Citation
Modulation of inlet ebb tidal deltas by severe sea

Material Information

Title:
Modulation of inlet ebb tidal deltas by severe sea
Series Title:
UFLCOEL-96010
Creator:
Devine, Paul T., 1971-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publication Date:
Language:
English
Physical Description:
xvi, 114 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Coastal and Oceanographic Engineering thesis, M.S ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 85-90).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Paul T. Devine.

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University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
35717419 ( OCLC )

Full Text




UFL/COEL-96/O1 0


MODULATION OF INLET EBB TIDAL DELTAS BY SEVERE SEA by



Paul T. Devine Thesis


1996













MODULATION OF INLET EBB TIDAL DELTAS BY SEVERE SEA


By

PAUL T. DEVINE















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF MASTER OF SCIENCE



UNIVERSITY OF FLORIDA


1996













ACKNOWLEDGMENTS


I would like to extend special thanks to Dr. A. J. Mehta for his intricate attention to detail, and constantly keeping me focused on the path of least resistance by challenging me to resist my impulses. I thank Dr. D. M. Sheppard for opening my eyes to lands west of the Atlantic. I thank Dr. R. G. Dean for always having an open ear, and for being so diplomatically delicate in his responses. I appreciate the understanding of all nine of my office mates who were a part of my regimented lunch routine. I would like to express my sincere gratitude to everyone who gave me their time and energy; without their assistance the road would have been additionally windy and infinitely bumpier.

This study was partially funded through contract DACW39-94-K-0043 from the Coastal Engineering Research Center (CERC) of the U.S. Army Corps of Engineers Waterways Experiment Station, Vicksburg, MS. Thanks are due to Mr. Gary Howell of CERC for project support and management.


ii













TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS .............................................1ii

LIST OF FIGURES.................................................. vi

LIST OF TABLES................................................... x

LIST OF SYMBOLS................................................. xi

ABSTRACT ...................................................... xv

CHAPTERS

1 INTRODUCTION .............................................I
1. 1 Problem Statement........................................... 1
1.2 Delta Mining............................................... 3
1.3 Some Previous Studies on Ebb Deltas............................. 9
1.4 Outline of Presentation ...................................... 23

2 PARAMETERIZATION OF EBB DELTA VOLUME ................... 24
2.1 Introduction............................................... 24
2.2 Delta Volume ............................................. 24
2.3 No-Inlet Geometry Parameterization............................. 28
2.4 Delta Geometry Parameterization............................... 29

3 DELTA EROSION MODEL ..................................... 40
3.1 Introduction............................................... 40
3.2 Profile Erosion............................................. 42
3.3 Volume Calculation......................................... 43
3.5 Erosional Time-Constant ..................................... 43
3.6 Depth of Limiting Motion .................................... 46
3.7 Deposit Profile............................................. 48

4 DELTA VOLUME AND EROSION ............................... 51
4.1 Introduction............................................... 51
4.2 Dependence of Delta Volume on Profile Parameters..................51


iii








4.3 Changes in Delta Volume .................................... 55
4.4 Case Studies .............................................. 67

5 SUMMARY AND CONCLUSIONS............................... 81
5.1 Summary and Conclusions.................................... 81
5.2 Recommendations for Future Investigations....................... 83
5.3 Note of Caution............................................ 84

REFERENCES .................................................... 85

APPENDICES

A FORTRAN CODE FOR LEAST SQUARES FIT FOR THE
NO-INTLET PARAMETERS ..................................... 91

B MATLAB CODE FOR LEAST SQUARES FIT
OF VI, AAND MPARAMETERS................................. 93

C MATLAB CODE FOR LEAST SQUARES FIT FOR
PARABOLIC RELATION OF A-PARAMETER...................... 96

D MATLAB CODE FOR THE LEAST SQUARES FIT OF POWER-LAW
RELATION WITH HYPERBOLIC A-PARAMATER ................... 98

E MATLAB CODE FOR THE LEAST SQUARES FIT FOR
PARABOLIC RELATION OF M-PARAMETER ......................99

F MAThAB CODE FOR GAUSSIAN FIT OF VIRTUAL
ORIGIN PARAMETER ....................................... 101

G FORTRAN CODE FOR MODULATION OF DELTA VOLUME ......... 104 BIOGRAPHICAL SKETCH.......................................... 114


iv













LIST OF FIGURES


1. 1: A schematic description of an ebb delta, including ebb and flood channels and a
swash bar platform (from Hayes, 1973)............................... 2

1.2: Bathymetry from Boca Raton Inlet, Florida (from Coastal Planning and
Engineering, 1993).............................................. 2

1.3: Flow chart showing criteria to be evaluated for ascertaining the feasibility of
delta sand mining. Return pathway emanating from a particular set of criteria implies that these criteria were not satisfied, thus requiring selection of a new
site (from Mehta et al., 1996) ...................................... 4

1.4: Wave spectra from stations near Norderney, Germany (adapted from Niemeyer,
1985)........................................................ 4

1.5: Representation of the grid system for calculating delta volume, and the no inlet
contours for a typical inlet (from Dean and Walton, 1973) ................. 14

1.6: The length of active profile extends from the shoreline to the depth of closure,
hid. The crossover depth, h.0, separates nearshore and offshore zones within the active length. Dashed curve corresponds to a storm profile, whereas the monotonic curve represents profile formed under comparatively mild wave
conditions (from Mehta et al., 1996)................................ 20

1.7: Schematic drawing of an idealized cross-shore profile near an inlet and
episodic change in profile geometry due to wave action, where "y" is the
distance offshore, "h" is the depth of the inlet profile, "y'," is the distance from
the beginning of the channel to the origin of the profile defining the seaward
slope of the delta, "U0," is the current emanating from the inlet, "U c" is the current over the delta crest, "h0" is the depth of the inlet channel, "h d is the
depth of closure and "h,0" is the crossover depth (from Mehta et al., 1996). ... 20

1.8: Diagram depicting the three different delta classifications (from Hoekstra,
1988)....................................................... 22

2. 1: Delta planform schematic .......................................... 25


v








2.2: Schematic of delta elevation profile................................... 26

2.3: Least squares fit of PBC R-3 1978 and 1990 data to Eq. 2.2 .................. 30

2.4: Sample placement of profile origin, and baseline on the ebb delta at New Pass,
Florida...................................................... 30

2.5: Profiles # 1-4 from Jupiter Inlet delta, February, 1980...................... 32

2.6: Profiles #5-8 from Jupiter Inlet delta, February, 1980...................... 32

2.7: Profiles #9-11 from Jupiter Inlet delta, February, 1980..................... 33

2.8: A-Parameter data from Jupiter Inlet delta, February 1980, and corresponding
parabolic fit .................................................. 34

2.9: Profiles #1-4, fit with parabolic relation for A(n) and VI(n) from
Appendix A.................................................. 34

2. 10: Profiles #5-8, fit with parabolic relation for A(n) and VI(n) from
Appendix A.................................................. 35

2.11: Profiles # 9-11, fit with parabolic relation for A(n) and VI(n) from
Appendix A.................................................. 35

2.12: M-Parameter fit with A derived from hyperbolic relationship ................ 37

2.13: Polar plot of virtual origin, VI data, and the corresponding average VI values
for February, 1980 Jupiter Inlet survey. Numbers on the exterior of the plot
are the profile angles with respect to the updrift shoreline. Concentric circles
are lines of equal radii in meters ................................... 37

2.14: Average VI data normalized by the maximum alongshore and offshore distances
of the virtual origin distribution, and the corresponding Gaussian fit with K =
1.52, February, 1980 Jupiter Inlet survey .............................. 38

2.15: Plot of the 37 data points of VI for input into delta modulation model. Numbers
on the exterior of the plot are the profile angles with respect to the updrift
shoreline. Concentric circles are lines of equal radii in meters .............. 38


vi








3.1: Bruun Rule of erosion, where "s" is the recession, "1" is the active profile length,
"a" is the sea level rise, "d" is the depth of active sediment movement, "e" is
the berm height, and "z" is the point of no net sediment transport (from
Bruun, 1988) ................................................. 41

3.2: Bruun Rule of erosion, with deposit slope. (from Bruun, 1988) ...............41

3.3: Beach-profile response to waves and surge where R_0 is the recession at
equilibrium, and R(t) is the recession at a certain time, t ...................44

3.4 Differential angular planform area, where 0 is in degrees................... 44

3.5: Delta radial profile response where R., is at equilibrium, and R(t) is at a specified
time, t............................................................ 47

3.6: Planform view of the delta illustrating the assumed magnitudes and approach
angles for the breaking waves, H B' on the crest of the delta ............... 48

3.7: Nondimensionalized deposit slope, 6 = 0.2443461 ....................... 50

3.8: Deposit slope for an arbitrary set of values of 6, S, R(t) and Hm .................50

4. 1: Isometric (a) and side (b) views of an arbitrary delta volume with parameters:
CW= 100 m, HC =3m, Ani= 0.05,Cni= 0.7, AK= 0.079, Amfl=O.05,
MKO=.34, Mm =0.8,K= 1.5 m, o =0.35 m, VIm, = 1400 m, VI. = 800m. .53

4.2: Isometric (a) and side (b) views of an arbitrary delta volume with parameters
set to those in Figure 4. 1, except with ni==0.675 ....................... 53

4.3: Dependence of delta volume on the no-inlet shape and scale parameters, An and
Mni. The remaining delta parameters are equal to those in Figure 4.1 .........54

4.4: Plot of non-dimensional time-dependent profile recession versus phase of storm,
'rrt/Td, with P3 = 0, corresponding to no lag in profile response and, P3 = c2
selected for determining delta response.............................. 56

4.5: Plot of delta volume during storm versus storm surge, S, for variable wave
height H0 and 73= r/2. The initial delta condition is depicted in Figure 4.1. . 58

4.6: Plot of delta volume during storm versus storm surge, S, for varying wave height
H. and P3 = 7c/2. The initial delta condition is depicted in Figure 4.2 ......... 60


vii








4.7: Plot of delta volume during storm versus storm surge, S, for variable wave height
H. and f3 = 7c/2. The initial delta condition is that of Figure 4.1 with Vhmx =
1000 and Vimy = 500, effectively producing a smaller delta ...............60

4.8: Plot of delta volume during storm versus storm surge, S, for variable wave height
H0 and P3 = 7r/2. The initial delta condition is that of Figure 4.2 with VImx =
1000 and Vimy = 500, effectively producing a smaller delta ...............60

4.9: End of storm radial profiles for the steep no-inlet condition with [(a) and (b)],
and without [(c) and (d)] the accretionary portions of the profile included.
Theta refers to the profile angular orientation with respect to the updrift
shoreline. The equilibrium profile is the solid line, and the maximum
recession profile is the dashed line.................................. 62

4. 10: End of storm profiles for the initial condition in Figure 4.2 with [(a) and (b)],
and without [(c) and (d)] the accretionary portions of the profile included.
Theta refers to the profiles angular orientation with respect to the updrift
shoreline. The profile is the solid line, and the maximum recessed profile is
the dashed line ................................................ 63

4.11: Planform views of the evolution of the top of delta of Figure 4.1 with increasing
values of storm surge and changes in incident wave height, H,. Solid line is the initial condition and the dashed lines correspond to increasing values of
storm surge from 0.5 mn to 3.5 mn in increments of 0.5 mn, with the largest
deviation from the initial condition occurring at the largest surge ............65

4.12: Planform views of the evolution of the top of delta of Figure 4.2 with increasing
values of storm surge and changes in incident wave height, H0. Solid line is the initial condition and the dashed lines correspond to increasing values of
storm surge from 0.5 mn to 3.5 mn in increments of 0.5 mn, with the largest
deviation from the initial condition occurring at the largest surge ............65

4.13: Isometric (a) and side (b) views of the maximum erosion of the delta of Figure
4.1 due to incident wave height, H.-= 5.5 mn, maximum surge, S = 3.5 mn, and
P=n2...................................................... 66

4.14: Isometric (a) and side (b) views of the maximum erosion of the delta of Figure
4.1 due to incident wave height, H,0 = 5.5 mn, maximum surge, S = 3.5 mn, and
= irf2...................................................... 66

4.15: Bathymetric chart of Jupiter Inlet (from Coastal Planning and
Engineering, 1994) ............................................. 69


viii








4.16: Ebb delta volume versus year with model-calculated growth envelope for
Jupiter Inlet with a = 0.17, H. = 0.54 m, and a = 0.27, H10 = 0.68 mn (from
Dombrowski, 1994) ............................................ 69

4.17: Plot of delta volume at Jupiter Inlet and WIS hindcast wave data for the time
period 1956-1993 (from USACOE, 1996) ........................... 70

4.18: Plot of the Jupiter Inlet delta volume versus maximum hindcast WIS wave
height during the preceding year................................... 70

4.19: Bathymetric chart of South Lake Worth Inlet (from Olsen and Associates, Inc.
1990)....................................................... 72

4.20: Ebb delta volume versus year with model-calculated growth envelope for
South Lake Worth Inlet with a = 0.03, Ho = 0. 19 m, and a = 0.60, H. =
0.28 m (from Dombrowski, 1994).................................. 73

4.21: Plot of delta volume South Lake Worth Inlet and WIS hindcast wave data for
the time period of 1965-1993 (from USACOB, 1996) .................... 74

4.22: Plot of the South Lake Worth Inlet delta volume versus maximum hindcast WIS
wave height during the preceding year .............................. 74

4.23: Bathymetric chart of East Pass (from USACOB, 1990)................... 76

4.24: Plot of delta volume at East Pass and WIS hindcast wave data for the time period
1965-1976 (from USACOE, 1996) ................................ 76

4.25: Plot of East Pass delta volume versus maximum hindcast WIS data during the
preceding year ................................................ 77

4.26: Bathymetric chart of the area surrounding Katiakati Inlet, New Zealand,
including the ebb delta (from Hume et.al., 1996)....................... 79

4.27: Ebb delta at Katiakati Inlet (New Zealand) ebb delta protrubance from the
shorline over a 50 year period (adapted from Hume et.al., 1996) ............79


ix













LIST OF TABLES


1. 1: Inlets where ebb delta mining has been performed .......................... 6
1.2: Benefits, adverse impacts and monitoring at inlets given in Table 1. 1............7
1.3: A summary of previous delta studies .................................. 17
4. 1: Dependence of delta volume on the no-inlet scale parameter for a given delta
seaward slope................................................. 54


x













LIST OF SYMBOLS


a = Sea level rise in Bruun Rule definition A = Power-law relation scale factor AK = Scale factor in determining the parabolic relationship for A AmIN = Minimum value of A for eleven fits of digitized data ANI = No-inlet scale factor AREA(r) = Projected angular differential area between two given radial distances

B = Berm height in convolution method C = Constant in convolution method CW = Flood channel width d = Depth of active sediment movement in Bruun Rule definition DH(n,r) = Difference in elevation between the delta height and the no-inlet contour

