settling sedi-
ment. The settling velocity and the probability of deposition are dependent, in
general, on the interparticle collision frequency, and therefore on concentration.
Hence, it is useful to examine deposition in various ranges of concentration in
order to provide simplified descriptions for the time rate of change of concentra-
tion.
Three concentration ranges defined by two characteristic concentrations, C1
and C2(>C1) can be realistically identified. In the range C typically ranges from 102 to 103 mg 1~1 depending upon the type of sediment-
fluid mixture, mutual particle interference is relatively weak, and Ws may be
assumed to be independent of C. Furthermore, the probability of deposition, p,
is reasonably described by:

S= 1- (2)
Tcd
where rb is the time-mean value of the bed shear stress and red is referred to as
the critical shear stress for deposition. For Tb < Tcd, all initially suspended sedi-
ment eventually deposits, and for Tr Tcd there is no deposition, since p = 0
(Krone 1962). Given initial suspension concentration, Co, Eq. (1) can be in-
tegrated under these conditions to yield:

S= -exp (3)
Co Tc h
where h is the flow depth. Equation (3) is a simple exponential decay law implying
suspension dilution by deposition.
In the concentration range C2> C> C, where C2 ranges from -5 x103 to
104 mg 1-1, the concentration is high enough for interparticle collision and asso-
ciated kinetics of particle aggregation to become quite important. The time-con-
centration relationship is described experimentally by:

pk'
log C = -k log t+k" (4)
h
where p is given by Eq. (2) and k' and k" are empirical coefficients whose
magnitudes reflect the influence of aggregation on settling. The critical shear
stress is typically different in the two concentration ranges. In flume studies using
mud from the San Francisco Bay in salt water, Krone (1962) found Tcd = 0.060 N
m-2 in the lower concentration range (< C1, where C, = 300 mg 1-1) and 0.078 N
m-2 in the middle range (Ci to C2, where C2 = 104 mg 1-1). This difference im-
plies the formation of stronger aggregates, in the latter case, under continuing ag-
gregation due to interparticle collision.
Finally, in the high concentration range (> C2), the time-concentration rela-
tionship is found to be similar to Eq. (4), with pk'/h and k" replaced by empirical
coefficients, which particularly reflect the hindered nature of the settling process.
This type of settling is characterized by the formation of a continuous aggregate
network through which the interstitial water must escape upward for settling to
occur.







Laboratory Studies on Cohesive Sediment Deposition and Erosion


The basis for the forms of Eqs. (3) and (4) is found by considering aggregation
kinetics and deposition simultaneously. In the Appendix, a brief phenomenologi-
cal explanation has been provided.
Any physical or chemical factor which influences aggregate size, density or
shear strength affects the settling velocity. Consequently, marine and estuarial
sediments exhibit a wide range of settling velocities, from 10-7 to 10-3 m s~-. At
present, reliable correlations for estimating either Ws or Ted are unavailable. Ws
is particularly sensitive to the rates of flow shearing, so that laboratory-deter-
mined values cannot be easily scaled to prototype. A recommended approach is
to determine Ws in the field using in situ settling tube samplers, and to evaluate
Tcd from laboratory flume tests (Mehta 1986).


3.2 Sediment Sorting

An assumption inherent in Eq. (1) is that the sediment has uniform properties.
Thus, for example, Eq. (3) is characterized by only two sediment-related parame-
ters, namely Ws and rcd. This is an adequate description for highly cohesive
clayey sediments which form strong aggregates of uniform or well-sorted com-
position. On the other hand, when a wide size range occurs, e.g., from coarse silt
to clay, and the sediment is weakly cohesive, the depositional behavior deviates
from that of a uniform sediment, since both Ws and Ted must be represented as
distributions in some manner related either to size or to concentration. Con-
siderations on this type of approach, albeit a simple one, summarized below, shed
light on the experimentally observed time-concentration relationships during
deposition (Mehta and Lott 1987).
Equation (3) may be redefined for the present purpose as:
N N Tb\ W~;
C= IE C = E Coiexp 1 b- t (5)
i=1 i= Tc/ hj
where i is the index for the N classes into which the settling velocity, concentra-
tion, and the critical shear stress for deposition (redefined as Tr) have been divid-
ed, in a manner similar to that for cohesionless sediments. Note that by virtue
of the fact that the term 1 (rb/ci) is not defined for all b > rci for a given class
i, the condition, namely, Ci = Coi for Tb ci, must be invoked for each class
when using Eq. (5).
Before proceeding further with Eq. (5) it should be noted that when Eq. (4)
is combined with Eq. (1), a dependence of Ws on C becomes apparent. It
signifies the role of aggregation; increasing concentration increases the interparti-
cle collision frequency, forming stronger aggregates with effectively larger settling
velocities, when settling is not hindered. A simple power law is adequate in many
cases:
Ws= kC (6)
where k depends on the type of sediment-fluid mixture. Consideration of inter-
particle collision kinetics based on the work of Overbeek (1952) and Krone (1962)
shows that n should be 1.33. From settling column tests in which aggregation








A. J. Mehta


is well-advanced and the rate of continuing aggregation very slow, n is found to
vary from 0.8 to 2. In flumes, under continuing aggregation, a specific value of
n is difficult to identify as a consequence of the time-dependent processes in-
volved, although n = 1.33 appears to be applicable in the middle concentration
range between C1 and C2 (Krone 1962). Nevertheless, as the simplest case con-
sidered here, n = 1 will be selected for an evaluation of Eq. (5). This selection im-
plies that the distribution of the settling velocity, 0 (Ws), is analogous to the as-
sociated distribution, 0 (Coi), of initial concentration. Since the sum of Coi over
N classes is equal to the total initial concentration, Co, Coi is obtained from:

Co = 0(Coi)-Co= 0(w,;)Co (7)
where 0(Wst) is assumed to be bounded by Ws and Ws,, the minimum and the
maximum values, respectively, of Ws. Arguments leading to Eq. (7) imply that,
in associating the settling velocity with concentration within each class, the effect
of aggregation has been accounted for, to some extent. However, in treating the
entire particle population on a class-by-class basis, the physical meaning of Eq.
(6) has essentially been considered in a heuristic sense.
In a manner analogous to Eq. (6), a power-law relationship between the criti-
cal shear stress, tri, and the corresponding W, may be assumed as:

ci = k.W (8)
where k, would be numerically equal to Tcd, the critical shear stress for uniform
sediment, for which m = 0. There is a qualitative analogy between Eq. (8) and the
well-known constitutive relationship between flow velocity and bed shear stress.
Equation (8) hypothesizes that increasing settling velocity is associated with in-
creasing 7Cj. Such an implication is consistent with the nature of the depositional
process under turbulent flow. Only those aggregates which can withstand the high
velocity gradient and associated shear near the bed can ultimately stick to the bed
by cohesion, i.e., deposit. The remainder break up and are re-entrained in the
water column. Stronger aggregates with larger critical shear stresses are therefore
associated with effectively larger settling velocities.
The lowest value of Tci, i.e., Zc, has the same physical meaning as rTd in Eq.
(2) for all Tb I cd, i.e., -Tl is the critical shear stress below which all sediment
eventually deposits. The associated minimum settling velocity is Ws. Likewise,
the corresponding maximum values are zcN and WsN. Given these values, Eq. (8)
may be restated as:
Ssi [ln(rcN/rc)/In(WN/SW,)]
Trci = si\ (9)

Finally, combining Eqs. (5), (7), and (9) yields:

C 1 N
Co Co i= 1
N [In (rr c IT )/Il(W,,I/W,)]
=I (W) exp 1- hb)1 st (10)
i=71 C s.i )h I h


1









Laboratory Studies on Cohesive Sediment Deposition and Erosion


Table 2. Kaolinite deposition test parameters

Run No. Initial Bed shear Min. settling vel., Characteristic Exponent,
cone., Co stress, Tb W's (ms-1) stress, rc, m
(mg1-1) (Nm-2) (Nm-2)

1 1126 0.333 6.66 x 10-5 0.084 0.49
2 1120 0.223 6.66x10-5 0.041 0.62
3 968 0.126 1.00x 10-5 0.500 0.14


0 20 40 60 80 100

W,,[=(W .W,1)x 10 (ms')


1:


i I i I I i I I I I i
1-10



I-



11

- 9



7


Z 1]2 13 14(=M)
, I I I I 1 i i l i I l i


which is subject to the condition, Ci = Co, for Tb > i, for each class i. For a
uniform sediment, this equation reduces to Eq. (3).
Equation (10) may be tested against data on deposition of kaolinite in distilled
water, under turbulent flows. These tests were conducted in an annular rotating
flume described in detail elsewhere (Mehta 1973). The flume consisted of an an-
nular channel filled with the sediment-water mixture, and an annular ring flush
with the water surface. By rotating the channel and the ring in opposite directions
at predetermined speeds, the radial secondary currents were minimized near the
bed, and the bed shear stress was found to be nearly constant across the channel
width. Deposition data from this apparatus are used here mainly to illustrate the
basic mechanisms which lead to sorting. Kaolinite (median, dispersed particle size
1 gm, cation exchange capacity 9 mEq. per 100 g) weakly flocculates in distilled
water. In each test, a suspension of initial concentration Co was at first complete-
ly suspended at a high bed shear stress, rb= 1.5 N m-2, then allowed to deposit
at a lower Zb. Values of Co and rb for three selected tests are given in Table 2. The
flow depth, h, was maintained at 15 cm.
The settling velocity histogram (N= 14) shown in Fig. 1, where Ws =
Wsi- Ws, is based on results from a standard hydrometer test using undispersed


. 20


Fig. 1. Settling velocity histo-
gram representing the distri-
20 bution, O(Wsi), for kaolinite,
based on the data of Yeh
(1979)


Y . i i T T I I I I I I r ?







A. J. Mehta


1.0 1 1 1 I I -. Fig. 2. Time-concentration rela-
o e Data tionship during kaolinite deposi-
Eq.10 tion; comparison between Eq.
n 1 7 (10) and data of Mehta (1973)
Run 1,C=877 mgl'1



uJRn
0.8 /



0 0


w \ / Run 2,Cs=504 mgl

o --
U O 0 0 0
= 0.4
N


0
0.2



Run 3,Cs=0 mgl1
0.0 L I
0 2 4 6 8 10 12 14
TIME, t (hr)


kaolinite by Yeh (1979). It will be assumed that this distribution, q~(Wsi), would
be applicable to the flume conditions. Tests conducted at high Tb by Mehta
(1973) indicated that little sediment could deposit above rb = 1 N m-2, which
may therefore be selected as the value of TcN.
Agreement between Eq. (10) and the data in Fig. 2 seems satisfactory con-
sidering the assumptions involved; a deviation being most noticeable in run 1. In
general, the simple relationship between settling velocity and critical shear stress
given by Eq. (8) seems justified. Furthermore, this agreement essentially
highlights the significance of the settling velocity and the bed shear stress as the
key deposition-controlling parameters. Magnitudes of the minimum settling
velocity, Wst, obtained by calibration in Table 2 are comparable to those obtain-
ed from deposition tests in a 100-m-long flume with the same type of sediment-
water mixture, using a mass balance approach (Dixit et al. 1982). For Tcl, Mehta
(1973) reported a mean value of 0.18 N m-2 for the entire test series from which
the runs in Table 2 have been selected. This value is within the range of calibrated
values of re1 in Table 2.
Exponent m in Eq. (8) has been evaluated in Table 2. It is observed that for
runs 1 and 2, in which a portion of the initially suspended sediment remained
suspended indefinitely at steady state (represented by concentration, Cs), m
values were close to each other. In run 3, in which all the sediment was deposited,
m( = 0.14) was much lower. At low stresses, settling aggregates are not broken up








Laboratory Studies on Cohesive Sediment Deposition and Erosion 435

easily and kaolinite behavior approaches that of a uniform or well-sorted sedi-
ment (m = 0).
The occurrence of steady state suspension concentration, Cs, in runs 1 and 2
is inherently indicative of sediment segregation or sorting. At a given bed shear
stress, sediment comprising those classes corresponding to ri deposit. Sediment properties at steady state will therefore be different from those
of the total sediment. Partheniades et al. (1966) conducted deposition tests using
a similar sediment-water mixture in a smaller annular flume. Given Co =
14862 mg 1-', h = 20cm andb = 0.2 N m-2, C, = 5710 mg 1-1 resulted. The me-
dian dispersed particle size of this steady state suspension was -0.1 gm com-
pared with 1 4m of the material initially suspended. Although this test was con-
ducted at a fairly high concentration, a sorting trend is clearly implied, since
larger particles had preferentially settled out.
The main purpose in presenting the aforementioned analysis is to emphasize
that sorting is an inherent feature of fine-grained sediment deposition, particular-
ly for such weakly cohesive materials as kaolinite. An analogy can be invoked be-
tween sorting of this nature and longitudinal particle size gradients which occur
in prototype depositional environments including river deltas. There, under
decreasing velocities resulting from flow area expansion, particle size in the
deposit oftentimes decreases with distance. Dixit et al. (1982) also demonstrated
the occurrence of size gradients in the longitudinal direction in the 100-m-long
flume cited previously.
It is evident that fine-sediment sorting is a complex phenomenon which is
strongly contingent upon the type of sediment as well as the flow field. In some
cases, cohesive aggregates composed of strongly bonded clay particles deposit
before weak, silty particles of lower settling velocities. In such a case, a gradient
of increasing (primary) particle size with distance can in fact result (Dixit et al.
1982).


4 Erosion

4.1 Modes of Erosion

The terms erosion and resuspension are often used synonymously when dealing
with erosion of estuarial beds. Resistance to erosion is contingent upon a number
of factors including sediment composition, pore and eroding fluid compositions,
and the degree of consolidation of the deposit. The deposit itself may be in the
form of a static, high density suspension (without an effective stress) or a bed
(with a measurable effective stress). The bed may be soft, partially consolidated,
with a high water content (> 100%), or it may be a more dense, settled bed of
lower water content.
The mode of erosion varies both with the magnitude of the bed shear stress
and the structure of the deposit. Three modes have been identified: (1) aggregate-
by-aggregate, surface erosion of a bed, (2) mass erosion of a bed, and (3) re-en-
trainment of a high density suspension.







A.J. Mehta


The hydrodynamic regime can be conveniently divided into that determined
by steady or quasi-steady (e.g., tidal) current and that related to oscillatory flows,
particularly those resulting from wind-generated waves. These two regimes will be
discussed separately.


4.2 Erosion Due to Current

The time rate of increase of suspended sediment mass per unit bed area, m, is de-
scribed, in a functional form, by:
dm
d =f(tb -=Ts V2 I n) (11)
dt
where rb-rs is the bed shear stress in excess of the bed shear strength with
respect to erosion, Tb, and v,... vn are resistance defining parameters. Laborato-
ry determined expressions of the form of Eq. (11) have been based on surface ero-
sion studies on soft beds with nonuniform properties, and on dense, uniform
beds.