DVOL(r) = Angular differential volume between two radial distances e = Berm height in Bruun Rule definition f (t) Time dependent storms surge forcing g Acceleration due to gravity GAUS = Modified Gaussian distribution fit to VIyN(n) h = Depth of profile in Figure 1.7


xi








h= Crossover depth in Figure 1.7 hd = Depth of closure in Figure 1.7 ho Depth of the inlet channel in Figure 1.7 H = Profile Depth Hb(n) Breaking wave height HNI No-inlet profile depth Hm(n) = Depth of limiting motion Ho Unrefracted wave height in shore normal direction HS = Depth of the crest of delta = Active length of profile in Bruun Rule definition M = Power-law shape factor MK = Scale factor in determining the parabolic relationship for M MMAX= Maximum value of M for eleven fits of digitized data MM = No-inlet shape factor n = Index referring to the value of the variable of particular profile number

OF = Offset from virtual origin to delta crest P = Spring tidal prism P. Wave power r = Radial distance from origin: index referring to the value of the variable at particular radial location r, r Specific radii between which the differential area is calculated r.(n) = Radius at the depth of limiting motion


xii








R = Radial distance from origin R(t) = Time dependent virtual origin recession

R= Equilibrium recession of the radial virtual origin s = Profile recession in Bruun Rule definition S = Storm surge T = Wave period Td = Storm duration

T= Tidal period

Ts Characteristic erosion time-constant U0 Current emanating from inlet

=c Current over the delta crest

VI(n) = Virtual origin for shoal seaward delta profile

=I Temporary virtual origin during least square fitting of A, VI parameters

VIy(n) = Alongshore component of VI for use in determining Gaussian distribution

VIyN(n) = Normalized alongshore component of VI VIyM = Maximum value of the alongshore component of VI VIXM = Maximum value of the offshore component of VI X(n,r) = Normal distance from shoreline to a point on delta Xb = Surf zone width in convolution method y = Distance offshore in Figure 1.7


xiii








YO Distance from the beginning of the channel to the origin of the profile in Figure 1.7

z = Point of no net sediment transport in Bruun Rule definition 2a0, = Spring tidal range

a = Ratio of normal incident wave energy to tidal energy at inlet = Ratio of erosion time scale to the storm duration

6 = Angular offset for determining deposit slope 60 = Angular separation in between radial profiles

=W Unit weight of seawater

= Scale factor for fitting Gaussian distribution of VIyN data

a = Standard deviation of VIyN

0 = Angular orientation of present profile relative to updrift shoreline = Time differential

~, 6 = Coefficients for modification of the deposit profile


xiv













Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science MODULATION OF INLET EBB TIDAL DELTAS BY SEVERE SEA By

Paul T. Devine

August, 1996

Chairman: Dr. Ashish J. Mehta
Major Department: Coastal and Oceanographic Engineering

Sandy ebb deltas in the microtidal sea environment subject to storm waves and surges are represented in terms of an idealized geometry guided by measured offshore profiles in the vicinity of inlets, and the method of Dean and Walton for calculating delta volumes. Characteristic delta features include an arcuate planform shape, ebb channel, marginal flood channel boundaries, a swash platform and offshore slopes that are defined by a generalized power-law akin to that commonly used for delineating beach profiles. Delta volumes calculated by using realistic values of the geometric constants are shown to result in values that are comparable to those measured at inlets.

A simplified model for assessing the response of the delta to severe waves and associated storm surges is developed by using the convolution method of Kriebel and Dean. In this model, erosion of the delta occurs due to a recession of the offshore portion of the delta. It is found that the characteristic erosion time-constant for the delta to attain


xv








equilibrium is an order of magnitude greater than that corresponding erosion time-constant for beach erosion. This finding, which is a reflection of the relatively slower response of the delta than beaches to eroding forces, is seemingly in agreement with natural events, and requires further exploration through detailed pre- and post- storm monitoring of inlet deltas. The model is used to show that reductions in delta volume due to wave forcing are commensurate with volumetric changes recorded at several inlets.


xvi













CHAPTER 1
INTRODUCTION


1.1 Problem Statement

When planning a beach nourishment project it is often found that an economical, beach compatible offshore sediment source is not available (Walther, 1995). In recent years, therefore, the trend has been to look to the ebb deltas at sandy inlets for a comparatively inexpensive source of beach quality sand. At present, the potential effects of mining the delta for sand on the littoral system cannot be accurately predicted. Some possible effects of mining are alterations in the inlet hydraulics and sediment transport pathways, focusing of wave energy on the nearby shoreline causing erosional "hot spots," and deprivation of the downdrift shoreline of its sediment supply due to a reduction in the natural by-passing ability of the inlet system.

According to Bruun and Gerritsen (1959, p. 82), "A submerged bar in front of an inlet or harbor entrance on a littoral drift coast will often function as a 'bridge' upon which sand material is carried across the inlet or entrance. Every channel dredged through the bar will, therefore be subject to deposits. Both bar and tidal flow by-passing include cases with irregular transfer of large amounts of materials in migrating sand humps or by change in the location of channels." Thus, since the delta could be the primary sediment transport pathway to the downdrift shoreline, it is necessary to have a better understanding of how the inlet ebb delta responds to oceanic forcing. Figure 1. 1 depicts a schematic of an arcuate ebb


I










2


4L








BOCAZA RATON~ INE
















M" LINELDA A"IA N1 99 Figure 1.1: Ahetc desripio Bof atn bblet, Finldin ebbo atfloo channels and aEswashebrg pltfr9 (rm3aes)97)

BOARTO NE








3

delta, including ebb and flood channels and a swash bar platform. Figure 1.2 is the bathymetry of a typical sandy microtidal inlet ebb delta system. This study is concerned with the response of such deltas to forcing by episodic waves and the associated storm surges. As a basis for this work, we will first consider criteria for delta mining and illustrate examples of mining from available sources.

1.2 Delta Mining

Using knowledge of the beach fill template and length of beach nourishment project, a volume requirement of sand can be determined. In order to make an educated decision whether to mine this volume of sediment from the delta, three criteria must be satisfied. The first criterion is the availability of this volume of sediment, and the corresponding cost for transportation and placement on the beach. Too small a volume, or too large a pumping distance for the dredge could exclude the sediment source. The second criterion is the composition and size of sediment available for mining. A sediment size smaller than native will provide a smaller dry beach width than the same fill volume of native sediment (Dean and Dalrymple, 1996). The third criterion is based on assessments of physical and ecological impacts of the proposed operation. Acceptable changes to the hydrodynamic and sediment transport processes surrounding the mining area must be predicted. Some probable environmental impacts to the benthic habitats due to inlet modifications are briefly mentioned by Mehta and Montague (1991). Figure 1.3 is a flow chart showing the three sets of criteria that must be satisfied when considering delta mining.

Excluding impacts to the ecological system, the main issues concerning influences to the physical system due to delta mining are rate of infilling of the sand borrow pit and














4


EQIRED SAND VOLUME






CRITERIA FOR SAND AVAXABLITY AND COST OF TRANSPORT





RITERLA FOR COMPOSMlON AND SIZE COMPATSY













Figure~~~~~~~~~~~~~~~~RTO 1.:FoIcatsoinErtra obDvlutdfrascrannNhDfaiiiyo
delta~ ~ ~ ~ ~~~~~rTEI sand miigReunptwaEmntn rmaparEtlrsto rtraipista








these 1.teFawrehnot stiiedteuring sbeelecton fof asnewtasie (fro Meaelty ao. 1996).










Offshore (I) S 1000,'e






S Soo~



to Inshore (11I



0.00 0.06 0.12 0.18 D.24. 0.30 0.36 0.1.2 0.486


Frequency (Hz) Figure 1.4 Wave spectra from stations near Norderney, Germany (adapted from Niemeyer, 1985).








5

changes to the nearby shorelines. One cause of shoreline change would be the reduction in sediment supply to the downdrift shoreline caused by impoundment of littoral sediment in the dredge pit. Bruun and Gerritsen (1959) describes the transfer of sand from the updrift to downdrift sides of the inlet as occurring over the, "shoal or offshore bar." A dredge pit could possibly interrupt the main sediment pathway across the delta in a bar by-passing type of inlet system, and thereby change the shorelines in the vicinity. Another cause of shoreline change would be modification of the wave climate due to the reduction of the wave sheltering capability of the ebb delta due to mining. Figure 1.4 shows measured wave spectra at three stations near Nordemney in Germany (Niemeyer, 1985). Note that there is a substantial reduction in wave energy from the offshore station I to the ebb delta sheltered station II.

Examples of delta mining operations are summarized in Table 1.1. Table 1.2 provides a summary of information on benefits, adverse impacts and monitoring of mining at inlets in Table 1.1. These include seven inlets in Florida: John's Pass (Walther and Douglas, 1993; Army Corps of Engineers, Jacksonville District, personal communication), Longboat Pass and New Pass (Applied Technology and Management, 1992; 1993a; 1993b), Redfish Pass (Tackney and Associates, 1983; Coastal Planning and Engineering, 1992), Boca Raton Inlet (Coastal Planning and Engineering, 1993), Jupiter Inlet (Coastal Planning and Engineering, 1994) and Nassau Sound Entrance (Olsen and Associates, personal communication). Five examples are from South Carolina: Port Royal Sound Entrance (Bodge et al., 1993), Fripp Inlet (Coastal Science and Engineering, 1990a;1I990c), Port Isidro Entrance (Coastal Science and Engineering, 1989; 1993),









6


Table 1. 1: Inlets where ebb delta mining has been perfred. _____Inlet Mining Site Year Volume Placement Method of
_____________(Mi) Location Dredging John's Pass, FL Seaward side of 1988 405,000 Updrift beach 61 cm, northern delta lobe ____________Cutterhead Longboat Pass, FL Seaward side of 1993 1,020,0 Downdrift Dustpan dredge
_____________delta _______ beach _______New Pass, FL Seaward side of 1993 720,000 Updrift beach Dustpan dredge
_________________ delta _____ _______ ______Redfish Pass, FL Center of delta from 1981 501,000 Downdrift 53 cm channel to seaward 1988 1,220,000 beach I Cutterhead
_________________extent of delta ____________ ______Boca Raton, FL Top of delta 1985 169,000 Downdrift 61 cm
______________ ______ beach Cutterhead Jupiter, FL Seaward side of 1995 392,00 Downdrift 76 cm
____________delta _____ beach Cutterhead Nassau Sound, FL Outer, updrift and 1994 2,140,000 Updrift beach 76 cm.
relict portion of cutterhead
delta _____ ______Port Royal Sound, SC Seaward edge of 1990 596,00C Downdrift 76 cm.
delta __________ beach Cutterhead Fripp, SC North delta of 1974 469,00( Updrift beach 51-61 cm entrance 1980 1,080,00C pipeline Port Isidro, SC Landward edge of 1990 524,00 Beach eroded 76-84 cm delta by entrance pipeline
________ ~~flood channel ______Captain Sam's, SC Closed off migrating 1983 134,00 Operation Earthmovers; and old entrance, (by tides meant to bulldozers, creating a new and nourish 99,000 in3 to entrance updnift of waves) downdrift beach close old
the old one _____ _______channel Hog, SC Shore-attached delta 1990 288,000 Updrift beach Hydraulic hoe at
______________ ______ __________low tide
Townsend's, NJ Updrift entrance 1978 483,00( Updrift beach 76 or 91 cm swash bar complex 1983 626,00 _______ Cutterhead Townsend's, NJ Downdrift entrance 1987 1,030,00( Surrounding 76 or 91 cm swash bar complex _____ beaches Cutterhead Great Egg, NJ Undetermined 1992 to 4,900,00( Downdrift Dustpan and portion of delta 1994 ____ beach Hopper dredges Absecon, NJ Spit attached to 1986 765,000 Downdrift 76 or 91 cm
_____________north jetty __________ beach Cutterhead I

Captain Sam's Inlet (Kana and Mason, 1988) and Hog Inlet (Coastal Science and


Engineering, 1990b;1992). Finally, three examples from the New Jersey coast are:

Townsend's Inlet (Ippolito and Sorensen, 1990), Great Egg Inlet (New Jersey Department of










7


Table 1.2: Benefits, adverse impacts and monitoring at inlets given in Table 1. 1.

Entrance Benefits Adverse Impacts Monitoring
John's Pass, FL Beach was restored; Increased beach erosion Borrow area shoaled at the reduced shoaling in in the vicinity due to rate of 24,000 m3' from entrance channel due to reduced sand by- 1988 to 1992 sand trapping in borrow passing
area
Longboat Pass/ New Calculated wave None were predicted to Between Dec. 91 and Dec. Pass, FL refraction patterns occur; no impacts were 92 Longboat Pass borrow showed a reduction of monitored area volume increased by sediment "trapped" by 150,000 in3; however, deltas, and a more even between Dec.'92 and spreading of wave Apr.'93 (due to March 13energy to the south of 14 storm) borrow area each entrance volume decreased by
____________ 4 41,000 m3'
Redfish Pass, FL Erosion protection for No specific studies Approximately 80,000 m3 downdrift shoreline; were performed of fine-grained material accretion to the north of was carried into the borrow the entrance, and south area within 18 months after of the project 1981 project; between 1989 and 1991 35,000 mn3
filled both (1981 and 1988)
________________borrow areas
Boca Raton, FL Beach erosion Feeder beach within Beach 1 kmn south of contained, improved 600 m of entrance entrance grew by an navigational conditions eroded critically; beach average of 12 in; the entire over delta and nourishment project delta, including borrow maintenance of water planned for 1995 using area exceeded pre- project quality in Lake Boca delta sediment volumes
Raton ______________________Jupiter, FL Erosion protection for None were predicted to Pre- and post-project downdrift shoreline occur, including surveys of fill area to be focusing of wave carried out energy on jetties,
changing of littoral
pattern or increased
salinity in Loxahatchee
_________________River___________Nassau Sound, FL Refraction analysis for None were predicted to No monitoring of the relict borrow area showed a occur delta region reduction of wave
energy on shoreline, and
an increase of energy in
the sound, resulting in
decreased sediment
__________________transport_________________________










8


Table 1.2 Continued __________ ________Port Royal Sound, SC Mitigated chronic None were predicted to No monitoring of delta erosion problem with a occur
predicted 8 year project
life___________
Fripp, SC Temporary beach No studies were Rapid recovery of borrow nourishment performed; no impacts area, approximately were monitored 153,000 mn3 accumulated in
___________________________________delta since 1980 Port Isidro, SC Dredging the delta None were predicted to Sediment filled the borrow moved the channel 125 occur; no impacts were area, and the channel m offshore, removing monitored slowly m-igrated landward the source of scour, and towards its equilibrium
______________renourishing the beach position
Captain Sam's, SC Relict delta "pushed" None were predicted to Entrance began migrating ashore by wave action occur; no impacts were to the south at it's previous nourished the beach at monitored rate the rate of 130,000 Mi3!
between Mar.'83 to May
'85; totally 1,150,000
_____________ m_ iby_1993 _________Hog, SC Emergency nourishment Delta filled with Position of Hog, Inlet for heavily armored sediment at the expense channel did not shift sections of shoreline of deltas further toward Myrtle Beach following, hurricane offshore and the shoreline; six months after Hugo downdrift shoreline; the project, 95% of the dry 7,100 M3 of remedial beach was recovered due to nourishment became nourishment and seasonal necessary to guard effects
___________________ ~downdrift shoreline ___________Townsend's, NJ Beach nourishment Miningr redirected the Critical beach erosion ebb channel northward along Avalon shoreline, through the delta, and growth of a large spit resulting in changed in the interior of the channel hydraulics entrance where the channel once occurred
Townsend's, NJ Emergency nourishment, No studies were done; Monitoring to verify redirection of channel no impacts were channel position
monitored ___________Great Egg NJ Beach nourishment No studies were Monitoring of delta system preformed planned
Absecon, NJ Beach nourishment No studies were 43% of fill remained in preformed 1991, some sediment was lost offshore; no
_______________ _______________ _______________monitoring of delta



Environmental Protection, personal communication) and Absecon Inlet (Weggel and


Sorensen, 199 1). The minimum volume of material transported was 1.34 x 101 M3 at Captain








9

Sam's Inlet to a maximum of 4.9 x 106 m3 at Great Egg Inlet, and in the majority of cases the material was placed on a segment of the beach downdrift of the inlet. The method of dredging included the use of cutterhead dredges, dustpan dredges and a hydraulic hoe at Hog Inlet. Artificial closure of Captain Sam's Inlet was a novel method making use of natural forces to transport relict delta sediment to the downdrift beach. Closure of the old entrance was carried out by earthmovers and bulldozers. It should be emphasized that the information in Tables 1. 1 and 1.2 is based on the given citations only, and therefore does not include any subsequent studies, e.g., monitoring, that may have been carried out at the inlets considered.

Although as noted, each of the beaches in Tables 1.2 received the benefit of additional sediment within their system, in some cases there was no pre-project study to predict possible adverse effects on the nearby shoreline due to mining of the delta. Also, post-project monitoring was not always performed. Where it was performed, adverse effects were recorded in all cases. If a standardized procedure were developed for delta mining site selection, prediction of impacts and post-project monitoring, the processes involved could be better understood in the future, and mining planned better.

1.3 Some Previous Studies on Ebb Deltas

In order to better understand the interaction of inlets with the downdrift shoreline, Bruun and Gerritsen (1959) discuss the two different types of sediment by-passing by natural action that occur at an inlet. By-passing over an offshore bar occurs when the ratio of the rate of littoral drift to the volume of flow through the inlet in one tidal cycle is high. On the other hand, by-passing by tidal flow action occurs when this ratio is low. Inlets exposed to tides and waves generally exhibit both types of bypassing. Also, a relationship is obta ined








10

between the intensity of the wave forcing and the magnitude of the by-passing since, according to Bruun and Gerritsen (1959, p.98) "experience demonstrates that such bypassing cannot exist without considerable wave action."

In response to the need for prediction of the navigability and stability of an inlet, Bruun and Gerritsen (1960) defined an inlet stability ratio. The ratio of the spring tidal prism passing through the inlet over one-half tidal cycle to the annual average rate of littoral drift reaching the inlet was considered as the relevant stability ratio. Large values of this ratio (>150) correspond to inlets which have good flushing characteristics, and large clearances over the delta. As the value of this ratio decreases the ebb delta becomes more pronounced, and the controlling depth of water above the delta decreases. When values of the stability ratio are small enough (<50) the natural channels are very shallow and unreliable becoming dangerous for even shallow draft vessels.

To further quantify the stability of an inlet, O'Brien (1971) defined a ratio, a, of the normally incident wave energy over a tidal period to the tidal energy through the inlet over the tidal period. Wave energy over one tidal period is a function of the wave power, P,. width of the inlet throat, w, and the tidal period, Tt. The tidal energy through the inlet over the tidal period is a function of the spring tidal range, 2a,,,, the spring tidal prism, P, and the unit weight of seawater, y,. Thus,


P~wTt (11) 2acosywP


Considering a representative wave height, H0, and period, T, wave power is defined as:








I1I


PO = 19 H 2 T(1.2)
0-32Tc




where g is the acceleration due to gravity. Mehta and Hou (1974) plotted the values of a versus tidal prism for many inlets of known stability. A line was drawn that separated the unstable high values of the coefficient from the stable low values, thus confirming the stability relationship (Eq. 1. 1).

A method was needed to predict the quantity of sediment to be removed from the inlet channel during maintenance dredging. For that purpose, Gole et al. (197 1) proposed an empirical formula for sedimentation in dredged channels within inlets by determining the percentage of the total littoral drift that will be entrapped by the increased depths and the corresponding decreased current velocities across the channel.

Realizing that inlet ebb deltas are comparatively large deposits of littoral material that is diverted from the shorelines downdrift of the inlets, Dean and Walton (1973) qualitatively described the sedimentary processes associated with inlet flood and ebb currents. The ebb currents were compared to a turbulent jet escaping a nozzle, while flood currents were considered to be analogous to a concentric sink flow pattern into the inlet. Since the turbulent ebb jet entrains water, and thus sediment from the adjacent shorelines, both flood and ebb currents have the effect of transporting sediment into the inlet from both the updrift and downdrift shorelines. Since the turbulent jet displaces the same volume of water as the sink flow, but is concentrated within a narrower area, higher ebb velocities exist, and these transport sediment offshore forming the ebb delta. Dean and Walton (1973) stated








12

that wave action will limit the volume of the delta to some equilibrium volume by transporting sediment deposited by the ebb currents back toward the inlet.

Dean and Walton (1973) also developed a method for determining the sediment volume in the ebb delta. In this method, a grid, as well as the elevation contours that would exist in the absence of the inlet, or the "no-inlet" contour lines, is superimposed on the plot. The difference between the no-inlet and delta elevation at each node of the grid box is calculated, averaged over the four corner values for the grid, and multiplied by the surface area of grid to find the delta volume within the grid box. The total delta volume is then the sum of all of the grid box volumes. This method was applied to twenty-three Florida inlets. Figure 1.5 is a representation of the grid system and the no-inlet contours for a typical inlet.

Continuing the work of Dean and Walton (1973), Walton and Adams (1976) analyzed the delta volumes of forty-four tidal inlets around the United States. The inlets were divided into three different incident wave energy groups, and the delta volumes were plotted versus tidal prism for each group. A power-law relation was fit to all three data sets. The differences in the power-law coefficients implied the dependence of delta volume on wave energy.

In order to better predict the life-span of, and processes involved in, channel dredging at tidal inlets, Galvin (1982) presented a method to determine the shoaling rates, and times for over-dredged channels to infill to the design depth. Galvin (1982) observed that the maximum rate of shoaling occurs immediately after dredging, shoaling rate is increased when dredging reduces the currents in the channel, shoaling rate increases when zero by-








13

passing occurs, and shallow dredged channels tend to approach the natural depth at a slower rate than a deep dredged channels.

Marino (1986) applied Dean and Walton's (1973) method to Florida inlets. A dimensional analysis was preformed to determine relationships between relevant inlet parameters. From this analysis and its application to Florida inlet data, Marino (1986) concluded that the delta volume not only depends on the tidal prism, but also on the ratio of throat width to channel depth.

In order to understand sediment transport processes in the vicinity of the tidal inlet, Ozsoy (1986) analytically modeled the sediment transport resulting from the turbulent jet. Ozsoy's (1986) results were: 1) Increasing bottom friction caused jet flow sediment concentrations to decrease and, in general, the resulting sediment deposition to become fanshaped and relatively close to the inlet mouth. 2) Decreasing the bottom slope caused sediment to be transported further offshore in elongated shoals flanking the channel. 3) Material with small settling velocities was jetted far offshore, while gains with large settling velocities were deposited closer to the inlet mouth. 4) Currents less than the critical value for the initiation of sediment movement caused sediment to deposit close to the mouth, while currents with a value much greater than critical caused sediment to be jetted farther from the mouth.

To improve the understanding of inlet delta dynamics, Gertel (198 8) used field data to relate the relative strengths of ebb and flood currents over different portions of the delta. It was shown that the resultant of the two flows having differing strengths and directions leads to flood and ebb dominated zones on the delta. Also, it was shown that ebb tidal deltas








14


Figure 1.5: Representation of the grid system for calculating delta volume, and the no inlet contours for a typical inlet (from Dean and Walton, 1973). derive their shape from the irregularity in the shear stresses produced from the summation of the two flows. Oertel (1988) further examined the combined effects of waveinducedalongshore current and the ebb and flood currents. Depending on the relative strengths of the alongshore and tidal currents, littoral material may be deposited as a spit originating from the end of the updrift barrier island, or transported into the channel to either remain there, or be jetted into either the flood or ebb tidal deltas. Oertel (1988) concluded that the downdrift biased flow field could change the position and angular orientation of the inlet channel, and the resultant shape of the ebb tidal delta. The extra sediment supply to the


Idealized No -Inlet Contour Lines


,Existing Contour LinesOcn


15'-


M.1-LW. S ho re I'ne-.Y
*. .* .:-


Ocean








15

delta system from the addition of littoral drift material could remain in the delta system or be by-passed to the downdrift shoreline.

Hayter et al. (1988) performed a laboratory study using a moveable bed model in order to examine the effects of both waves and tidal flows on inlet delta formation. One result of the study was that the delta volumes were larger in the experiments run with waves and tidal currents than in experiments using only tidal currents. An explanation for this phenomenon is that the presence of waves increases the bottom shear stress over the currentonly condition, suspending additional littoral material which is ultimately deposited in the enlarged ebb delta. Ultimately, Hayter et al. (1988) concluded that the delta volume was proportional to tidal prism, and inversely proportional to wave energy, agreeing with O'Brien.

In response to the recent trend of mining the ebb deltas for beach nourishment sediment, Mehta and Montague (1991) discussed the need for development of strategies to artificially by-pass sediment, while preserving the natural environment of the inlet. The inlet management plan includes: 1) maintenance of the inlet channel for navigation purposes. 2) restoration of the sediment by-passing pathway to the downdrift side of the inlet interrupted by dredging the inlet. 3) maintaining the pre-modification ecological balance in the vicinity of the inlet. An "active-passive boundary" was identified as the depth of closure defined by a certain storm return period. Sediment by-passing due to waves will occur at depths less than the active depth. Mining of delta sediment for beach nourishment purposes should therefore take place beyond the active-passive boundary, so that there are no significant








16

impacts to the natural state of inlet by-passing. Several possible impacts to the benthic habitats in the vicinity of the tidal inlets due to inlet modifications were discussed.

To quantify reduced by-passing across the dredge pit at an ebb delta, Walter and Douglas (1993) developed a method to predict the shoaling rate within the borrow area. The method was similar to the work on sedimentation in entrance channels by Gole et al. (197 1). Walther and Douglas (1993) considered two borrow pits of the same volume but differing dredged depths. For the particular input conditions of littoral drift, pre-dredged depth, and volume removed, the shallow pit was found to have twice the initial by-passing rate as the deep pit. The rate of increase in by-passing was larger for the deep pit, which returned to the pre-dredged condition in about five years, while the shallow pit required about fourteen years to equilibrate, with both pits eventually by-passing equal after equilibrium was achieved.

To determine the equilibrium volumes of ebb deltas, Dombrowski (1994) developed a diagnostic model to simulate the rate of delta growth strarting from a newly opened inlet until the combined shear stress due to currents and waves equals the critical stress for deposition, when further deposition ceases. Delta growth rate was shown to be a function of wave and tidal energy, suspended sediment concentration, and sediment grain size. Increasing the sediment concentration increased the rate of approach to equilibrium, but not the equilibrium volume. Increasing the sediment diameter increased both the rate of growth and the ultimate volume due to increasing shear stress needed to initiate sediment movement. Increasing the wave height decreased the rate of growth due to increases in the near bed orbital velocities, and associated shear stresses. Increasing the (X parameter defined by 0' Brien (197 1) according to Eq. 1. 1 had the effect of decreasing the delta volume. This










17


relationship between the delta volume and a was shown to be in agreement with the observed variation in delta volume at four microtidal inlets.


In order to evaluate the depositional characteristics of inlet tidal flows, Merz (1995) developed a computer code that combined previous analytical expressions for flood and ebb flows over sloping bottoms with bedload and suspended sediment transport formulas to predict sediment deposition over a tidal cycle. The model was applied to Jupiter Inlet and was shown to match the actual depositional characteristics of the delta.

Table 1.3 is a short summary of the above mentioned studies on ebb delta related


topics.


Table 1.3: A smmary of previous delta studies.

Source Significant Findings

Bruun and Described the two modes of sand transfer at inlets, bar by-passing; and tidal-flow by-passing. Gerritsen Defined the ratio of the rate of littoral drift to the tidal discharge through the inlet. A large ratio (1959) corresponds to bar by-passing and a low ratio corresponds to tidal flow by-passing. Waves and currents of an episodic nature are forces behind bar and tidal-flow by-passing. The result is
complexities in by-passing.

Bruun and Defined inlet stability ratio as the ratio of spring tidal prism passing through inlet during one-half Gerritsen tidal cycle to the average annual littoral drift reaching the inlet. Large values of the stability ratio (1960) correspond to stable and deep deltas, while small values correspond to unstable and shallow deltas.

O'Brien Noted that an inlet will be in equilibrium when the normally incident wave energy that tends to close (1971) the inlet is balanced by the tidal energy which keeps the inlet open. Determined that inlet stability is a function of wave power, width at throat, tidal period, spring tidal prism and the spring tidal
range.

Gole et al. Developed a formula to calculate the percentage of total littoral drift which will accumulate in a (1971) dredged channel due to increased depths, and the resulting, decreased current velocities across channel.

Dean and Described the nozzle and sink characteristics of tidal flows through inlets, both of which result in Walton net flow toward the inlet along the shoreline close to the inlet. Developed a method for measuring (1973) delta volume.

Walton and Grouped 44 deltas into three categories by wave energy. Related ebb delta volume to tidal prism Adams for each category, and determined that delta volume is dependent on both prism and wave energy. (1976)










18


Table 1.3: Continued

Galvin Developed a method to determine the time for channel shoaling to reduce project depth from the (1982) initial over-dredged depth to the design depth by calculating the channel shoaling rate.


Marino Described problems inherent in applying Dean and Walton's (1973) method to calculate delta (1986) volume at inlets. Found that the delta volume not only depends on the tidal prism, but on the ratio of throat width to channel depth.


Ozsoy (1986) Analytical model of a turbulent ebb jet produced by tidal flows. Related sediment fall velocity, bottom friction bathymetry, and initial velocity at the throat to sediment depositional patterns in
the delta area.


Hayter et a]. Moveable bed laboratory model study to determine the effects of wave action and tidal flow on the (1988) delta formation. Concluded that an increase in tidal prism, or a decrease in wave energy will increase the volume of the ebb delta.