4.2.1 Soft Beds

These beds, which usually are composed of freshly deposited muds undergoing
consolidation, exhibit nonuniform property variation with depth. Typically, the
density and the shear strength, Tr, increase with depth, z, in the top few cen-
timeters. The erosion rate, e(= dm/dt = h dC/dt) is given by (Parchure and
Mehta 1985):

ef

where ef is defined as the floc erosion rate and a is a rate coefficient. Illustrative
values are given in Table 3. It is evident that ey and a are dependent upon the
type of sediment-fluid mixture.
A characteristic feature of the erosion behavior represented by Eq. (12) is that
z-(z) typically increases with z. At a given rb, as bed scour proceeds, the rate of



Table 3. Erosion rate parameters a and ef

Sediment Investigator(s) a efx 105
(mN-2) (gcm- min- 1)
Bay mud Partheniades (1962) 8.3 0.04
Lake mud Lee (1979) 8.3 0.42
Kaolinite (tap water) Parchure and Mehta (1985) 18.4 0.50
Kaolinite (salt water) Parchure and Mehta (1985) 17.2 1.40
Estuarial mud Villaret and Paulic (1986) 7.9 5.30








Laboratory Studies on Cohesive Sediment Deposition and Erosion


erosion decreases because of corresponding decrease in the excess shear stress,
rb- r,. When -b = r,, a small amount of erosion, represented by Ef, continues to
occur because of the probabilistic nature of the bed shear stress and the spatial
variability in the shear strength (Parchure and Mehta 1985).



4.2.2 Dense Beds

Consolidated cohesive beds, in which the bed properties are uniform over depth,
i.e., s, is independent of z, copmprise this category. In Eq. (12), the erosion rate
consequently becomes constant at a given tb. A first-order approximation of this
equation can be interpreted as:

e Ib s
= --r, (13)
e.M rs

where em is a rate constant. The magnitudes of eM and Ts can vary widely
depending upon the properties of the sediment-fluid mixture and those of the
bed. Illustrative values are given in Table 4. In the tests of Ariathurai and
Arulanandan (1978) using Yolo loam, the eroding fluid temperature was varied
from 9.5 C to 42 C. This increase resulted in an order of magnitude increase in
the rate of erosion, as reflected by corresponding changes in eM and "s. The in-
crease in e is attributed to weakening of the interparticle electrochemical bonds
with increasing temperature, as suggested by the study of Kelly and Gularte
(1981).
Equation (13), although derived from surface erosion studies, has also been
used for simulating mass erosion in an approximate way. In mass erosion, the bed
fails at some level beneath the surface where the bulk shear strength is unable to
withstand the induced stress. Erosion occurs sometimes by dislodgement of large
pieces of the soil. The rate coefficient, sM, is typically much larger than that for
surface erosion under comparable conditions, and must be evaluated either ex-
perimentally or by calibration against available data for specific eroding condi-
tions. In reality, mass erosion is likely to be governed not only by the bed shear
stress, but also by the time rate of change of bed shear stress (Cervantes 1987).


Table 4. Erosion rate constant, eM, shear strength, r,

Sediment Investigators eM S
(g cm-2min-) (Nm-2)

Yolo Loam (9.5 C) Ariathurai and Arulanandan (1978) 8.3 x 10-3 2.70
Yola Loam (18 C) Ariathurai and Arulanandan (1978) 9.9x10-3 2.40
Yolo Loam (23 C) Ariathurai and Arulanandan (1978) 1.5 x 10-2 2.20
Yolo Loam (42 C) Ariathurai and Arulanandan (1978) 2.5 x 10-2 1.20
Estuarial mud Villaret and Paulic (1986) 9.7 x 10-5 0.20
Bay mud Villaret and Paulic (1986) 2.8 x 10-4 0.12






A.J. Mehta


4.3 Bed Structure

The description of erosion given above as well as analysis presented elsewhere
(Parchure and Mehta 1985) implies a three-zoned description of the zr(z) profile
as depicted in a somewhat idealized manner in Fig. 3. Zone 1 of thickness z,
which may be at most a few centimeters, can be considered to be bounded by
shear strength ro at z = 0 and rs, at z = zc. Zone 2 of thickness zd terminates at
depth Zc+Zd where rs = zs, below which zone 3 of constant shear strength, Tsm,
occurs. An important difference between zones 1 and 2 is that the gradient,
d-s/dz, is relatively much greater in zone 1 compared with 2. In zone 3,
dTs/dz = 0.
Equation (12) describes the erosion behavior within zones 1 and 2. Equation
(13) is applicable to zone 3. An example of Tr(z) profiles is shown in Fig. 4,
which shows results from two tests, both with beds of kaolinite in tap water, but
with consolidation periods of 1 and 8 days. Details of the experimental procedure
for obtaining such profiles have been outlined elsewhere (Parchure and Mehta
1985). In essence the bed, formed initially by deposition, was eroded by increasing
the bed shear stress, Tb, in steps of constant duration. In each step the suspen-
sion concentration first increased rapidly and eventually attained a near-steady
value. At this stage, therefore Tb T, = 0 or rb = s, at a known depth of scour,
z. In this manner, Tr was evaluated at different z and the Tr(z) profile con-
structed.
Figure 4 demonstrates the complexities of the bed formation and consolida-
tion processes which lead to the development of the observed shapes of the shear
strength profiles. For both beds, Tsm was 0.59 Nm-. Values of thicknesses z,
and Zd were 0.5 and 1.5 cm, respectively, for the 1-day bed and 0.25 and 0.50 cm,
respectively, for the 8-days bed. A possible explanation for the occurrence of a



BED SHEAR BED SHEAR STRENGTH,: (Nm')
so STRENGTH,s 0.1 0.2 0.3 0.4 0.5 0.6




Z, ZONE 2
Zd ZONE2
8 DAYS
1 DAY\
'---'sm 1.0- \
ZONE 3 \


1.5-
Fig. 3. Three-zoned schematic
description of bed shear strength Fig. 4
profile for cohesive beds (After
Parchure and Mehta 1985) 2.0
Fig. 4. Bed shear strength profiles after 1 day and 8 days of consolidation (After Parchure and Mehta
1985)








Laboratory Studies on Cohesive Sediment Deposition and Erosion


steplike structure in the 1-day bed could be that there was a change in the ag-
gregate structure due to crushing by dewatering and overburden at 1.5 cm below
the surface, thus resulting in a measurable increase in the shear strength below this
level (Krone 1963). At 8 days, the entire bed below 0.5 cm was crushed to yield
a uniform shear strength.


4.4 Shear Strength Estimation

As evident from the aforestated description, the type of sediment-fluid mixture,
the manner in which the bed is formed, e.g., by deposition or by remolding, and
the degree of consolidation govern the nature of the r,(z) profile. It is also
noteworthy that Ts defined here has a different physical meaning than the bulk
shear strength in the geotechnical sense, which is readily measured by standard
procedures. The quantity, r,, typically has a much smaller value than that ob-
tained, for instance, by the vane shear test.
After about 2 days following bed formation during which gelling is complete,
the influence of consolidation becomes the dominant factor (compared with the
mode of formation) controlling Ts. Since the principal quantity characterizing
consolidation is the bed density, an approximate but useful relationship between
z, and density has been established (Migniot 1968; Owen 1970; Thorn and Par-
sons 1980). Villaret and Paulic (1986) obtained for mud from the San Francisco
Bay in salt water:

Ts(= C(-B ) (14)
where Qg is the bed bulk (wet) density and = 1.0, given oB in g cm-3 and ,s in
Nm-2
A practical significance of Eq. (14) may be illustrated by further considering
test results using the San Francisco Bay mud. The predominant clay mineral con-
stituent in this mud was montmorillonite, followed by illite, kaolinite, halloysite,
and chlorite. The median dispersed particle size was 13 pm, and the cation ex-
change capacity was 61 mEq. per 100 g. Flume tests were conducted in salt water,
at preselected bed bulk densities ranging from about 1.2 to 1.6 g cm-3. The ero-
sion rates were approximated by Eq. (13). The rate coefficient, eS, was found to
be related empirically to T, according to:
EM = 6 exp (- T) (15)
with 6 = 1.06x 10-3 and = 2.33, given e4 in g cm-2 min- and r, in Nm-2.
The bed shear stress, B = yn u2/h"3, where y = unit weight of salt water,
n = Manning's resistance coefficient, and u = current velocity. This relationship,
combined with Eqs. (13), (14), and (15) resulted in the plot shown in Fig. 5, using
n = 0.020 and h = 10 m as typical selected values. The significance of this type of
a plot is evident; the rate of erosion is correlated with current velocity and bed
density, both of which can be readily measured. This type of a relationship, using
appropriate values of h and n, is generally applicable to the entire San Francisco
Bay in which the bottom material composition is spatially fairly uniform. An ex-
ample of application would be the estimation of the bottom retention times,







A. J. Mehta


SFig. 5. Rate of erosion variation with cur-
rent speed at three bed bulk densities for
pB=1.2gcm San Francisco Bay mud (After Villaret
and Paulic 1986)

1 x102 -





E


0


S'-3
5 .3




I 1.6 gcm



1 x 10 -


0 0.4 0.8 1.2
CURRENT SPEED, u(ms' )


based on the rate of erosion, for dredged material deposited at a given location
(h, u and n known) at different discharge slurry densities, QB.


4.5 Erosion Due to Waves

A characteristic feature of bed response to oscillatory flow is a weakening or
degradation of the mechanical as well as the erosional strength. Recovery follows
cessation of wave loading. This phenomenon is a consequence of the transmission
of both normal and shear stresses into the mud layer under dynamic loading. A
buildup of excess pore pressure can rupture the interparticle bonds resulting in a
breakup of the initial aggregate structure. Shear deformation also leads to the
same result.
The rate of erosion is specified by an expression of the same form as Eq. (13):


8 Tb- R
eW rR


(16)


where rb is the maximum applied shear stress at the bed during a wave cycle.
Although like r,, TR represents erosion resistance, the two quantities have a
slightly different physical meaning, since rR can change drastically with time and
depth during erosion.


i








Laboratory Studies on Cohesive Sediment Deposition and Erosion


Waves cause the bed to oscillate, with the result that the applied shear stress
is different from that over a rigid bed. Maa (1986) therefore developed a special
procedure for estimating Tb. First, the bed was shown to possess viscoelastic
properties. The equations of motion were then solved for the coupled water-mud
system, with the mud characterized by depth-varying density, viscosity, and shear
modulus of elasticity. The solution resulted in a description of the kinematic and
dynamic properties of the system under progressive, nonbreaking wave loading.
The kinematic description (velocities and diffusivity) was then used to evaluate
the bed shear stress at the mud-water interface. It was found that, in general, the
shear stresses predicted by this procedure were up to 30%7 larger than those which
would occur under the same wave conditions over a rigid bed. This difference is
a consequence of the out of phase motion between water and mud in the case of
an oscillating bed.
Using beds of kaolinite as well as an estuarial mud from Cedar Key, Maa
(1986) found ew to range from 8 x10-4 to 4x 10-2g c-2 min-1. This mud was
composed of montmorillonite, illite, kaolinite, and a small quantity of quartz.
The median dispersed size was 2 tm and the cation exchange capacity was
65 mEq. per 100 g. The period of bed consolidation was varied from 2 to 14 days.
The bed-weakening role of waves in relation to steady flow can be discerned in
the difference in the magnitudes of the rate constants, ew and ef, under com-
parable conditions. Thus, for example, for a particular bed of Cedar Key mud
(estuarial mud in Table 4), Villaret and Paulic (1986) obtained Ey = 9.7x 10- g
cm "min-1 under steady flow. Maa (1986) determined ew= 1.2x10-3g
cm-2 min- under waves, which implies an order of magnitude higher rate of
erosion under waves.
The effect of waves on bed resistance to erosion is dramatized in Fig. 6, in
which data for kaolinite beds of different consolidation periods are shown. Bed
shear strengths in the upper curve were obtained by Parchure and Mehta (1985)
under steady current. Representative mean values of bed shear resistance under
waves in the lower curve were obtained by Maa (1986). As an example, for a bed
of 2.5-day consolidation, bed resistance is observed to have been reduced from
about 0.25 N m-2 to 0.03 N m-2 due to wave action.

0.4
o No Waves
'E Waves
Z

"0
S0.2 Wave
u / Effect

Sr --

00
0 < ^-----I-------1-------
0 5 10 15
PERIOD OF CONSOLIDATION (days)
Fig. 6. Influence of waves on shear resistance to erosion







A.J. Mehta


S I lll I I I 1 111 1 1 |I- Ill I- Fig. 7. Suspended sediment con-
34 centration profiles during erosion
Sby waves. Elevations are measur-
537 min ed above rigid flume bottom sup-
S30- porting the mud (after Mehta and
o Maa 1986)
0
m 28 -Upper Layer(<<104mgl1)"


2 42
t 24 B .': ""'.'"":' Bed(i 104mgl"1)
0 n
- \ CONCENTRATION
< 300 min 9


-< Interface 1
W at 300 mi

L Interface at 537 min

10 104 105
SEDIMENT CONCENTRATION (mgl')

Waves essentially provide a mechanism for erosion and entrainment without
a significant, net horizontal transport. An important consequence is the genera-
tion of a high density suspension in the near-bed region. Figure 7 shows two
typical suspension concentration profiles obtained with Cedar Key mud in a labo-
ratory flume (Mehta and Maa 1986). They were obtained 300 and 537 min after
erosion initiation. Also indicated are the corresponding mud-water interfacial
elevations. The figure inset is a classification of the vertical structure of concen-
tration from suspension in the upper portion of the water column (, 104 mg 1-1)
down to the bed (>104 mg 1-1). A fluid mud layer occurs in the range of concen-
tration from 104 to 105 mg 1-1. The concentration profiles indicate that the ma-
jority of suspended sediment mass occurred in a relatively thin, 1-2 cm high
near-bed layer, with comparatively very low amounts near the water surface. The
high density layer influences near-bed turbulence and, consequently, the bed
shear stress. On account of this effect and the influence of waves on bed shear
resistance, the ratio (Tb R )/TR in Eq. (16) tends to exhibit a degrees of variabili-
ty which is not easily quantified. The approximate nature of Eq. (16) therefore
becomes evident.
The generation and accumulation of fluid mud during initial stages of wave
loading is a consequence of a high rate of bed erosion and a much lower rate of
upward entrainment of the resultant near-bed high density suspension. The rate
of entrainment is governed by the densimetric properties of the stratified suspen-
sion and on mass diffusion characteristics in the water column. The suspension
concentration eventually reaches a saturation limit. From Fig. 7 it is evident that
this limit had been attained by 300 min with a concentration of -105 mg 1-,
since its magnitude did not increase further. The rate of upward entrainment is
restricted by the low vertical wave diffusion coefficient as well as low velocity gra-
dients in the upper portion of the water column. Mehta and Maa (1986) found






Laboratory Studies on Cohesive Sediment Deposition and Erosion


the ratio, e,/e, where e, is the rate of entrainment of fluid mud, and e is bed ero-
sion rate obtained from Eq. (16), to vary typically from 0 to about 1; the latter
value implying a steady state condition.



5 Concluding Remarks

It is important to recognize that the rate of deposition under steady turbulent
flows is not only contingent upon the concentration regime, but also on the size
or settling velocity distribution of the fine-grained material. Highly cohesive clays
form uniform aggregates; however, weakly cohesive materials, composed of a
range of sizes from coarse silt to clay, do not behave in a composite manner. Sort-
ing by size is a characteristic feature of the depositional behavior of poorly sorted
sediment.
While steady current erodes and advects the sediment, waves in themselves
principally weaken and fluidize the bed. As a consequence of the restrictive ability
of waves to entrain sediment in the upper portion of the water column, a high
density fluid mud layer is generated just above the bed. Current in the presence
of waves advects the fluid mud. The advected fluid mud is the principal source
of sediment in areas such as docks and harbors prone to sedimentation, since the
upper portion of the water column may carry a relatively small sediment load.
The transport behavior discussed so far has focused on physical aspects
without reference to biological influences. It is well known that biological
variability can markedly affect estuarial cohesive sediment transport, particularly
in low to moderate energy environments through, for example, the influences that
micro- and macrofauna have on erodibility. A relevant review has been provided
by Montague (1986). Paulic et al. (1986) investigated the role of microbial films
on bed surfaces to erosion. Under appropriate intensity of sunlight, the bed shear
strength of a very thin (few mm) layer of surficial bed material easily doubled over
that of the abiotic substrate.
Future research related to transport formulations noted can be considered in
two categories. One pertains to abiotic cohesive sediments. An extensive review
of the manner in which formulations of the type presented here are used, in
mathematical modeling, has been provided by Hayter (1983). This review also in-
herently highlights several limitations of the results. Among other issues, it seems
essential to better understand the relationship between the settling velocity and
aggregation, particularly as influenced by the turbulent shearing rates. Also, when
dealing with flume studies, better quantification and measurement of the bed
shear stress is highly desirable, including the effects of high concentrations on the
near-bed turbulence intensities. Finally, erosion rates under the combined action
of waves and currents need further experimental considerations.
There is insufficient information at present on biological effects on cohesive
sediment transport. Although some useful work has been carried out in this area,
quantifiable data, which can ultimately be used in evaluating biological response
to transport via mathematical modeling, is hardly available. This is the second
category of recommended future research area.