Mehta and Discussed the need for development of strategies, to artificially by-pass sediment, while preserving Montague the natural environment inlets. Discussed elements of inlet management plans, and the "active(1991) passive delta" concept. Sediment by-passing due to waves occurs in depths less than the passive delta, and mining of delta sediment for beach nourishment purposes should take place beyond the active-passive, boundary so that there are no significant impacts to the natural state of inlet bypassing. Several possible impacts to the benthic: habitats in the vicinity of the tidal inlets due to inlet
modifications were discussed.

Walther and Applied Gole's (197 1) theory on by-passing/sedimentation rates around a dredged channel to two Douglas hypothetical borrow sites at an ebb tidal delta. Initially the deeper site had half the by-passing rate (1993) of the shallow site, but returned to the pre-dredged condition in 9 years, where the shallow site took 14 years to recover.

Dombrowski Diagnostic model considering the effects of wave energy, suspended sediment concentration, and (1994) grain size on delta growth, and ultimate equilibrium volume. It was shown that increasing sediment concentration increased the rate at which the delta achieved equilibrium. Increasing wave energy decreased the equilibrium volume, but increased the time to achieve equilibrium. A larger sediment size increased the equilibrium volume due to the larger shear stresses needed to mobilize the sediment. The relationship between wave and tidal effects was found to agree with previous
observations.

Merz (1995) Continuation of Ozsoy's (1986) work. Wrote a computer code which determined bed and suspended sediment loads due to both ebb and flood tidal current forcing. If offshore slope, or the friction factor are increased, the deposition patterns are held closer to shore and become narrower in the Iongshore direction, while the deposited depth increases. Depositional patterns for the Jupiter Inlet
simulation agreed with the actual depositional patterns surrounding the inlet.


If ebb deltas are to be repeatedly mined for beach nourishment, prediction of the shoaling rates within the borrow area is extremely important. The decision concerning if and








19

where to borrow sediment from the delta must be made considering the possible effects to the surrounding shorelines due to mining, and requirements for refilling of the pit for renourishment. As noted, in response to this issue Mehta and Montague (1991) defined "active" and "passive" zones, which correspond to the frequency and severity of sediment transport due to episodic wave conditions. The active zone represents the area of the most frequent wave action, and where sediment by-passing customarily occurs. It is in the active zone that delta mining should be avoided, so that any potentially adverse effects to the surrounding shorelines can be prevented.

Mehta et al. (1996) suggested that the limit to the active zone of sediment transport can be found by applying, with minor modifications, concepts derived from beach profile dynamics. As shown in Figure 1.6, the seaward limit to the active zone of sediment transport due to severe wave conditions is defined by, hid, the depth of closure. The depth at which there is no net sediment transport is defined by the crossover depth, h..0. The profile from the shoreline to the so-called crossover depth will experience erosion due to severe storms, while the profile from the crossover depth to the depth of closure will experience accretion in the form of a bar. It should be noted that the depth of closure, the length of active profile and the crossover depth are directly related to the return period of the wave episode, or increasing bottom response time (Dean et al., 1993). Thus, for example, the depth of closure for the Atlantic coast of Florida has been estimated to be from 4 mn to 7 m (Dean and Grant, 1989), while on the Genkai Sea in Japan the depth of closure has been estimated to be around 35 m (Kojima etaL, 1986).








20


lid

hco BAR h EROSIN- ---- ----


Figure 1.6: The length of active profile extends from the shoreline to the depth of closure, hid. The crossover depth, hcc, separates nearshore and offshore zones within the active length. Dashed curve corresponds to a storm profile, whereas the monotonic curve represents profile formed under comparatively mild wave conditions (from Mehta et al., 1996).


hoc
ho h

-A BARD DELTA CREST
1.0.
h = f2(y)



Figure 1.7: Schematic drawing of an idealized cross-shore profile near an inlet and episodic change in profile geometry due to wave action, where "y" is the distance offshore, "h" is the depth of the inlet profile, "yo" is the distance from the beginning of the channel to the origin of the profile defining the seaward slope of the delta, "U,," is the current emanating from the inlet, "U c" is the current over the delta crest, "k0" is the depth of the inlet channel, "h is the depth of closure and "h,0" is the crossover depth (from Mehta et al., 1996).








21


In Figure 1.7, a shore-normal bottom profile, which extends from the inlet channel to the depth of closure, is shown. Since the ebb current (U0) decreases to almost a negligible value (U~) at point A, the profile, h(y), between point A an~d B can be considered to be acted on by waves only. One can then assume that the pre-storm seaward slope of the ebb delta can be described by a function h = fl(y), and the storm seaward slope of the ebb delta as h = f2(y). The post-storm delta profile exhibits erosion in the active zone of transport, and accretion in the passive zone. If the recession of the seaward profile were to exceed the landward extent of the delta crest at point A, then wave action would penetrate the delta, thus possibly affecting the nearby shorelines significantly. The sediment which rebuilds the eroded delta profile after the storm may be transported into the eroded area either by the inlet currents, by littoral current, or by waves from the bar area. Additional modifications to the delta profile will depend on how much accretion occurred in-between wave events, and the severity of the next event. The active zone landward of the crossover depth can only be determined by the instantaneous configuration. Thus, the interpretation of the active zone of delta for mining purposes is dependent on the episodic return period of storm forcing.

It has been noted by Dombowski (1994) that a delta will approach an equilibrium volume if it is acted on by a steady state wave environment. However, Dombrowski (1994) also noted large fluctuations in the volume of sediment which defined the delta at Jupiter Inlet. It is hypothesized here that these fluctuations are a result of episodic storm events. Thus, it is the main objective of this study to develop a method to simulate the change in volume of the delta due to such episodic events. In general, the processes which occur at












22


inlets are very complex, and the problem as a whole is best attacked in parts. The results


from this study should provide a new perspective into one of these processes, namely the


erosion of deltas due to storm waves and associated surges.


This study will focus on microtidal ebb deltas, because deltas in the mesotidal and


macrotidal environment tend to behave differently. This is because the tidal energy in the


latter environments is larger compared to the available wave energy, so that the relative roles


of waves and tides are different from those at microtidal systems. Figure 1.8 is a diagram


depicting three different delta classifications and some examples. This study deals with the


environment of the bottom left third of that figure.



ELONGATE Ibirdsfoot)
RIVER

ELONGATE DOMINATED (birdsfoot)
*Solo wet season MISSISSIPPI

PO LOBATE LOBATE P HUANG
HO
DANUBE
Porong wet season\

MA HA AM


CUSPAT NILE NGR\ STRAIGHT/ GANGES. IRREGULAR BRAHMAPUTRA AMAZON

Solo dry season STRAIGHT Lorong.2g season ESTUARINE/ SENEGAL FL Y EMBAYED ORD

=A TIDAL INLETS DOINTD


STRAIGHT IRREGULAR _____ ESTUARINE/ EMBAYED



Figure 1.8: Diagram depicting the three different delta classifications (from Hoekstra, 1988).








23


1.4 Outline of Presentation

Chapter 2 deals with the construction of a generalized delta based on relevant delta characterizing parameters. A method is developed to generate the required "no-inlet" bathymetry for defining delta volume. The delta surface is constructed from equations representing the channel section, the seaward slope of the delta. The method by which the delta parameters are calibrated is described. Chapter 3 describes the delta erosion process and the methods on which the process is based. Chapter 4 investigates the sensitivity of the delta volume to the choice of the no-inlet profile. The results of the delta erosion model applied to a generalized ebb delta are discussed, and qualitatively related to case studies of delta evolution at four different inlets. Finally, in Chapter 5 the study is summarized and general conclusions are presented. This chapter concludes with some recommendations for future studies related to the subject.













CHAPTER 2
PARAMETERIZATION OF EBB DELTA VOLUME

2.1 Introduction

For the purpose of this study, it is necessary to develop a geometric method for construction of the ebb delta volume. The volume is represented by a series of generalized mathematical expressions characterized by seven delta related parameters. A specific delta can be simulated by varying these parameters until the surface generated by the mathematical expressions mimics the actual shape of the delta in question.

2.2 Delta Volume

The standard procedure to determine delta volume involves constructing parallel contour lines which would exist if no inlet were present. The depth differences between the no-inlet bathymetry and the actual bathymetry of the delta determine the volume of the ebb delta in question. This method is described in detail in Dean and Walton (1973), and was briefly mentioned in Chapter 1.

A schematic planform diagram of the delta is shown in Figure 2. 1. The delta baseline is defined as zero distance offshore, and as a result the flood channel width, CW, is defined as having a negative value. The shore-normal distance, X, is defined as: X(n,r) = r SINO -CW (2.1)


24








25


n 3



n=2 IW

cW 0 x
yV Baseline I


AShoreline RMAX Jn


Alongshore Distance

Figure 2. 1: Delta planform schematic.


where n is the integer for delta radial profile number, r is the radius along the profile and 0 is the angle of the profile with respect to the updrift shoreline. In constructing the delta surface, n = 37 profiles are developed for an adequate representation of the delta surface. Thus, each profile represents a 60 = 50 differential slice of delta. A general elevation profile is shown in Figure 2.2. The assumed pre-storm erosion delta profile is shown as a solid line, and the differential delta volume is identified by the hatched area.

The first step in developing the delta volume is to define the "no-inlet" profile. This profile is assumed to take the power-law form of Eq. 2.2, (Dean, 1977), where H is depth, X is normal distance offshore, A is a "scale factor," and M is a "shape factor."


H =AX m (2.2)


















HC


cwj


26


4- VI(n) -P OF(n)


Theoretical __seaward slope \ HS Intersection of channel profile and seaward slope N. H(n,r) = A(n)*[r-VI(n)] M(fl)

Intersection of seaward slope and no inlet profile


HNO~,r) = AN, X(n,r) NI

H(n,r) = HS + (HC-HS) TANH(7t)12 (HC-HS)/2*
*TANH (-iT + ,T/2*r/[VI(n)+OF(n)])


Radius, r


Figure 2.2: Schematic of delta elevation profile.


The form of Eq 2.2 selected for representing the no-inlet contours, where subscript NI means ''no-inlet'' is:


H NI = ANI X MNI



The determination of the variable scale and shape parameters AN and MM, is described in Section 2.3. The volume of sediment above the no-inlet elevation is considered part of the pre-storm delta.

The maximum depth in the channel from the actual delta bathymetry is used to set the depth of the ebb channel, HC (Figure 2.2). The width of the flood channel, CW, is set equal to the average distance from the shoreline to the delta baseline. Depth of delta, HS is








27

assumed constant for every radial profile, and is taken to be equal to the depth of the no-inlet profile at a distance offshore equal to the flood channel width, i.e., HS = A NICW MNI (2.4)



Delta depth, HS, is defined thus to avoid any discontinuities when considering delta profiles that are parallel to the shoreline, i.e., corresponding to 0 = 0.

In order to generate the seaward slope of the radial profiles of the delta, Eq.2.2 is modified by changing the A and M parameters, so that they exhibit a dependance on their angular position on the delta with respect to the updrift shoreline. The distance offshore is changed to distance from the radial origin of the delta, r, and a virtual origin, VI(n) is added to the profile, i.e.,


H(n,r) = A(n) [r-.VI(n)] M(n) (2.5)



Determinations of VL(n), A(n), and M(n) are given in Section 2.4. The virtual origin defines a reference point for the beginning of the seaward profile, and sets the depth of the theoretical seaward slope to zero at the origin. The seaward slope is the portion of the delta slope above the intersection with the channel profile. When the depths over the seaward slope exceed the corresponding depth of the no inlet profile, the value of the seaward slope is replaced by the no-inlet depth.

Prior to developing the flood channel portion of the delta, the intersection of the channel profile and the seaward slope must be determined. This intersection occurs at a








28

radial distance equal to the virtual origin of the seaward slope plus a radial offset, OF(n) (Figure 2.2) defined as,


r uc
OF(n)=L ]13M(n) (2.6) [A(n)where OF(n) is the distance from the virtual origin to where the seaward slope equals the delta depth. Next, a hyperbolic tangent relation is assumed for the channel profile, because of its zero slope characteristics at the end-points. Then an equation is developed so that the channel depth decreases from HG at r = 0 to HS at r = VI(n) + OF(n), i.e.,


H(n,r) = HS + (HC-HS)tanh(7r/2)- HC HS tanh(7 -+ T/2 [ r~)OFn] (2.7)





2.3 No-Inlet Geometry Parameterization

Historic surveys were used as a source of the shore-normal profiles at locations far enough updrift from the delta being studied, and far enough downdrift from the closest updrift inlet, so as not to be influenced by the delta. As an example, the profile chosen for evaluating the no-inlet condition for Jupiter Inlet, a typical microtidal entrance on the east coast of Florida, was Florida DNR Palm Beach County survey monument R-3, which is approximately 2,440 mn updrift of that inlet. Two surveys taken of Palm Beach County monument R-3, in 1978 and 1990, were combined to obtain a representative no-inlet profile. Eq. 2.4 was fitted to this profile by the least squares method to obtain the AN, and MN1








29

parameters. Appendix A gives the code used for calculating these two parameters. The result of the averaging and fitting of Eq. 2.2 is given in Figure 2.3.

2.4 Delta Geometry Parameterization

Bathymetric plots were used for determining the parameters HC, CW, A(n), M(n) and VlI(n) for constructing the delta. A location that was "central" on the delta was designated as the origin. Placement of this origin was somewhat arbitrary, and it is difficult to draw a distinct criterion for this placement. However, in general, it should be noted that the origin should be in the ebb channel, so that a line drawn through it is just seaward and parallel to both the updrift and downdrift flood channels. In case there is no discernable flood channel, the line should be drawn over, and parallel to, the delta crest, or at the inflection in the shorenormal profile. In case there is a considerable delta offset, i.e., asymmetry with respect to the updrift and downdrift shorelines, the line should cross just seaward of the recessed shorelines flood channel, and traverse the seaward shoreline. If there is a significant angular difference between the shorelines, the line should be directed over the crest of the most discernable ebb/flood channel, and traverse the other shoreline. The average depth of the channel region should be selected as HC, and the average distance from the shore-parallel line to the shoreline as CW. Figure 2.4 is an example of placement of the profile origin, with shore-parallel and shore-normnal lines.

For convenience of delta representation, eleven radial profiles were digitized from the delta surveys, spacing them every 1 8', from 180 to 1620. Two additional profiles were digitized at 90 and 1710* to better represent the behavior of the three remaining parameters, A(n), C(n) and VI(n), at very small and very large angles with respect to the updrift shoreline,













30


2 H 0.1 V X0.534


0 PB-R3-1978 0
0- 0 PB-R3-1990





00


8 00



10



0 200 400 600 800 1000 1200 1400 1600 Offshore Distance, X (in)


Figure 2.3: Least squares fit of PBC R-3 1978 and 1990 data to Eq. 2.2.