A.J. Mehta


Appendix

A phenomenological explanation of the observed depositional behavior can be
provided by briefly considering aggregation kinetics (Krone 1962). The rate of
deposition is given by:
dC pW,
-= -mr --, (A.1)
dt h
where m is the instantaneous mean mass of the aggregate and q is the number
of particles per unit volume. Given initial values, mo and r/o, under continuing
aggregation and depostion:

m = mO ) (A.2)

Furthermore,

1 1=7o (A.3)
1+(t/tc)
where tc is a characteristic coagulation time constant (Overbeek 1952). Combin-
ing Eqs. (A.1), (A.2), and (A.3) yields:
dC pW, ( ) C
P \, (A.4)
dt h \ 7 1- +(t/tc)
where it is noted that C = mr. During deposition under turbulent flows, the ratio
fro/fj, the average number of particles per depositing aggregate, tends to be con-
stant because of the limitation of aggregate size caused by shear (Krone 1962).
Consequently, integration of Eq. (A.4) leads to
C pWs lo t
In-=-- P In 1 (12)
Co h tc
Two cases are of special interest: t> tc, i.e., a very slow rate of aggregation and
t tc, i.e., a rapid rate of aggregation. In the first case, In (1 + t/tc)= t/t and the
form of Eq. (3) results. In the second, In (1 + t/tc) =in (t/tc) and the form of Eq.
(4) is obtained.

Acknowledgement. Support from the US Army Engineer Waterways Experiment Station, Vicksburg,
Mississippi, through the Assignment Agreement of the Intergovernmental Personnel Act, is sincerely
acknowledged.


References

Ariathurai R, Arulanandan K (1978) Erosion rates of cohesive soils. J Hydraul Dis ASCE
104(HY2):279-283
Cervantes EB (1987) A laboratory study of fine sediment resuspension by waves. Thesis, University
of Florida, Gainesville










Laboratory Studies on Cohesive Sediment Deposition and Erosion


Dixit JG, Mehta AJ, Partheniades E (1982) Redepositional properties of cohesive sediments deposited
in a long flume. Rep UFL/COEL-82/002 Coastal Oceanogr Eng Dept Univ Florida, Gainesville
Hayter EJ (1983) Prediction of cohesive sediment transport in estuarial waters. Dissertation, Universi-
ty of Florida, Gainesville
Kelly WE, Gularte RC (1981) Erosion resistance of cohesive soils. J Hydraul Dis ASCE
107(HY10):1211-1224
Krone RB (1962) Flume studies of the transport of sediment in estuarial processes. Final Rep Hydraul
Eng Lab Sanit Eng Res Lab, University of California, Berkeley
Krone RP (1963) A study of theological properties of estuarial sediments. Tech Bull 7 Committee on
Tidal Hydraul, US Army Eng Waterways Exp Station, Vicksburg
Lee DY (1979) Resuspension and deposition of Lake Erie sediments. Thesis, Case Western Reserve
University, Cleveland
Maa PY (1986) Erosion of soft muds by waves. Dissertation, University of Florida, Gainesville
Mehta AJ (1973) Depositional behavior of cohesive sediments. Dissertation, University of Florida,
Gainesville
Mehta AJ (1986) Characterization of cohesive sediment properties and transport processes in
estuaries. In: Mehta AJ (ed) Estuarine cohesive sediment dynamics. Springer, Berlin Heidelberg
New York, pp 290-325
Mehta AJ, Lott JW (1987) Fine sediment sorting during deposition. Proc Coastal Sediments '87
ASCE, Vol 1, New Orleans, pp 348-362
Mehta AJ, Maa PY (1986) Waves over mud: modeling erosion. Proc 3rd Int Symp River Sediment,
University of Mississippi, Jackson, 31 March-4 April 1986, pp 588-601
Migniot C (1968) A study of the physical properties of different very fine sediments and their behavior
under hydrodynamic action. La Houille Blanche (In French, with English abstract) 7:591-620
Montague CL (1986) Influence of biota on erodibility of sediments. In: Mehta AJ (ed) Estuarine
cohesive sediment dynamics. Springer, Berlin Heidelberg New York, pp 251-269
Overbeek JThG (1952) Kinetics of flocculation. In: Kruyt HR (ed) Colloid Science, Vol. I. Elsevier,
Amsterdam, pp 278-301
Owen MV (1970) A detailed study of the settling velocities of an estuarine mud. Rep INT 78 Hydraul
Res Station, Wallingford, United Kingdom
Parchure TM, Mehta AJ (1985) Erosion of soft cohesive sediment deposits. J Hydraul Eng ASCE
111(10):1308-1326
Partheniades E (1962) A study of erosion and deposition of cohesive soils in salt water. Dissertation,
University of California, Berkeley
Partheniades E, Kennedy JF, Etter RJ, Hoyer RP (1966) Investigations of the depositional behavior
of fine cohesive sediments in an annular rotating channel. Rep 96 Ralph M. Parsons Hydrodyn Lab,
Massachusetts Institute of Technology, Cambridge
Paulic M, Montague CL, Mehta AJ (1986) Influence of light on sediment erodibility. Proc 3rd Int
Symp River Sedimentation, University of Mississippi, Jackson, 31 March-4 April 1986, pp
1758-1764
Thorn MFC, Parsons JG (1980) Erosion of cohesive sediments in estuaries: an engineering guide. Proc
3rd Int Symp Dredging Tech, Paper Fl, Br Hydraul Res Assoc-Fluid Engineering, Bordeaux, pp
349-358
Villaret C, Paulic M (1986) Experiments on the erosion of deposited and placed cohesive sediments
in an annular flume and a rocking flume. Rep UFL/COEL-86/007, Coastal and Oceanographic
Eng Dept, University of Florida, Gainesville
Yeh HY (1979) Resuspension properties of flow deposited cohesive sediment beds. Thesis, University
of Florida, Gainesville








STRATEGY FOR FINE SEDIMENT REGIME INVESTIGATION:
LAKE OKEECHOBEE, FLORIDA

By

Ashish J. Mehta, Professor
Coastal and Oceanographic Engineering Department
University of Florida, Gainesville, Florida
U.S.A.

ABSTRACT

Results of an investigation of the fine sediment bottom regime and
wave resuspension potential are summarized for Lake Okeechobee, a
large shallow lake in the south-central part of Florida. Over an
indurated calcitic bottom compris ng the Caloosahatchee-Fort Thompson
Formation, about a third (528 km ) of the lake area is covered with
dark mud of which about 40 % by weight is organic matter of peaty
origin. The primary source of the allothigenous mud is the Kissimmee
River due north. The maximum thickness of the mud layer is on the
order of 80 cm, with a total volume of about 193 x 10 m The areal
extent of the mud zone over which wind wave-induced resuspension
occurs is believed to be strongly influenced by the mean water level
in the lake. Under typical storm wind waves a thin (-10 cm) layer of
fluid mud is generated quite rapidly with sediment concentrations on
the order of 20-40 g/l; the "quickness" of the mud being largely due
to the structural characteristics imparted by the fibrous organic
component as well as the occurrence and release of gaseous (possibly
methane) pores in the mud fabric. Concentrations at the water surface
during storm are believed to be very much lower, on the order of 0.1
g/l. In the shallow margins of the mud zone, the 10-20 cm thick top
layer of mud oscillates even under mild wave action caused by
moderate breeze, thus presumably contributing to the mechanics of
nutrient exchange between the bottom and the water column.


1. INTRODUCTION

In order to elucidate the nature of water quality problem due to
phosphorous controlled eutrophication in Lake Okeechobee, Florida,
an investigation of Jhe fine sediment regime was carried out as a
component of a major study on the phosphorus dynamics of this lake.
Lake Okeechobee (Fig. 1) is roughly circular, 48 km wide with a
maximum depth on the order of 4.5 m, in the south-central part of
Florida. Transport in the lake is largely episodic, being governed
by wind-induced wave action. Given the need to examine the role of
sediment dynamics in governing internal loading with respect to
phosphorus as an algal nutrient, the specific study objectives were:
1) to map the fine sediment regime of the lake bottom, and 2) to
investigate the resuspension potential of mud. Thus the investigative
strategy called for developing an understanding of the areal extent
of the mud zone, depth-variation in mud properties, and mud response
to wave action. In general, waves can influence bottom mud in two
ways; there can be a horizontal (back and forth) motion of mud
leading to its fluidization and subsequent retention of the fluidized
state, and there can be particulate erosion of the mud bed leading
to accumulation of suspended matter in the water column especially
under storm waves, and subsequent settling of the eroded material
during calm weather. In turn these processes to a significant extent
govern the dynamics of phosphorus exchange between the mud and water








phases (Somlyody et al., 1983). Important findings related to mud
properties and dynamics are summarized in this paper. Details are
found elsewhere (Kirby et al., 1989; Hwang and Mehta, 1989; Mehta and
Jiang, 1990).


2. PHYSICAL SETTING AND SEDIMENTARY PROPERTIES

Lake Okeechobee is the largest lake entirely within the borders of
the United States. The overall basin configuration has not changed
since the early Pleistocene although it has been a site of subsidence
since at least the early Tertiary, and a thick sequence of Miocene
clay in its axis has resulted in slow differential compaction to
perpetuate the basin configuration. The sequence of Tertiary/
Pleistocene deposits (Fig. 2) is topped by thin calcareous rock
strata, probably forming the Caloosahatchee-Fort Thompson Formation.
This formation constitutes the basement of the lake, which has three
or more basins separated by "reefs" or ridges forming its floor
(Brooks, 1984).

A large part of the central basin of the lake is overlain by a thin
layer of dark, organic-rich (about 40 % by weight) mud which is
believed to be a significant storage for phosphorus. To examine the
nature of the mud bottom, high resolution side-scan and shallow
penetration seismic profiling were carried out, and complemented by
shallow vibrocore sampling. The resulting mud thickness contour map
of Fig. 3 shows mud thicknesses to be at the most 80 cm, generally
occupying the deeper pat, of the lake. The total mud volume is
estimated to be 193 x 10 m The primary source of mud is believed
to be the Kissimmee River, and the deposit has been accumulating for
over at least 6,300 yr BP. Overlying the bedrock, around the southern
and the northeastern periphery of the lake, is a thick peat bed
dating from 5,490 yr to 2,670 yr BP. Extending over much of the
northern part of the lake and overlying the peat in places is a thin
layer of quartz sand of recent, fluviatile origin (Kirby et al.,
1989).

Material less than 74 micron in size accounts for between 75 and 90%
(by weight) of mud, the remainder being mainly quartz sand and some
shell debris of ancient marine origin. This marine connection is also
manifested in the seismic sub-bottom profiles, e.g. Fig. 4, which is
a short, interpreted section along a geophysical profile line running
north -to south and passing through the center of the lake. A
noteworthy feature is the paleochannel probably incised by tidal
flows, and subsequently infilled by allothigenous sediment. Note also
the presence of a uniform mud layer. The predominant clay mineral in
mud is kaolinite, with smaller amounts of sepiolite and smectite. The
large organic fraction appears to be of peaty origin, providing a
fibrous component to the mud, which easily fluidizes under wave
action. Furthermore as a result of the3 organic matter, the
particulate density of the mud is 2.14 g/cm Gas, believed to be
methane, was ubiquitous in collected mud samples. Thus gas bubbles
always appeared on the water surface during the coring operation in
the mud area, and as "pock-marks" created by gas seeps on side-scan
sonographs. In x-radiographs they appeared as dark cavities (Kirby
et al., 1989).

A typical variation of mud density with depth is shown in Fig. 5. As
observed the top -10 cm of the mud layer is comparatively low in
density, followed by a rapid increase in density leading to
comparatively uniform density mud below. The peculiar low density








structure at the top is indicative of the occurrence of organic-rich
mud of comparatively uniform, fluid-like consistency. Under non-
eroding conditions, the thickness of this fluid mud layer can be
characterized by two levels, the upper level of lower density being
defined by the concentration at which the settling sediment flux
begins to become hindered by the presence of too much sediment in
suspension. In .Fig. 6, the settling flux, F is plotted against
suspension concentration, C, of the lake mud based on experiments in
a laboratory column. Hindered settling is observed to occur at
concentrations in excess of 4.4 g/l corresponding to the observed
peak value of F = F This concentration value, C is therefore
used to define the upper level of fluid mud in Fig. 5, in terms of
the corresponding bulk density, p .

Theoretically, the lower level of fluid mud is defined by the
elevation below which the mud is at least partially particle-
supported, i.e. there is a measurable effective stress (Mehta, 1989).
However, due to the fact that no in situ pore pressure measurements
could be made in the lake, an operational definition was used to
identify the level separating fluid mud from the cohesive bed below
in terms of the vane shear strength. The plot of Fig. 7 between the
vane shear strength, tr, and the mud bulk density, p, was developed
using measurements made on vibrocore samples collected from the lake.
Despite the obviously large scatter in the data, a plausible mean
relationship between T and p is apparent. For the present purposes,
the mud is considered to be in a fluid state for densities less than
pg = 1.065 g/cm when T is zero. This density value corresponds to
a concentration, CZ, of 122 g/l, which defines the lower level of
fluid mud in Fig. 5. There is thus an 11 cm thick fluid mud layer
according to the profile of Fig. 5. The operational definition of the
fluid mud layer in a general sense is given in Fig. 8, where zf is
the thickness of the fluid mud layer.

Since bottom coring was carried out under fair weather conditions,
the presence of fluid mud implies that the mud is fluidized
relatively easily, i.e. it is "quick", even by relatively gentle wave
action in the lake. The occurrence fluid-like mud on the order of 10
cm thickness was confirmed by its presence in the top portions of the
collected vibrocore samples. Mud dynamics under wave action noted
below also provided corroborative evidence.

3. RESUSPENSION BY WAVES

Modeling mud resuspension by waves requires knowledge of the settling
behavior of the sediment as characterized by the settling velocity-
suspension concentration relationship (Fig. 6), and the relationship
between erosion rate specifying parameters and the bed density
(Mehta, 1988). The erosion flux at the bed, Fb = -[(b s)'sl'
where t is the applied wave stress amplitude, T is the bed shear
strength and the erosion rate coefficient, EM, is equal to the value
of F when T = 0.5t. The variations of t and E with bed bulk
density for the Okeechobee mud derived from laboratory flume
experiments are shown in Fig. 9. With respect to the bed shear
strength (Fig. 9a), three domains can be specified: no erosion;
surface erosion, i.e. particulate erosion at the bed surface; and
mass erosion, in which the bed (of a given uniform density) fails
entirely. Values of the corresponding erosion rate coefficient for
surface and mass erosion are given in Fig. 9b. The occurrence of mass
erosion of this particular sediment suggests that the sediment
density and strength are quite uniform over the layer that erodes.