0 R-26




0 R-27



















Figure 2.4: Smple placemet of profileorign ndbslneo heebdlt2tNe5as Florida.5









31


respectively. These profiles were loaded into a program that: 1) interactively determined which digitized data point was the first on the seaward slope of the delta, 2) set the temporarily selected value of the virtual origin, Vrr, as a fraction of the first data point, 3) interpolated the distances and depths over a selected 10 m interval from Vrr to the last data point, 4) shifted the data by a distance equal to the Vrr so the first distance and depth values would be zero, 5) converted the data to a log-log format for input into the function "Polyfit" which found, M(n) = slope and A(n) = exp(y-intercept), 6) calculated the least squares error, 7) incremented Vrr by the selected value of 1 mn and, 8) executed the process until V equaled the distance of first depth point on the seaward slope of the delta. The value of Vrr that had the smallest error in the least squares fit of A(n) and M(n) was selected as VI(n), the final value of the virtual origin for that particular profile. Appendix B gives the code for fitting a digitized radial profile to Eq.2.5. Plots of the eleven profile fits for the selected February, 1980 Jupiter Inlet survey are shown in Figures 2.5, 2.6 and 2.7. It was necessary to describe the variation of the three variable parameters, A(n), C(n), and VI(n) in Eq.2.5 as functions of angular orientation on the delta planform. For that purpose, the values of all eleven A(n) were obtained through a code which fitted a parabolic equation to the data, i.e.,




A(n) =[A K (6O-n/2)]2 +AmN (2.8)



The value of AmIN was set equal to the smallest A(n) value in the data set, and AK was varied until the least squares error was the smallest. Appendix C gives this code which fits Eq.2.8




















0


0.426 H = 0.305- (R-1 39.5) 2-~

4

6

8.

10 9 deg. from upddft
0 500 1000 15
Radius, R (meters)


H = 0.127- (R-95.51)0.1 2







136 deg. from updfift


0 500 1000
Radius, R (meters)


V
0.519
2- H =0.189* (R-1 04.7)

4,



8.

10,8deg. from updrift
0 500 1000 15(
Radius, R (meters)


2 '4

a

8


1500


IV-.
0


H = 0.13- (R-1 18.3) 54deg. from upddft


500 1000
Radius. R (meters)


)0


1500


Figure 2.5: Profiles #1-4 from Jupiter Inlet delta, February, 1980.


0 0.775
H =0.062- (R-i123.3) 4

6,

8

0,72 deg. from upddft
0 500 1000 151
Radius, R (meters)

0 0.81
H = 0.058- (R-246.9) 2,

4.

6,

8

11108 deg. from updrift


0 500 1000
Radius, R (meters)


0.899 H =0.031' (R-i 55.5)
2



a6

8

irn 90 deg. from updtif


00


I
a
a,
0


1500


0 500 1000
Radius, R (meters)


0 500 1000
Radius, R (meters)


1500


1500


Figure 2.6: Profiles #5-8 from Jupiter Inlet delta, February, 1980.


32


I
a
0)
0


I
a
0)
0


H =0.165' (R-337.9)0.1 2,\

4

6

8.

10C 126 deg. from updrif


0


















4

6

8 -H = 0.266- (R-385.8)0.1 10 144 deg. from updrift
0 500 1000 15(
Radius, R (meters)


2

4

6


8


0 500 1000
Radius, R (meters)


I


0


0 500 1000
Radius, R (meters)


1500


Figure 2.7: Profiles #9-11 from Jupiter Inlet delta, February, 1980. to the data of A(n). Figure 2.8 shows the fit of the parabolic relation to the A(n) data for the February, 1980 Jupiter Inlet survey. Using the virtual origin data for the eleven profiles, and the parabolic relationship for A(n), values of M(n) were then solved for using the least squares method. Appendix D gives the code for this calculation. Plots of the eleven profile fits to find M(n) for the February, 1980 Jupiter Inlet survey are given in Figures 2.9, 2. 10, and 2.11. The values of all eleven M(n) were then inputted to a code which fitted a parabolic equation to the data, i.e.,



M(n)=MMAX-[MK (O-ic/2)]2 (2.9)


I


0


33


0

2, 4

6,

8 'H = 0.742- (R7.)0.1 10162 deg. from updrift


1500


0


0.317
H = 0.487- (R-795.9) 171 deg. from updrift


00











34


1

0.9 0.8 0.7 0.6 < 0.5

0.4 0.3

0.2 0.1


0 05 1 1.5 2 2.5 3 01. RadiansI


Figure 2.8: A-Parameter data from Jupiter Inlet delta, February 1980, and corresponding parabolic fit.


0 500 1000
Distance, R (meters)


0 500 1000
Distance, R (meters)


0.0
H =0.374* (R-104.7)0.9 2

.6




8

10 8 deg. from updrift
0 500 1000 1S
Distance, R (meters)

n.


1500


2 14




8


1500


0 500 1000
Distance, R (meters)


)0


1500


Figure 2.9: Profiles #1-4, fit with parabolic relation for A(n) and VI(n) from Appendix A.


AMIN = 0.031
Least squares AK value =0.466




)K



W


)K/

W/
W/


0.355 H = 0.465- (R-1 39.5)
2






8

I,9 deg. from updrift


I

a
w
0


0.2
H =0.224* (R-95.51)0.2 2,

4 6,



i136 deg. from updrift


H = 0. 117' (R1-118.3)0.5 54 deg. from updrift















0 .0 H = 0.052- (R-123.3)0.4
2






8

,172 deg. from updrift


0




2

4


6

8


500 1000 15
Distance, R (meters)


0.823
H =0.052' (R-246.9)








[108 den. from orf


500 1000
Distance. R (meters)


15


I a.
0


00


M


0.
H =0.031- (R-155.5)0. 2

4

6,

8

10 190 deg. from upddft
0 500 1000 15t
Distance, R (meters)

0
0.69 H. =117' (R-337.9) 2

4,

6

8

10, 126 deg. from updrift
0 500 1000 15(
Distance. R (meters)


00


:30


Figure 2.10: Profiles #5-8, fit with parabolic relation for A(n) and VI(n) from Appendix A.


0 500 1000
Distance, R (meters)


0 500 1000
Distance, R (meters)


v







H = 0.374- (R-579.9)0.1 8

n162 deg. from updiift -


1500


0 500 1000
Distance, R (meters)


1500


Figure 2.11: Profiles # 9-11, fit with parabolic relation for A(n) and VI(n) from Appendix A.


35


CLC

a


.IL~ -


0


2

4 S

6

8 -H = 0.224- (R-385.8)0.4 1n144 deg. from- updrift


nS.


CI
0
0


15001


2

4

6

8


H = 0.465- (R-795.9)0.2 171 deg. from updrift


in,.









36

The Value of Mm~x was set equal to the largest M(n) value in the data set, and M ~was varied until the least squares error was the smallest. Appendix E gives the code, which fits the parabolic relation (Eq. 2.9) to the data of M(n). Figure 2.12 shows the fit of the parabolic relation to the M(n) data for the February, 1980 Jupiter Inlet survey.

A method was developed to take the eleven virtual origin values and interpolate them so that thirty-seven data points were generated, as required for the delta modulation method described in Chapter 3. A listing of the following method is given in Appendix F.

The VI(n) values obtained from the code in Appendix A were asymmetric because the Jupiter Inlet delta is skewed in the downdrift direction. This skewness is a result of the relative strength of large northeast storm wave energy causing a significant southward longshore drift, versus the relatively small tidal energy. To simplify subsequent treatment, the raw VI values are converted to a symmetrical form by averaging. Thus, Profile #1 was averaged with profile #11, profile #2 with profile #10, etc. This averaging was done in order to obtain a symmetric delta. Figure 2.13 is the polar representation of the fitted VI values and the corresponding average VI values for the February, 1980 Jupiter Inlet survey. The eleven average VI values were converted from the polar to the rectangular coordinate system, VIx(n), and normalized, VIxN(n), by the maximum value, VIxm, according to: VIx(n) =VI(n) COSO (2.10)



VIxN,(n) = VIxM(n (2.11)

























0.8 F


0.7


2 0.5 I


0.4!F


K






MMA 0.9

Le.s sqae Kvau .5


Is.


0.3F- /


0.2 F


0.1


0 0.5 1


1.5
Radians


2 2.5 3


Figure 2.12: M-Parameter fit with A derived from hyperbolic relationship.


120 150



)K
XI


90 500


400 300 200 3 10 Wl


Rfln I W I UI


210 20


330 300


270


Figure 2.13: Polar plot of virtual origin, VI data, and the corresponding average VI values for February, 1980 Jupiter Inlet survey. Numbers on the exterior of the plot are the profile angles with respect to the updrift shoreline. Concentric circles are lines of equal radii in meters.


0.9


37


0











38


1.2 r


190.8


S0.6
0


9 0.4
0
Z

0.2


-1.5 -1 -0.5 0 0.5
Normalized Alongshore Distance


1 1.5


Figure 2.14: Average VI data normalized by the maximum alongshore and offshore distances of the virtual origin distribution, and the corresponding Gaussian fit with K = 1.52, February, 1980 Jupiter Inlet survey.


120 150













210




240g


60 600 400 30 20













30 300


270


Figure 2.15: Plot of the 37 data points of VI for input into delta modulation model. Numbers on the exterior 'of the plot are the profile angles with respect to the updrift shoreline. Concentric circles are lines of equal radii in meters.


X X






)K X


C CK


180


0








39


The standard deviations, a, of the VIx data were then evaluated from:



CF E VIxN(n)2 (2.12)




It should be noted that there is no mean term in the aF expression since a symmetrical delta has zero mean V;,N(n). A modified Gaussian distribution was next fitted to the VI ,dn) data by the least squares method, varying the ic value in Eq.2.13 until a best fit is achieved. The Gaussian distribution is:



GAUS(n)= K expf [VkxN(n)]2 (213 202 ) (2.13)(j



Figure 2.14 shows a plot of the Gaussian fit in the normalized coordinate system, which was necessary for this representation. The values were scaled up by their maximum values, and the relationship was used to solve for VI(n) in selected 5' increments for input into the delta modulation code (Chapter 3). Figure 2.15 shows the thirty-seven data points input into that code.













CHAPTER 3
DELTA EROSION MODEL

3.1 Introduction

After developing a means for geometrically describing the delta volume, a method for modulating the volume is derived. For that purpose, and approach based on Kriebel and Dean's (1993) convolution method for time-dependent beach profile response to forcing by waves and associated storm surge was used to generate post-storm deltas.

The basis for the convolution method is the Bruun Rule of erosion (Bruun, 1982). Bruun Rule is simply a response of beach profile to sea-level rise. This response is determined by shifting the profile (assumed to be in equilibrium with the prevalent sea conditions) upward by sea-level rise, and then landward until there exists a conservation of sediment mass eroded from the nearshore zone and deposited in the offshore zone, out to the limiting depth for sediment movement. A graphical representation of the Bruun Rule is shown in Figure 3. 1. The limit to the zone of sediment movement in the profile was defined by Bruun (1982) as a depth equal to twice the breaking wave height. The profile discontinuity at the limiting depth (vertically equal to "a", and horizontally equal to "s" in Figure 3.1), which is created by shifting the active profile up and back, is replaced with a deposit slope (Bruun, 1982). A diagram depicting the sea-level rise, landward shift of equilibrium profile and resulting deposit slope is given in Figure 3.2.


40









41


a SEA LEVEL RISE e






C d h



DEPOSIT ION
T R amp '



Figure 3. 1: Bruun Rule of erosion, where "s" is the recession, "1" is the active profile length, "a" is the sea level rise, "d" is the depth of active sediment movement, "e" is the berm height, and "z" is the point of no net sediment transport (from Bruun, 1988).




AFTER RISE

*\-BEFORE RISE
DEPOSIT SLOPE


Figure 3.2: Bruun Rule of erosion, with deposit slope. (from Bruun, 1988).








42


3.2 Profile Erosion

The convolution method assumes that the profile responds to a storm surge, S, analagous to sea level rise in the Bruun rule of erosion. The resulting profile recession is given by:


R~t) =R_ (I -T (31





where R_. is the equilibrium response of the profile to the steady state storm surge, S, as determined by the Bruun Rule, R(t) is the erosion at a specified time t, and T, is a characteristic erosion time- constant. If a time dependent storm surge forcing, f(t), is used then the R(t) is found by solving the equation:

R(t-t
T,
R(t) =-T Jffr) e s cT (3.2)




Solving this integral with a function which closely mimics most storm surges, f(t) sin 2(7ctTd),I where TD is the storm yeilds:


R(t)1 (I1_ p2 exp( -27ct) I [cos27ct/TD +sin2Tctfr]1 33
R.~ 2 (1 +p2) PTD (I +p2))




where ~3= 2iTTd. The erosion time-constant, T, was determined by Dean and Kriebel (1993) by running a numerical erosion model for sandy beaches. During these numerical









43

tests, the water level was elevated, the profile was allowed to equilibrate, and the time record of recession data fitted to Eq. 3. 1. The resulting equation for the time-constant is:



T= C H / + +(3.4) g"12 A"13[ 0.8B H



where Hb is the breaking wave height, A, is the scale factor for the profile, g, is the acceleration due to gravity, hb is the depth of breaking, B, is the berm height, mn is the beach face slope, Xb, is the surf zone width, and, C, is a constant. A graphical representation of the results of the convolution method is shown in Figure 3.3. It should be noted that this method is not dependent on the wave period, and assumes the wave heights are constant for the entire storm duration.

3.3 Volume Calculation

In order to calculate the volume of sediment above the no-inlet contour, the differential area between each radial profile was calculated according to,


ARE~r)=360 i(2r(35


where 80 is in degrees and r, and r2 are the specific radii between which the area is being calculated. Figure 3.4 shows a sketch of the differential area. The corresponding differential volume is then calculated by taking the difference in elevation, DH(n,r,), between the delta envelope and the no-inlet contour at each of the four points at the corners, and then multiplying by the projected planform area according to:








44


BREAKING WAVES EQUILIBRIUM RESPONSE


Figure 3.3: Beach-profile response to waves and surge where R_. is the recession at equilibrium, and R(t) is the recession at a certain time, t.
















Updrift Baselne




Figure 3.4: Differential angular planform area, where 0 is in degrees.









45


DH(n,rl) = H Nj(n,rl) -H(n,r1) (3.6)




DVOL(rl) =AREA (DH(n,rl) + DH(n,r2) + D n+1 ,r,) + DH(n +1 r2)) (3.7)







The total volume is the sum of all of the differential volumes, DVOL, for all of the selected radii between each of the angular sections.

3.4 Profile Erosion Model

The convolution method was applied to modulate the idealized ebb delta volume under wave and surge conditions. The equilibrium recession of the virtual origin and the seaward slope of the delta to the depth of limiting motion, H, for a constant surge level, S, was calculated for each selected 5' differential slice of the delta. Waves acting on each profile were assumed to be refracting in such a way that the wave energy was considered to propagate radially toward the profile origin. The recession for each profile was then found by shifting the active profile up by the selected maximum storm surge, and towards the profile origin by R., which was incremented by 1 m intervals until the volumes eroded in the nearshore zone, and accreted in the offshore zone were equal. The deposit slope connecting the seaward end of the shifted profile with the initial depth of limiting motion was lengthened with every increment in recession and, as explained later, was idealized as a modified sine-square curve, with the initial slope of the deposit slope matching the slope of the delta profile at the depth of limiting motion. The time-dependent recession, R(t), was








46

then calculated from Eq.3.3 with an assumed value of P3, the dimensionless time-constant. Finally, the change in volume of the delta was calculated as the sum of volumes eroded between the pre- and post-storm profiles. A graphical representation of the convolution method applied to an single ebb delta radial profile is shown qualitatively in Figure 3.5. The code for modulation of the ebb delta volume is given in Appendix G.

3.5 Erosional Time-Constant

The calculation of equilibrium recession, R_, of a delta radial profile is simply a geometrical exercise, but to calculate the time-dependent recession, R(t), a time-constant, T1, is needed. As noted further in Section 4.3, because of a lack of post-storm surveys of deltas, and no preceding analytical or numerical methods for determining the change in delta volume due to storm effects, the TS relation Kriebel and Dean (1993) proposed for application to beach profiles could not be applied to the delta profiles. As a result, in order to apply Eq.3.4 a value was assigned to P3 that gave reasonable recessions of the seaward slope of the delta for extreme storm conditions.

3.6 Depth of Limiting Motion

In order to apply the Bruun Rule, the limiting depth of sediment movement, H, must be

found for each radial profile. A sine function relation was used to simulate refraction of the breaking wave heights, Hb around the delta.


H b(n) =H,,sinO (3.8)



Where HO is defined as the unrefracted wave height in shore normal direction. As noted









47


P


Radius


Figure 3.5: Delta radial profile response where R. is at equilibrium, and R(t) is at a specified time, t.


earlier, the depth of limiting motion is taken to be twice the breaking wave height representative of that particular profile (Bruun, 1982), i.e.,


H.(n) = 2 H b(n)


(3.9)


Figure 3.6 is a planformn view of the delta, which illustrates the relative magnitudes and approach angles for the waves breaking on the crest of the delta.


R I I~



Area of Erosional No-Inlet Profile ~ Depth of Limiting Motion Equilibrium Response

Area of Accretion









48


Figure 3.6: Planformn view of the delta illustrating the assumed magnitudes and approach angles for the breaking waves, HB, on the crest of the delta.


3.7 Deposit Profile

The convolution method assumes a constant deposit slope connecting the seaward end of the shifted profile to the initial depth of limiting motion. When considering large surges over the delta profile, this unrealistic constant deposit slope tends to become a significant portion of the post-stormn profile. Thus, to introduce a better approximation, the deposit slope was modified in order to better resemble a natural profile and to eliminate the abrupt change in slope at the end-points. A sine-square relation was chosen for the deposit profile, since it would be possible to match the slope at the end-points to the slope of the delta profile at the depth of limiting motion, and still achieve the necessary change in elevation between the end-points. Thus, the equation of the deposit slope is described by: H(n,r)=Hm + S (*j + 1) (3.10)


Hb(n)= Ho sin Ho I Crest of Delta









49


sin 2 1 -2[rm(n) r]
R(t)



=sin 2 IS + (28-iT/2)IJnn ill
R(t) L



Where 8 is the angular offset and Rm(n) is the radius to initial sediment mobilization depth, Hm. The delta volume modulation code in Appendix G calculates a value for the slope of the delta profile at the depth of limiting motion, and solves for 8, which sets the initial slope of the deposit profile equal to the slope of the delta profile. Figure 3.6 is a non-dimensional plot of the deposit profile with an arbitrary 8. Figure 3.7 is a plot depicting the deposit profile, for arbitrary values of 8, S, R(t) and H.. The solid lines correspond to the delta profile, while the dashed line is the deposit profile.













50


0

-0.1


-0.2

-0.3


~5-0.4'--0.5~'-0.6~.-0.7-0.8


-0.9


0 0.2 0.4 0.6 0.81 [Dm(fl) D(n,r)]IR(t)



Figure 3.7: Nondimensionalized deposit slope, 6 = 0.2443461.


6.8;,






7.2



7.4



P.6 7.8



8



8.2 -


4
7 4 A


700 800785
Radius, R (in)


4
4
4


4


R(t)


4
4 4 4
4 4 4 4
4 4
4


Figure 3.8: Deposit slope for an arbitrary set of values of 5, S, R(t) and H..


800


850













CHAPTER 4
DELTA VOLUME AND EROSION

4.1 Introduction

In this chapter geometric deltas are constructed, and the effects of differing no-inlet profiles on the resulting delta volume are studied. Values of the no-inlet shape and scale factors are varied, producing both steep and flat profiles, and the corresponding changes in the delta volume are documented. Then, realistic ranges of wave and storm surge forcing are used to erode the delta, and the reduction in delta volume as well as changes in the location of the top of the delta are examined. Finally, several case studies related to delta volume change are presented and discussed.

4.2 Dependence of Delta Volume on Profile Parameters

In order to define the delta volume, the intersection of the delta profiles with the noinlet profile must be found. Under certain combinations of the parameters A(n), M(n), VI(n), An and Mni, the power-law, i.e., Eq.2.5, for delta profiles and the equation for the no-inlet profile, i.e., Eq.2.3, do not intersect. Therefore, the parameters for input into Eq.2.5 had to be chosen so that this non- intersecting situation did not occur.

Using the relationships for the coefficients A(n), M(n) and VI(n) derived from the least squares fitting of the data from the Jupiter Inlet delta, a characteristic delta was developed. The input parameters for this delta were: CW = 100 m, HC =3 m, AK = 0.079, Amin _:0.05, K~ = 0.34, Mnax = 0.8, K = 1.5, 0 = 0.35 m, Vj = 1400 mn, Yj = 800 m.


51









52

These particular values were chosen so that the resulting delta would have a maximum volume of approximately 10' m3 above the no-inlet profile. It should be noted that the relatevely small selected value of AK produced a much flatter parabolic curve shown in Figure 2.8.

For a given set of A(n), M(n), and VI(n) in the seaward slope equation, i.e., Eq.2.5, the delta volume was found to be sensitive to the slope of the no-inlet profile, i.e., Eq.2.2. When a steep no-inlet profile was chosen, the seaward slope of the delta intersected the noinlet profile in deeper water and at a larger radial distance from the profile origin, resulting in a larger delta volume than for the same seaward slope parameters intersecting a flatter noinlet profile. Figures 4.1 and 4.2 show isometric and side views of the initial delta seaward slope specified above, intersecting a steep and flat no-inlet profile, respectively. Figure 4.3 is a plot of the delta volume versus the A,,i scale parameter for different values of the KiNJ shape parameter. This plot illustrates the significant dependence of delta volume on the choice of the no-inlet profile. Table 4.1 attempts to quantify this sensitivity of the delta volume to the definition of the no-inlet profile for a specific delta seaward slope, in terms of delta volumes for two values of the no-inlet profile scale parameter, and 10% deviations from these values. As observed, the larger scale parameter, corresponding to a steeper profile, had larger differences in volume when varying the scale parameter by 10%, than for the flatter profile.

Thus, in conclusion, it is noted that the geometric parameterization of the delta volume has quantified the significance of the choice of the no-inlet profile in the determination of the volume of sediment contained in the delta. Generally, the profiles











53


2500 3000


010


0 500 1000 1500 2000 Offshore Distance (mn)


2500 3000


Figure 4.1: Isometric (a) and side (b) views of an arbitrary delta volume with parameters: CW = 100 m, HC = 3 m, A. = 0.05, C~ = 0.7, AK =0.079, Amin = 0.05, MK = 0.34,Mma0.8, Kc 1.5 m, c=0.35 m, VImx 1400 m, VIn = 800 m.





:__ _(a) . . .. . .







0 5250003000


E 5 C, i


* (b)


0 500 1000 1500 2000 Offshore Distance (mn)


2500 3000


Figure 4.2: Isometric (a) and side (b) views of an arbitrary delta volume with parameters set to those in Figure 4. 1, except with C,1i = 0.675.


K(b)










54


8




6



2 04




2


x 10


0.00


0.05


0.10 Ani


0.15


0.20


Figure 4.3: Dependence of delta volume on the no-inlet shape and scale parameters, An and Mni. The remaining delta parameters are equal to those in Figure 4. 1.



Table 4. 1: Dependence of delta volume on the no-inlet scale parameter for a given delta seaward sloe.

+1-A ~ 10% A~j Vol (m3) % Change in Volume

0.6 0.070 -- ----3.66 x 106 -----0.063 2.87 x 106 -22 0.077 + 4.66 x 106 +27

0.6 0.020 ------4.86 x 106 ----0.018 4.22 x106 -13 0.022 + 5.53 X106 +14


downdrift of inlets tend to be much steeper than the profiles updrift of the inlet. Thus, for example, if the downdrift no-inlet profile were used instead of the updrift profile, the result would be a significantly larger delta. Therefore, when for instance planning a beach


* ...... 0 .................................................


MnMn 0.6








Mhi0.5









55

nourishment project using delta sediment, it is important to accurately represent the no-inlet profile for delta volume calculation.

4.3 Changes in Delta Volume

In order to calculate the decrease in the delta volume due to severe seas, the method of Kriebel and Dean (1993), described in Chapter 3.2 was applied to each of the radial profiles. In summary, this method assumes a time-lag between storm forcing and profile response. Time-dependent profile recession is defined as a function of the ultimate profile recession and the erosional time- constant for that particular profile. The ultimate recession is defined as the maximum recession if the storm forcing conditions were allowed to become the new ambient conditions. Ultimate recession, as described in Chapter 3. 1, was investigated by Bruun (1982). The Bruun Rule of shoreline erosion due to a rising sea level states that the ultimate profile recession is derived by shifting the profile (out to the depth of limiting sediment motion defined by the ambient wave conditions) upward by the elevated water level and then landward until the volume of sediment per unit beach width eroded in the nearshore zone equals the corresponding volume accreted in the offshore zone.

In order to apply the method of Kriebel and Dean (1993), it was necessary to define both the specific portion of the radial profile to be shifted, and the erosional time-constant. The profile to be shifted is the entire seaward slope of the delta from the virtual origin out to the depth of limiting sediment motion. A value was set for the erosional time-constant which resulted in a maximum profile recession under storm conditions of approximately onehalf of the ultimate recession. The maximum time-dependent profile recession is shown in Figure 4.4. It is the intersection of the line of the non-dimensional time-dependent profile










56






0.8 orcig .Maximum Recession
0.7 ........ . .. . . . . . . . . . . . . .

0.6 ........ . .. . . .. .. . . . .. . . . .. . .. . .. . . .
0 0
0.5 R esponse....... .. .. .. ... . .. .. . .. .. ... .. .

0.4 ........ . . . . . . . . . . . . . . . . . .

0.3 ........ .. . . . . . . ... . . . . . . . . . .

0.2 ....... . .. . . . .. . . . ..:. . . . . . . .. . ... .

0.1 ........ . .. . . . .. . . . . .. .

0G
0 0.5 1 1.5 2 2.5 3 phase of storm (radians)


Figure 4.4 Plot of non-dimensional time-dependent profile recession versus phase of storm, 7ctTd, with P3 = 0, corresponding to no lag in profile response and, 7 C/2, selected for determining delta response.



response, RJR(t), derived with no lag between the sin 2(TitT ~) storm surge forcing and profile recession (corresponding to P~ = 0 in Eq. 3.3) with the line of non-dimensional profile response with a time lag between forcing and response corresponding to the selected value of P3 = 7r/2. It should be noted that the maximum profile recession will always occur prior to the end of the storm event. Profile response after that time is recovery, which has not been considered in this study.


With reference to the choice of 7 r/2, note that since at a beach both the berm and the swash zone are eroded, and are non-existent at a delta profile, values of the erosional time-constants chosen by Kriebel and Dean (1993) for beach profile response cannot be applied to delta erosion. Thus, in order to investigate the characteristic maximum storm









57

induced changes in the delta volume, a value for T, in Eq.3.3 was chosen to be equal to one quarter of the storm duration, i.e. T, = Td~/4, which yielded P3 = rCI2 from Eq.3.3. The reasoning behind choosing this value was that the resulting maximum delta erosion was seemingly reasonable relative to the ultimate delta erosion that would occur if the delta were allowed to equilibrate with respect to the increased maximum water level and characteristic wave height.

The Bruun Rule of erosion assumes profile recession in such a way that there exists a conservation of sediment eroded in the nearshore zone, and accreted in the offshore zone, as shown in Figure 3. 1. In the present analysis, the delta volume during the storm is defined as initial volume above the no-inlet profile minus the eroded volume, as shown in Figure 3.5. Defining the delta volume in this manner does not include the accretional portion of the delta profile. However, this definition seems to be qualitatively consistent with the usual way in which delta volumes at inlets are measured from surveys.

The method of Kriebel and Dean (1993) for cross-shore profile change simulation has the greatest accuracy when applied to a shoreline with straight and parallel depth contours. If waves break at a non-normal angle to the shoreline, the resulting longshore sediment transport will be constant along the shoreline, and only the cross-shore component of transport will change the beach profile. When anomalies in the shoreline exist, the shorenormal and tangential components of wave height do not remain constant, due to the changing angle of breaking waves with respect to the shoreline. As a result, both cross-shore and the longshore sediment transport vary along the shoreline in the vicinity of the anomaly.










58


X0 0



9.4A
0 ~ ~ ~ ~ H 05=1 5 3 3 4 45M5
9.3-urg (in)...

Figure............ 4.5:... Plot... of..... delt vou ed rn.som vru.som sre..o aibe aehih

9.an2f The.initia delta.. co diio is.. depicte in.... Figure....... 4 .1.....


In~~~~~~~~~~~~~~~~~~~~H thi caetecos-hr rfl eouinmdl(eut milhaelre)ror hnih

cas of1 straight. and... parallel.......... contours.............
AnEtiadetisalresoeieaoayanthprsnatepatmdltg















eire in5 tePlost-sorm chlaractuerigstom heralpols armsuthe, anlr oariaetatio wiht



clothss sheie cresoe Itoie poilehttedtion of reutilhe arer ortion of the










59



X5.2




5 . . . . . .. . . .. . .. . . . . .. . . .





0..0.5. ..1..1.5 2 5 3 .5... .4. .4 .5.. ..5
5 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ug (in)...... ... ...... ................ .....Z..... ....