This observation is corroborated by the density profile of Fig. 5,,
particularly with respect to the top -10 cm thick layer.

Using the aforementioned relationships for settling and erosion, and
employing a simple vertical sediment mass transport numerical model
(Hwang and Mehta, 1989), the evolution of the vertical concentration
profile was simulated under selected storm wave conditions. Profiles
such as the one in Fig. 5 were used to represent bed density
variation with depth. For a given wave period and height, the bottom
stress amplitude was calculated in the model via application of the
linear wave theory. Manning's n, characterizing bottom resistance,
was taken to be 0.011. In Fig. 10a the manner in which the suspension
profile would evolve over an 11 hr period starting with a clear water
column and no fluid mud column is exemplified for a typical 4 s storm
wave of 0.9 m height in a 4.6 m deep water column. Note the rather
rapid formation of a fluid mud layer which, assuming the validity of
the definition based on Fig. 8 for this case involving settling as
well as erosion, would be 9 cm thick at 11 hr, with a mean
concentration of 39 g/l. (Other simulations indicated concentrations
on the order of 22 g/l for somewhat different but equally realistic
hydrodynamic and sedimentary initial conditions; see Hwang and Mehta,
1989). Note however that the corresponding bed scour depth would be
only 1.3 cm; thus a very thin bed layer is observed to generate an
order of magnitude thicker fluid mud layer. Such layers,
characterized by a significant concentration gradient, have been
observed in wave dominated environments (Kemp and Wells, 1987). Note
also in Fig. 10a the very slow rise in the suspension concentration
in the upper water column due to characteristically low rates of
upward mass diffusion under wave action. At 11 hr the concentration
at the surface rose to only about 100 mg/l, very close to 102 mg/l
reported by Gleason and Stone (1975) in the southern part of the lake
during a storm. If wave action were discontinued at 11 hr, the
profiles of Fig 10b would result due to sediment settling under calm
conditions. At 35 hr, or 26 hr after waves ceased, the material is
observed to have settled to the bed, and the water column clarified.

Selecting a 3 s, 0.6 m high wave as representing a "common" wave
condition in the lake and a bed shear strength of 0.5 Pa (Fig. 9a),
it can be shown that the critical water depth for erosion would be
3.4 m (Mehta and Jiang, 1990). In order words, the bed can be
considered to undergo resuspension in areas where the actual water
depth- is equal to or less than 3.4 m. Based on this concept, an
approximate correlation between the area of mud bed that can
potentially be influenced by wave resuspension and the water level
in the lake can be obtained, as shown in Fig. 11. It is observed that
when the lake level is less than 0.5 m below datum, the entire mud
bottom area of 528 km is subject to wave action. On the other hand,
when the level is, for example, 1.5 m above the datum, the affected
area is reduced to 48 km The shape of the curve further implies
that the bottom area influenced by wave action is most sensitive to
water level in the range of 0 to 1.0 m. Notwithstanding evident
limitations in constructing this relationship which, for example,
does not account for changes in wave conditions themselves at a given
water level, this "mean" description does suggest a significant
dependence of the bottom area acted on by the waves and water depths.
In turn this strong dependence suggests that seasonal water level
variation in this lake is likely to be a major factor in affecting
bottom resuspension and bottom mud motion characteristics.

In general, the bed shear stress required to initiate particulate
erosion of the bed surface is greater than that required to cause








mud, once fluidized, to oscillate (Mehta and Jiang, 1990). This
implies that while resuspension may be important mainly when'
significant wave action occurs in the lake, there can be oscillatory
motion of mud under milder conditions which, in turn, may explain why
the mud seems to persist in the fluidized state. These considerations
are noted in the sequel.


4. WAVE-INDUCED MUD MOTION

In order to examine the nature of mud motion induced by wave action,
an instrumented tower was deployed at a site shown in Fig. 1 near the
Okeechobee waterway. The mean water depth was 1.43 m and mud
thickness 0.55. m. Water surface variation was measured with a
pressure transducer, and an electromagnetic current meter was used
to measure wave-induced water motion 87 cm below the water surface.
To measure mud motion a small accelerometer was embedded in mud 20
cm below the mud surface, where the mud density was 1.18 g/cm A
simple analytical model was developed to aid in understanding the
data (Mehta and Jiang, 1990). The model assumed a shallow water
condition, the water column was considered to be inviscid and mud was
assumed to be fluidized under continued wave action, hence
represented as a highly viscous fluid. Mud viscosity was measured in
a rheometer; the kinematic viscqsity at the density of 1.18 g/cm was
found to be equal to 1.76 x 10 -6m s, which indicates a very large
viscosity compared to water (10 m/s).

Figure 12 shows a typical wave spectrum obtained under a steady,
moderate breeze (~20 km/hr) from the westerly direction. The wave
period corresponding to the dominant frequency of 0.42 Hz was 2.4
sec, with a significant height of 8 cm. Calculations (Mehta and
Jiang, 1990) show that at 20 km/hr the wind-generated wave height
would be four-fold larger over a rigid bottom. Analytically, the
damping of wave due to energy dissipation is embodied in the wave
attenuation coefficient, k defined by a = a exp(-k x), where a is
the wave amplitude at a distance x and a is the amplitude at x 0.
Thus greater damping over the mud bottom in Lake Okeechobee implies
a larger value of kI than in the case of a hypothetical rigid bottom
in the lake.

In Fig. 13 the measured (horizontal) water velocity amplitude
spectrum is compared=with that predicted by the model using the wave
spectrum of Fig. 12 as input. Given the model limitations,
particularly with respect to the assumption of mud as a high
viscosity fluid, the agreement between data and prediction appears
to be acceptable. Note that in the range of viscosities and wave
frequencies characteristic of the problem, mud response typically
tends to be viscoelastic (Barnes et al., 1989). This type of
agreement in Fig. 13 however seems to breakdown in Fig. 14, in which
the measured (horizontal) mud acceleration amplitude spectrum is
compared with that predicted. In particular, the shallow water model
inherently ignores acceleration frequencies greater than about 0.45
Hz. Nevertheless, the model does generally corroborate mud motion at
the forcing frequency of about 0.42 Hz.

Referring further to Fig. 14, the data as well as the model indicate
the occurrence of measurable acceleration at about 0.04 Hz. This
behavior can be attributed to a forced second order wave that results
from an interaction between the different frequencies of the forcing
wind wave, as for example occurs in the case of the commonly observed
surf beat over relatively flat open coast beaches (Mehta and Jiang,








1990). Note that seiching in Lake Okeechobee occurs at a much lower-
frequency, on the order of 10 Hz. While energy contribution at 0.04
Hz frequency was also found in the wave spectrum (Fig. 12) and in the
water velocity spectrum (Fig. 13), the mud acceleration spectrum is
seemingly enhanced at the 0.04 Hz forced frequency in comparison with
the spectrum at the 0.42 Hz forcing frequency. This relative
enhancement is due to the strong frequency dependence of the wave
attenuation coefficient, k Model results for example yielded k =
0.0034 m at 0.42 Hz and 0.0013 m at 0.04 Hz.

The significance of these results on mud motion is that they indicate
the occurrence of motion as much as 20 cm below the mud surface in
the shallow margin of the lake under comparatively very mild wave
action. It can be shown that for example at 0.03 Hz the maximum
displacement of mud was on the order of 2 mm which is small, but
presumably of sufficient magnitude to influence the nutrient exchange
processes.


5. CONCLUDING DISCUSSION

Given the relatively mild wave regime, the bottom area in Lake
Okeechobee that is underlain by mud undoubtedly contributes
significantly to sediment dynamics in contrast to areas covered by
sand, peat and other more indurated materials; hence in turn the
muddy zone of the lake is of critical interest as far as
understanding internal nutrient (e.g. phosphorus) loading is
concerned. Under "normal" wind conditions there is evidence to
suggest that the top 10 to 20 cm thick mud gently but regularly
oscillates, and thereby persists in a fluidized state. This behavior
is aided by the fact that approximately 40 % of the mud is composed
of organic matter, a large part of which is of fibrous, peaty origin,
which prevents rapid dewatering of the mud even under calm conditions
by virtue of the structural character imparted by the fibrous
material.