Fiur4.6.Po of.... delt volume during.......... stor vesu storm.. suge -S, for va.in wave.heigh
H0an =~/2 heiita dla oniio s eice i igr 42


proil can... be.... justified.. on.... the...... bai.ta.hetnenilco pnnto .hew v. eeg.a.h
prflwhc sno osdee eecudbersosil o tasotigtiEsdmn

awa from the ... delta .. region, toward ....... the..... adjacent shoelies

The delta .. recession ...... model was ..executed.for..the.initial.delta.. configurations.in.Figures

4.1~ ~ ~ ~..... and 4.2,5 force by. difrn.omiain.o.aehigt.ntomsr.. Fgues4.





andur 4.6: ePlots ofthmmu delta volume duringth storm, versus storm surge forvaynwvehit incrang wave heihta delta woit o tee adeflate oinerls Figure s 4.4ad2.8ar simfilean o Fiufe .n 4.6 foan ital bhathyetrywihalmr compfthwat distrbuto ofe they virotul origin reading thearadialhextjaensorfteirta riiefecieysiuae




the reductios in the mniudet tidlum cursjing the seimentu ofsorse, ndth







corresponding reduction in the delta volume, as predicted by O'Brien (1971). It was found












60


3.2



3 .9


CD

0
E E 2.8 'E



2.6


X 10


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Surge (in)


Figure 4.7: Plot of delta volume during storm versus storm surge, S, for variable wave height H0 and P3 = -x/2. The initial delta condition is that of Figure 4.1 with Vhmx = 1000 and Vimy =500, effectively producing a smaller delta.

X 10


1.8 1.7




1.6


0




E 1.3
E
S1.2 1.1


1


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Surge (mn)


Figure 4.8: Plot of delta volume during storm versus storm surge, S, for variable wave height H0 and P~ = iT/2. The initial delta condition is that of Figure 4.2 with Vfrnx = 1000 and Vimy = 500, effectively producing a smaller delta.


Ho 315(m) ......



Ho 4:(M).. Ho 4.5(m) Ho =5:(m) .. .. .. .. .. .. .. .. .. .. .. .. . .. .. ..I .. .. ..( .. .. .


..... . .... .... ................. ...................... ........ H o = .4 :(m ) ..... : ......



. ............... ....... ......... .................................................... .........

Ho 4:5 (m)

........ ......... .......... ......



..........
......... ................ -5:(M )- :



.......... .......... ....... ............ .......... .........................................


Ho 5:
.5 (M)
........... .......... ......... .......... ........ ......... .......









61

that for the given initial depth of the delta crest, small waves did not mobilize sediment to a great enough depth for any considerable profile adjustment to occur. As a result, the delta with the flatter no-inlet profile had both a larger percentage of its initial volume eroded, as well as a larger total volume of sediment eroded for the same wave and surge conditions. It should also be noted that delta erosion was a function of both wave height and storm surge. The dependence of profile recession on storm surge is inherent to the method of Kriebel and Dean (1993). As a result, there would be no profile erosion in the case of of increased wave action without an accompanying storm surge. This effect is evidenced by the zero change in delta volume when forced by zero surge and any wave height in figures 4.5, 4.6, 4.7 and 4.8. Increased wave action from typical tropical or "Northeaster" extratropical storm systems will always have an associated storm surge and setup; therefore the above mentioned effect is very unlikely to occur in nature.

Plots of the delta profile recession for the steep and flat no-inlet conditions acted on by the maximum wave and surge conditions considered are given in Figures 4.9 and 4. 10, respectively. Views (a) and (b) are of profiles at 900 and 450 degrees with respect to the updrift shoreline, whereas views (c) and (d) are of the same profiles with the accretionary portions of the profiles removed. The ultimate recession is depicted by the solid line, and the maximum recession during the storm is depicted by the dashed line. For the flat no-inlet profile case, sediment was mobilized over a much larger portion of the radial profile, and much larger recessions of the virtual origin occurred than in the steep no-inlet profile case. It should also be noted that in the extreme erosional case depicted in Figure 4. 10, there was









62


Ho = 5.5 (in)


0

2

4

6

8 10


E)
W












EC


2..

4

6

8 10
0


1000 2000 Radial Distance (in)


3000


surge = 3.5 (m):

theta.= 90





(a)


U

2

4

6

8 101


n


Ea
0)







0L


0 1000 2000 3000
Radial Distance (in)


1000 2000 Radial Distance (in)


3000


Figure 4.9: End of storm radial profiles for the steep no-inlet condition with [(a) and (b)], and without [(c) and (d)] the accretionary portions of the profile included. Theta refers to the profile angular orientation with respect to the updrift shoreline. The equilibrium profile is the solid line, and the maximum recession profile is the dashed line. a large recession of the delta seaward slope, which caused an increase in the depth of the delta crest. Such a reduction in the height of the delta can cause a larger percentage of wave energy to be transmitted across the delta, which could possibly have an adverse effect on the stretch of coastline no longer partially sheltered by the delta.


2

4

6

8 10


surg6 = 3.5 (in):

.theta=45





(b)


0 1000 2000 3000
Radial Distance (in)


r


surge =3.5 (in):

theta= 90 h(6 f


surge = 3.5 (in):

*theta=45



(d).. .. . .. . . . . .. .


L









63


Ho = 5.5 (in)


0

2





0 10



2 8 10


0


0

2

4

6

8 10


surge = 3.5 (m):

theta 90

.Nh



(a)


) 1000 2000 3000
Radial Distance (in)


surge = 3.5 (in):

....theta:= 90






(c)


a)
0


2

4

6

8 10


surgo = 3.5 (m)::

tha* 4





(b)

) 1000 2000 3000
Radial Distance (in)


0 1000 2000 3000 0 1000 2000 3000
Radial Distance (in) Radial Distance (in)

Figure 4. 10: End of storm profiles for the initial condition in Figure 4.2 with [(a) and (b)], and without [(c) and (d)] the accretionary portions of the profile included. Theta refers to the profiles angular orientation with respect to the updrift shoreline. The profile is the solid line, and the maximum recessed profile is the dashed line.


The plots of the extreme erosional case in Figure 4. 10 can explain the slight up-turn in the minimum volume versus surge plot occurring for storm surges greater than 3 mn in Figures 4.6 and 4.7, and greater than 2 mn in Figure 4.8. As the surge became large relative to the total thickness of the delta above the no-inlet profile, the accretionary offshore portion of the profile was dominated by the deposit slope. Because delta volume increases when


A


surge = 3.5 (m):
...................
theta:= 45
.. . . . . . . . . . . . . . ... . ..

..........
.................. .....

the a'
. . . . .
.........................
(d)
. .. . ... .. .. .. .. . ... ... .. .. ... . ..









64

storm surges became large relative to the delta thickness, the deposit slope determined by Eq. 3.9 incorrectly simulated a large portion of the accretionary region of the radial profile. However, it should be noted that despite this problem, that assumed form of the deposit slope is an improvement over the linear deposit slope used in the Bruun rule of erosion, and provides a better qualitative description of the eroded profile.

Planform views of the evolution of the top of delta for four different wave heights and storm surge increasing from 0.5 to 3.5 mn in increments of 0.5 m for the steep and flat no-inlet profiles are shown in Figures 4.11 and 4.12, respectively. The recession of delta nose was larger in the case of the flat no-inlet contours than for the steep no-inlet contours, as also evident from Figures 4.9 and 4. 10. The plots in Figures 4.11 and 4.12 have apparent "hinge points" about which the top of delta recession swung with increasing storm surge. This hinge point is a result of the assumed mode of wave refraction around the delta, as described in Section 3.6. As the depth of sediment mobilization due to wave action decreased along with the angle between the profile and the nearest shoreline, the surf zone width on the delta became so small that little or no profile recession occurred. Also, the profiles in the range of 0' to WO with respect to the nearest shoreline for the extreme normally incident wave height of HO = 5.5 mn were not acted on by large enough waves to cause any significant profile adjustment.

The three isometric and side views of the delta volume due to the maximum storm forcing conditions for the steep and flat no-inlet profiles are in Figures 4.13 and 4.14, respectively. The decrease in profile erosion for small angles is evident in the isometric views. Since both the steep and flat no-inlet profiles had the same delta seaward profile
















1000C 800 600


400

200


1000C 800 600

400 200


-2000 -1000 0 1000O 2000


0.
-2000 -1000 0 1000 2000


a,
U
C (0

a,
0


1000 800 600


400

200


1000

800 600

400 200


0 1. 1 01 __ __ __ __ __ 1-2000 -1000 0 1000 2000 -2000 -1000 0 1000 2000 Alongshore Distance (in)

Figure 4.11: Planform. views of the evolution of the top of delta of Figure 4.1 with increasing values of storm surge and changes in incident wave height, H0. Solid line is the initial condition and the dashed lines correspond to increasing values of storm surge from 0.5 m to 3.5 m in increments of 0.5 m, with the largest deviation from the initial condition occurring


at the largest surge.
1000

t800
C
S600 a,400
0
S200
0


1000800 600

400 200-


01
-2000 -1000 0 1000 2000


1000 t800 n 600

a,400
0
S200


01C
-2000 -1000 0 1000 2000


1000 800 600

400 200


-20 00 -1000 0 10 00 20 100


-2000 -1000 0 1000 2000


Figure 4.12: Planform views of the evolution of the top of delta of Figure 4.2 with increasing values of storm surge and changes in incident wave height, H0. Solid line is the initial condition and the dashed lines correspond to increasing values of storm surge from 0.5 m to 3.5 m in increments of 0.5 m, with the largest deviation from the initial condition occurring at the largest surge.


C
a

(0


(a)


T Ho 4M Dehta Nose


65


(b)
Ho 4.5(n


(c)
Hinge -*- Ho.S5()


(d)
S Ho=.5.5 (m)


(a)

Hinge :Z


(b)
<...> Ho =4.5~,


(c)

.1 Ho 5(m,)


(d)
H= S.S (,

\X.--












66






0(a
0





-5

a.
-200



0 0 000 1500 2000 2500 3oo 000









........................... .............. ...........

5 . . . .


10 ............... ........ ..

10 500 1000 1500 2000250 30



Ofshr Ditac (m)






-5...................


......................


5 00100 0~


101500 2000 2500 3000 20


O0shr Ditacb(n


Figure~~ 4.14:...... Isometric..... (a)... an.id.b)vew.f.h.mxm m.rsinofte.etao.Fgr
4.1~~~ ~~~ due...... toicdetwv .hih,.. 55..mxmu.ug.S35madf =-t2









67

shape and the same initial nose position, a larger shore-normal recession of the flat no-inlet profile delta is evident in the two side views.

4.4 Case Studies

In connection with the above analysis, the following case studies illustrate the role of episodic sea wave conditions in modulating ebb delta volumes. For relating historical delta volumes with episodic extreme sea conditions necessary for the case studies, the hindcast Wave Information Studies, or WIS, data were acquired from the US Army Corps of Engineers (USACQE, 1996). WIS data used are wave heights calculated from historical wind speed and direction in variable depths of water at approximately every 0.50 longitude along the Florida panhandle, and approximately every 0.25' latitude along the Atlantic coast of Florida. The calculated delta volumes at the inlets chosen, i.e., Jupiter Inlet, South Lake Worth Inlet, and East Pass, were plotted versus the corresponding extreme WIS wave height during the preceding year. Note that similar plots were also made using, for example, the mean wave height of the preceding year. However, the maximum wave height, being an indicator of the extreme storms condition, yielded the best correlative results.

4.3.1 Jupiter Inlet. Florida

Jupiter Inlet in Florida is a natural entrance connecting the Loxahatchee River to the Atlantic Ocean. The spring tidal range in the vacinity of this Inlet is 1.0 mn (Dombrowski, 1994). This inlet was unstable, and has had a history of numerous openings and closures as well as updrift migration. In order to stabilize the inlet, rock jetties were constructed in 1922, extended in 1929 (Marino, 1986), and again in 1968, when the updrift fillet of sand had shifted the shoreline to the end of the updrift jetty (DCOE, 1969). Figure 4.15 is a








68

bathymetric chart of the area surrounding Jupiter Inlet, including the ebb, delta (Coastal Planning and Engineering, 1994). Figure 4.16 is a plot from Dombrowski (1994) showing delta volumes versus year with two model-calculated growth curves with a = 0. 17 (from Eq. 1. 1), H0 = 0.54 mn, and a = 0.27, H0 = 0.68 mn. The significance of this plot is that is shows how the changing wave climate changes the rate of delta development and the ultimate value of delta volume for a given value of tidal prism at the inlet.

Figure 4.17 is a plot of delta volume at Jupiter Inlet and WIS wave heights from Station Number A20 13, located in 45 mn of water, versus year for the period 1956 to 1993. In order to relate the change in delta volume to the episodic wave events, the measured delta volume is plotted versus the highest WIS wave height during the preceding year in Figure 4.18. The spike in the wave record, and the drastic decrease in delta volume between the 1979 and 1980 surveys, can be attributed to the influence of Hurricane David, which made landfall in the vacinity of Jupiter inlet on September 3, 1979. Although only the relationship between maximum wave height during the preceeding year and delta volume is being investigated, it is assumed that the large wave events have an accompanying storm surge. It should be pointed out that both the north and south jetties were extended in 1968, in order to stabilize the mouth of the inlet and improve navigation. The two lines in Figure 4.18 correspond to the delta in the pre- and post-jetty extension conditions. It appears that there is an inverse relationship between the wave height during the preceding year and the delta volume for both the pre and post jetty extension conditions. Therefore, the extension of the je tty system, and the corresponding increase in delta volume would explain the much smaller delta volume in 1957 than in 1993, even though in the preceding years extreme wave heights











69







AT A






.2 2__ __ __

:2V2.3'


.#N
-17
Prmr Bro Suc




.. ~ Fo 1995 Nrmr orwsoure






Figure 4.15: Bathymetric chart of Jupiter Inlet (from Coastal Planning and Engineering, 1994).


0.8

~0.7

0.6

;:s 0.5

S0.4
0
-> 0.2


.a0.1


0.0


1940 1950 1960 1970 1980 1990 2U0 Year


Figure 4.16: Ebb delta volume versus year with model-calculated growth envelope for Jupiter Inlet with a = 0. 17, H0 = 0.54 m, and a = 0.27, H0 = 0.68 m (from Dombrowski, 1994).


.............. ...... ..1............... ................................... .................



07




........ ............

........... .... ._ ......... ._ ........................












70


8 X 10


E



04



1955 1960 1965 1970 1975 1980 1985 1990 1995
Year

8







2


0
1955 1960 1965 1970 1975 1980 1985 1990 1995
Year


Figure 4.17: Plot of delta volume at Jupiter Inlet and WIS hindcast wave data for the time period 1956-1993 (from USACOE, 1996).


7.5

7

6.5


6,
E
05.
0


4.5

4

3.5


4.5 5 5.5 6 6.5 7 7.5
Maximum Ho (in)


Figure 4.18: Plot of the Jupiter Inlet delta volume versus maximum hindcast WIS wave height during the preceding year.


1967.
.-.. ............. 1993 ............................................
0:
..- .... ......... 1986 ... ...............................................

1979







........ ........ ...Pre.-Jotty Extentiorr .... -Post-detty-Extention ...








1980


I









71


were almost the same. It should be noted that the volumes for Jupiter Inlet in 1978 and 1981 included in Figure 4.16 were not included in Figure 4.17, because the small scale of the National Ocean Service nautical charts used to calculate those volumes greatly increased the probability of error in volume.

Customarily, the addition of jetties will cause the littoral sediment to be jetted further out into deeper water, causing the resulting delta to attain a much larger volume than in the no-jetty configuration (Marino and Mehta, 1986). Tomlinson (1991), in a study of the Tweed River Entrance in Australia whose jetties had been extended by approximately 400 m in 1960, calculated an accretion in the delta region of approximately 2x 106 in'. He stated that a new equilibrium will occur when the controlling depth over the delta decreases to the previous controlling depth, and the sediment by-passing pathway is re-established by the delta crest completely connecting with the downdrift sand bar system. Thus, from the effects of jetties apparent in Figure 4.18, it can be considered that fluctuations in delta volumes at microtidal inlets must be examined carefully for likely causative factors, in this case both waves and structural modifications.

4.3.2 South Lake Worth Inlet. Florida

South Lake Worth Inlet was artificially opened and stabilized in 1927. The spring tidal range near this inlet is 1.24 mn (Dombrowski, 1994). A sand transfer plant was installed near the end of the north jetty in 1937. In 1967 the plant was moved seaward by 36 mn and its pumping capacity was enlarged in conjunction with the north jetty extension of 125 mn. Figure 4.19 is a bathymetric chart of the area surrounding the inlet, including the ebb delta.









72


SOUTH LAKE~T INLET











Fiue .9 ahyerc hrto Suh aeWot Ilt fomOsn7 n AscitsIc
1990).50 EE


Significant shoreline offset between theupdrAiando drtshelesfapoxmey




75meit tthsilt sviil nFgr 41.TeebdetCcrtdata vrg e
rateof ,85 m3/r fom 955 o 179,and9,55 m3yr rom 979to 990







Asinte c9 amchr of JptrIlthS ot sheowsth Ith changin wae climateowilles moIfy. thenifrat fodeltae deeopmset, aewnas the ultimte det olume. Dhombrowesk (1994rodidel not incl the 1990 voJuierIlet because large phwstanf dhelt arachangn theliate gien bydthe method of Davis and Gibeaut (1990), which was used to obtain the delta base area from the











73


0
-I





C 4)


2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0


1920 1930 1940 1950 1960 1970 1980 1990 Year


Figure 4.20: Ebb delta volume versus year with model-calculated growth envelope for South Lake Worth Inlet with a = 0.03, H0 = 0. 19 m, and a = 0.60, H 0= 0.28 m (from Dombrowski, 1994).



tidal prism. In that connection it should be pointed out that if the time-dependent growth curves are correctly redrawn, they would abruptly change slope at the 1967 data point, corresponding to the extension of the jetties, and achieve an equilibrium volume greater than that in the 1990 survey sometime beyond the turn of the century.


Figure 4.21 is a plot of delta volume at South Lake Worth Inlet and WIS wave height from Station A201 1, located in 90 mn of water, versus year for the period 1965 to 1993. It should be noted that the first data point in Figure 4.21 is the only value prior to the major jetty extension. An inverse relationship between wave height and delta volume in Figure 4.18 is not apparent in Figure 4.22. The fact that the changes in wave height seemingly did not affect the delta volume is because that during the time considered, the delta was still in the process of accumulating sediment, not having achieved its new equilibrium volume due to changes in the jetty system. Therefore, if we isolate the 1967, 1968 and 1969 cluster


r-.... ...... .... . ...... ... ..... ....... .. ......... .........
....... ...... .. ... ... .. ........ .. ............ .. ............







a0.03:

.~~~~~~ ~ ~ ~ 0............... 8.... ........ .... J.. .... .....

. *... .. .. .. . .. . .. .. ..... ... ... ..... ... . . .... .. .I.. ... ... ..
--------- ------ --------__ L__ _












74


0
E
w2 1.5
0
CO



0.5 194


xi W


1970


1975


1980
Year


1985


1990


1995


8








0


1965 1970 1975 1980 1985 1990 1995
Year

Figure 4.21: Plot of delta volume South Lake Worth Inlet and WIS hindeast wave data for the time period of 1965-1993 (from USACQE, 1996).


P xlc


2.2

2

1.8 E1.6

E
.21.4
0

-5 1.2




0.8 0.6


3.5


4


4.5 5 Maximum Ho (in)


5.5


6


Figure 4.22: Plot of the South Lake Worth Inlet delta volume versus maximum hindcast WIS wave height during the preceding year.


Jetties Extended
................ ................................ ................


. ..... ............. ................................ .................................


X
. ..... ......... ................. ............ ................


C(.990







...........69 .............979.. ........ ....


.. .. . .. . 1 : . . .. . . .. . . .. . . .. .. . .. . . .

... ... ... .. . . . . .. . .. . ...967. . . . .. . .


65









75

corresponding to the years close to the jetty extension, we find that the 1990-1979 (dashed) line does indicate the anticipated inverse relationship between delta volume and wave height. It should be noted that the volume for 1978, which was included in Figure 4.20, was not included in Figure 4.21 because of the small scale of the NOS nautical chart used to calculate that volume.

4.3.3 East Pass, Florida

A navigation channel was dredged at East Pass in 1930. The spring tidal range at this inlet is 0.43 mn (Dombrowski, 1994). The channel was deepened and widened in 1945, and required subsequent maintenance dredging to sustain the 3.7 mn project depth. In 1967, the U.S. Army Corps of Engineers began the construction of converging rubble-mound jetties with a weir section in the west jetty to stabilize the mouth of the pass and improve navigation. In 1977, a spur jetty was added to the landward end of the east jetty in order to divert the ebb channel toward the centerline of the jetties. In 1985, the weir section in the west jetty was closed. The inlet channel is continuously dredged across the ebb delta in order to avoid hazardous navigation situations that tend to occur due to the rapid channel migration and shoaling (Morang and Irish, 1996).

Figure 4.23 is a bathymetric chart of the area surrounding East Pass, including the ebb delta. Figure 4.24 is a plot of the measured delta volumes at East Pass (from Morang and Irish, 1996) and hindcast WIS wave heights from Station G1028, located in 24 mn of water, versus year for the period 1965 to 1975. Figure 4.25 is a plot of delta volumes versus the highest WIS wave heights during the preceding year. It appears that there is an inverse relationship between the wave height during the preceding year and delta volume. As noted,












76


SCALE =610 m


Figure 4.23: Bathymetric chart of East Pass (from USACOE, 1990).


1970 1975 1980
Year


1985 1990





02 .....


1965 1970 1975 1980 1985 1990 1995
Year

Figure 4.24: Plot of delta volume at East Pass and WIS hindcast wave data for the time period 1965-1976 (from USACQE, 1996).


(106


-73
E
ao 2.8
E
> 2.6

02.4

19


. . . . .. . . . . . . . . . . . . . . .


X6
. . . . .. . . . .. . . . . . . . . . . . . . . .


65


1995









77






2. X106
1967





E

75
1969


2.3 1.. . . . .. . . . . . . 970 . . .. . ... .
1974
2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 Maximum Ho (in)

Figure 4.25: Plot of East Pass delta volume versus maximum hindcast WIS data during the preceding year.


construction of the converging jetty system was begun in 1967. Customarily, the addition of jetties causes the littoral sediment to be jetted further out into deeper water causing the resulting ebb delta to attain a much larger volume than for the no-jetty configuration. Therefore, the addition of a jetty system would not be responsible for the reduction in the delta volume as seen in Figure 4.25. Apparently, the relative reduction in delta volume due to increased wave heights was much more significant than the likely increase in delta volume due the equilibration of the delta system under the jettied configuration. Although WIS data were not available for the period extending to 1990, delta volumes did increase by aapproximately 0.7x 106 M3 above the pre-jetty volume in 1967.










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On October 4, 1995, Hurricane Opal occurred with an estimated 4.45 mn storm surge and a maximum wind speed of 67 in/sec. The elevated water level overtopped the barrier island, and in conjunction with the increased flood tide through the inlet and fresh water runoff, caused an extreme elevation in the Choctawhatchee River Basin. As a result, considerable water exited through East Pass. There was an extreme reorientation and erosion of the inlet channel, but no appreciable change in the planform of the inlet ebb delta crest (from Morang and Irish, 1996). As found in the delta erosion model, the maximum change in delta volume occurred some time during the storm. A post-storm survey measured the accretion on the delta that was actually derived from channel sediment when the surge receded, and the high ebb currents deposited channel sediment onto the delta.

4.3.4 Katiakati Inlet. New Zealand

The Katikati Inlet in New Zealand is bounded by a rock headland acting as a jetty stabilizing a sandy coastline on the north and a sand barrier island on the south. The spring tidal range is 1.64 in (Hume et.al., 1996). Figure 4.26 is a bathymetric chart of the area surrounding Katiakati Inlet, including the ebb delta. The delta has been classified as a storage cell for sediment, being a poor tidal by-passer under normal circumstances, but a bar by-passing delta under north storm conditions. By examining 12 aerial photographs and relating them to historical storms, Hume et.al. (1996) determined that large storms had a significant effect on the morphology of the delta, and the time period of recovery to a similar pre-storm geometry took years.

In March 1975 Tropical Cyclone Alyson, which was classified as a 30 year storm, produced large waves for a three day period. The storm was responsible for changing the



















'N


K


.0i~

'S ~ ~
(~r


0 1000 2000., Z'








., .'V t0NGT0
1?1 1 1 . . . . .


I


55


5'



is.


Figure 4.26: Bathymetric chart of the area surrounding Katiakati including the ebb delta (from Hume et.al., 1996).


2300

2200 2100 2000 1900 1800 1700 1600 1500


1940 1950 1960 1970 1980 1990 Date


Inlet, New Zealand,


2000


Figure 4.27: Ebb delta at Katiakati Inlet (New Zealand) ebb delta protrubance from the shorline over a 50 year period (adapted from Hume et.al., 1996).


79


E
C Cu


0 I
0.


LU


. ......... ........ ................... ^ .................... ..................... ........
Ek 1 1
. ............. . ... ... ....... ... ....... ......... ......


.. .......... .... .........

.......... ..... ...... ............ ...... ----............... ............... ...............
..... ................... .............. ..... ...

.................. ..................... ..................... ...........
7
..... .... ................ .

. .................. ..................... ..................... .................. ......... ........... .................


ETDproSN E3 EMprWL









80

delta from a horseshoe-like tide-dominated geometry to a wave-dominated geometry that was flattened against the coastline. This storm event changed the morphodynamics of the delta for approximately a decade. Smaller storms, which did not cause the magnitude of change experienced during the storm of 1975, have correspondingly had smaller time-scales for readjustment to the pre-storm condition. Figure 4.27 is a plot of the extent of the ebb tidal delta (ETD) in the shore-normal (SN) direction, or protrubance of the ebb delta at Katiakati Inlet over the years. Note that the excursion of the proturbance, or the nose, is qualitatively consistent with the simulation given in Figure 4.12.













CHAPTER 5
SUMMARY AND CONCLUSIONS


5.1 Summary and Conclusions

In recent years at least sixteen inlet ebb deltas on the United States East and Gulf Coasts have been mined for beach nourishment sediment. Presently, the effects of these delta minings on the processes of the inlet/beach system are not well understood. However, it is known that the mining of sediment can change the wave refraction pattern, which in turn can result in changes in the magnitude and possibly the direction of sediment transport in the vicinity of the inlet.

The main objective of this study was to determine generalized responses of the delta volume to storm forcing, and from that to develop an understanding of how real deltas respond to storms. A geometrical delta was developed by fitting a power-law equation to radial delta profiles digitized from a typical microtidal ebb delta. Then, a previously developed method of beach profile response was modified for application to the delta profiles. Finally, the response of the delta was compared qualitatively to relevant case studies. The following is a brief summary of this work.

A generalized delta geometry was first developed. This delta was idealized as a set of radial profiles originating from a central point on the delta, with a hyperbolic tangent termi describing the inlet channel and swash platform, and a power-law equation for description of the seaward slope of the delta. The scale, shape and virtual origin parameters


81









82

characterizing the seaward slope equation were variable with respect to the radial profile angle relative to the updrift shoreline.

In order to determine the quantity of material in the delta, the elevations of delta profiles were referenced to the corresponding elevations of the profile that would exist if the inlet were not present, i.e., the no-inlet profile. The calculation of the delta volume thus obtained was found to be extremely sensitive to the choice of the no-inlet profile. Since there often exist large shoreline offsets or changes in profile slope between the updrift and downdrift sides of an inlet, considerable care must be taken when choosing the location of the origin and slope of the no-inlet profile when calculating the volume of an actual delta.

To simulate the reduction of ebb delta volume due to waves and elevated surge conditions, a method derived by Kriebel and Dean (1993) to predict time-dependent beach profile response was modified and applied to the seaward slope portion of the radial profiles around the delta. This method also attempts to predict the recovery process for beach profiles. However, since the recovery process of ebb deltas characteristically differs from that of beach profiles, the application of the model was limited to the duration of the storm over which erosion occurs. Because insufficient post-storm survey data exist to calibrate the erosional time-constant for delta profiles, a value was assumed which gave reasonable results of profile recession.

The results of the model tests, which ran a range of waves and storm surges over a selected ebb delta geometry, indicate that delta erosion is dependent on both waves as well as surge. Also, the relative magnitude of ebb delta erosion was found to be a strong function of the steepness of the no-inlet profile. Deltas with flatter no-inlet profiles are found to have









83

a much larger percentage of volume lost than deltas with steeper no-inlet profiles under the same wave and surge conditions. It was also found that the nose of the delta, or the region of the delta furthest away from the shoreline, showed considerable recession, while the delta region closer to the shoreline did not experience significant adjustment. The study by Hume (1996) on the ebb delta at the Katiakati Inlet in New Zealand, where the delta morphology was determined from aerial photographs for a period of approximately 50 years, seems to agree with the model results of the overall flattening of the delta against the shoreline during extreme storm events.

Comparisons of historical delta volumes with WIS wave data showed an inverse relationship between delta volume and the maximum wave height during the preceding year at Jupiter Inlet and East Pass, confirming the laboratory observations of Hayter et at. (1988) and the analyses of Walton and Adams (1976) and Dombrowski (1994). On the other hand, there was no distinct relationship between the delta volume and maximum wave height at South Lake Worth Inlet, presumably because the ebb delta there is still growing, and has yet to achieved a quasi-equilibrium with respect to the average wave conditions.

5.2 Recommendations for Future Investigations It is concluded that not enough surveyed delta bathymetries exist for a better understand of the processes and time-scales involved in the storm-induced delta erosion and recovery cycle. In order to make a more accurate prediction of the influence of increased wave height and surge on the delta volume, or the effects of delta mining and borrow pit recovery on the surrounding shorelines, a data base of periodic as well as post-storm bathymetric surveys must be accumulated.