The common occurrence of mud oscillation suggests the possibility of
a more rapid nutrient exchange between the bottom sediment and the
water column than would occur otherwise, as a result of an increase
in the effective permeability for constituent mass transfer in
general. The role of gas, ubiquitous in the muddy zone, in further
modifying constituent exchange is not presently known in this lake,
but is likely to be significant.

When wave action becomes more significant, as under storm winds, the
top 1-2 cm of the mud is scoured, resulting in the development of a
high concentration suspension layer no more than 10-15 cm thick, with
concentrations on the order of 20-40 g/l. Above this layer
concentrations remain quite small, on the order of 100 mg/l at the
water surface for example, even after hours of continued wave action.
Furthermore, this "filling" of the water column by sediment may be
quite strongly episodic, not only because of the episodic nature of
wave action, but also because, as noted, laboratory tests on the
bottom sediment indicate mass erosion, an "instantaneous" process in
which the bed fails when the bed shear strength is exceeded by the
wave-induced stress over a significant thickness of the bed, to be
an important characteristic of Lake Okeechobee mud. Further
definition of lake phosphorus dynamics linked to sediment transport
will require a strong focus on understanding these episodic
processes.








6. ACKNOWLEDGEMENT

Support provided by the South Florida Water Management District, West
Palm Beach, FL (through the Lake Okeechobee Phosphorus Dynamics
Study), and by the U.S. Army Engineer Waterways Experiment Station,
Vicksburg, MS (through Contract DACW-89-M-4639), is acknowledged.


7. REFERENCES

Barnes H.A., Hutton J.F. and Walters K. (1989). An Introduction to
Rheology. Elsevier, Amsterdam, 208p.

Brooks H.K. (1984). Lake Okeechobee. In: P.J. Gleason ed.,
Environments of South Florida, Present and Past II. Miami Geol. Soc.,
Miami, FL, 36-68.

Gleason P.J. and Stone P.A. (1975). Prehistoric trophic level status
and possible cultural influences on the enrichment of Lake
Okeechobee. Unpub. Rept., South Florida Water Manage. Dist., West
Palm Beach, FL, 133p.

Hwang K.-N. and Mehta A.J. (1989). Fine sediment erodibility in Lake
Okeechobee, Florida. Rept. UFL/COEL-89/019, Coast. and Oceanogr.
Engrg. Dept., Univ. of Florida, Gainesville, FL, 159p.

Kemp G.P. and Wells J.T. (1987). Observations of shallow water waves
over a fluid mud bottom: implications to sediment transport. Proc.
Coastal Sediments '87, ASCE, New York, 367-377.

Kirby R.R., Hobbs C.H. and Mehta A.J. (1989). Fine sediment regime
of Lake Okeechobee, Florida. Rept. UFL/COEL-89/009, Coast. and
Oceanogr. Engrg. Dept., Univ. of Florida, Gainesville, FL, 77p.

Mehta A.J. (1988). Laboratory studies on cohesive sediment deposition
and erosion. In: Physical Processes in Estuaries, J. Dronkers and W.
van Leussen eds., Springer-Verlag, Berlin, 427-445.

Mehta A.J. (1989). On estuarine cohesive sediment suspension
behavior. J. Geophys. Res., 94(C10), 14303-14314.

Mehta A.J. and JiangF. (1990). Some field observations on bottom mud
motion due to waves. Rept. UFL/COEL-90/008, Coast. and Oceanogr.
Engrg. Dept., Univ. of Florida, Gainesville, FL, 85p.

Somlyody L., Herodek S. and Fischer J. eds. (1983). Eutrophication
of Shallow Lakes: Modeling and Management. Int. Inst. Appl. Syst.
Anal., Laxenburg, Austria, 377p.





































Fig. 1. Bathymetric map of Lake Okeechobee, Florida. Depths are
relative to a datum which is 3.81 m above mean sea level.


N LAKE OKEECHOBEE S
Sea Level
1 Caloosahatchee-
Tamiami Limestone Fort Thompson
Formation

Hawthorn Formation
Wir Rooted Peat
*E Sand
*-- E Mud


Fig. 2. Stratigraphic succession
from Brooks, 1984).


in the Okeechobee area (adapted








































Fig. 3. Mud thickness contour map of Lake Okeechobee.







Mud Layer -2
Sediment Surface


Indurated Sediment -

Sub-Bottom Reflector
Paleochannel -8
Infilling


Fig. 4. Interpreted acoustic sub-bottom profile section along
geophysical line 4 (from Kirby et al., 1989).








0


10


20


30-


40


50
1.0


1.1 1.2


BULK DENSITY P (g/cm3)


Fig. 5. Typical mud bottom density (concentration) profile
vibrocore data from two nearby sites.


1



0.1



0.01



0.001


0.0001 L.
0.01


based on


0.1 1 10
CONCENTRATION, C (g/1)


Fig. 6. Sediment settling flux as a function
concentration.


of sediment



















0
6 g
0~
.0


0.



S


1 1.1 1.2 1.3 1.4

1.065 (g/cm3) BULK DENSITY (g/cm3)

Fig. 7. Vane shear strength versus mud density.


Low Concentration
Suspension, Fs
___________ Fs-- =F4-

Pu I
zf Fluidized Mud, Fs


SBedv =0
S Bed,Ty>0


CONCENTRATION OR DENSITY

Fig. 8. An operational definition of the fluid mud layer.





11


Z
0
O
I-
<

,-1
UJ










Z 2.0
C- Lake Mud


1.5 Mass Erosion
I-
Z
UJ
0: 1.0-
--
) Surface Erosion


w 0.5
) No Erosion
o (a)
So.o0
1.065 1.10 1.15 1.20

BED BULK DENSITY (g/cr3)






10
Lake Mud





S 10-1
z-
LU

u.

0 \


0 Surface Erosion

O

(b)
10
1.065 1.10 1.15 1.20

BED BULK DENSITY (g/cm3)




Fig. 9. a) Variation of bed shear strength with bed bulk density;
domains of surface erosion and mass erosion; b) Variations
(lines) of the corresponding erosion rate coefficient.






























5L
10'3


10.2 10-1 1 10 102

SEDIMENT CONCENTRATION (g/l)


SEDIMENT CONCENTRATION (g/l)

Fig. 10. a) Simulated evolution of suspension concentration profile
due to 0.9 m high, 4 sec waves in a 4.6 m deep water
column; b) settling of sediment once waves cease 11 hr from
start of wave action.









" 600
E


500
Mn
0-
c, 400
U,
rr
S300

LU
S200

0
S100


1.0
-1.0


WATER LEVEL RELATIVE TO DATUM (m)

Fig. 11. Lake area with muddy bottom subject to resuspension as a
function of water level.

50 i.i 11.


>C'

ZW


<

O0
UjLL
(n|


FREQUENCY (Hz)


Fig. 12. Measured wave energy spectrum at a
eastern margin of Lake Okeechobee.


shallow site in the


-0.5 0.0 0.5 1.0 1.5


r I


























' I 1 ^ 1
0.2 0.4 0.6 0.8
FREQUENCY (Hz)


Fig. 13. Water velocity spectrum corresponding to
of Fig. 12.

0.30


ci 0.24
^N I'

) Z 0.18 Calculated I i
zo
--
SMeasured I
< 0.12

O ;
FL I0
CL 0.06


0


the wave spectrum


0.2 0.4 0.6 0.8
FREQUENCY (Hz)


Fig. 14. Mud acceleration
spectrum of Fig. 13


spectrum corresponding


to the wave


300


240


180


120


60


F-


Cn
,,-
00


->
LU
O


C0




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs