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Title: Notes a short course in coastal engineering, University of Florida, November 19-21, 1975
Series Title: UFLCOEL
Alternate Title: Short course in coastal engineering, University of Florida, November 19-21, 1975
Physical Description: 34, 24 leaves : ill. ; 28 cm.
Language: English
Creator: Mehta, A. J ( Ashish Jayant ), 1944-
University of Florida -- Coastal and Oceanographic Engineering Laboratory
Publisher: Coastal and Oceanographic Engineering Laboratory, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1975
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Subject: Inlets   ( lcsh )
Hydraulic models   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
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non-fiction   ( marcgt )
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Bibliography: Includes bibliographical references.
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Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
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    References
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PART II

INLET STABILITY AND CASE HISTORIES

By

A. J. Mehta2
75/020
I. INTRODUCTION


Inlet Stability

Inlets which require frequent channel dredging due to gradual shoaling,

exhibit migration, or shoal up during storms, are in general unstable and

pose a problem to the engineer. This problem of inlet stability is a complex

one, because of the rather large number of variables that go into defining

stability. The reference here is to inlets on sandy coasts only, because

in the absence of sand or similar sedimentary material the problem does not

arise. Shell is also found in varying proportions with sand. Some of this

is, new, whereas in some areas it is ancient reworked material whose size

distribution is close to that of the sand with which it is associated.


Long-term Effects and Closure

Two facets of the stability problem concern us. The first is a relatively

long-term phenomenon, ranging from a few months to perhaps a decade or more,

during which either the inlet remains stable, or deteriorates due to shoaling

of the channel and a reduction in the tidal prism. The second is the phenomenon


Notes A Short Course in Coastal Engineering, University of Florida,
November, 19-21, 1975.

Assistant Professor, Coastal and Oceanographic Engineering Laboratory,
University of Florida, Gainesville, Florida.








of inlet closure, which often occurs as a result of a single storm.

Fig. 1 illustrates an example of the long-term progression of an un-

stable inlet. Here, the littoral drift is predominantly in the direction

of the arrow, and the tidal flow through the inlet is clearly insufficient

to counter the growth of littoral spit in the direction of the drift. In

Fig. 1 (a), a new inlet has been dredged across a barrier. Under the action

of tidal flow and waves, a characteristic throat section (minimum flow area)

has developed, as in (b). In (c), the littoral spit has extended itself and

begun to constrict the throat and lengthen the channel. This has resulted

in a corresponding increase in the overall resistance to flow and a reduction

in the tidal prism. In (d) the situation has worsened. Jetties, channel

dredging and/or sand bypassing may be required to maintain the inlet at this

stage. The progression described in this sequence may occur in a few months

or in a few decades, depending on the size of the inlet, bay, availability

of sand, and the direction and intensity of the seasonal wave climate.


Example 1-1

Fig. 2 shows Indian Pass in 1873, and again in 1926. This pass was

located south of Clearwater, Florida, connecting the Gulf of Mexico to a

waterway called the Narrows. A predominant southerly littoral drift is ob-

served to have considerably elongated the channel in the period of 54 years.

A breach across the narrow barrier island is seen to have created a new

inlet. The long channel had undergone considerable shoaling, and in 1929

the pass was closed by the Corps of Engineers inasmuch as it was unstable

and contributed to shoaling in the Intracoastal Waterway at the Narrows.

----------------------------Fig. 1 (e) illustrates the case of storm closure. In this situation,
Fig. 1 (e) illustrates the case of storm closure. In this situation,














THROAT -- -


EZ$>
L---.<.


(e)
Fig. 1. (a), (b), (c), (d) Long-term Instability of a
Newly Cut Inlet.
(e) Sand Movement During Storm Closure.


LiZ


[:


EE*

































INDIAN PASS"

1873


N













27 0 50'N
Fig. 2 82U0 50' W









1926

SCALE N
I--- 2000' ---*1

Fig. 2. Unstable Progression of Indian Pass, Florida.


DIAN PASS








sand is pushed toward the entrance from all directions, not just along-

shore. Since this often occurs in a matter of hours, it is clearly a short-

term phenomenon in relation to what was described earlier. Furthermore, a

unique set of conditions are required to bring about closure, i.e., the

flood phase of flow through the inlet under a low range of tide, high on-

shore wind, storm waves of high energy but low steepness which will carry

sand ashore, sufficient storm duration, insignificant fresh water outflow

through the inlet, shallow depths at the entrance and others. Because no

thorough field or laboratory investigations involving so many parameters

have been carried out, we do not, at the present time, have engineering

criteria for stable inlet design against storm closure.

It should be noted that the phenomena associated with long-term stability

and short-term stability, or closure, clearly overlap to some extent, and

that the distinction is, to an extent, a matter of convenience only. Clearly,

the onshore-offshore sediment motion as well as the frequency of storm oc-

curance have a role in characterizing long-term stability. It is however

reasonable to use such time-average parameters as the annual mean wave power,

rate of littoral drift, tidal characteristics and prism in defining long-

term stability. On the other hand, any criterion on closure must involve

the intensity and duration of the storm.

Long-term stability criteria have been proposed by O'Brien (1931),

Escoffier (1940), Bruun (1966), O'Brien (1971), O'Brien and Dean (1972),

Johnson (1973), Mehta (1975) and others. All these criteria assume that

sufficient sand is available to alter the inlet flow cross-section in response

to the hydraulic conditions. This situation ideally exists only in the case

of unimproved inlets on sandy coasts (Fig. 3 (a)). When jetties are succes-

sfully constructed to cut off the natural flow of littoral drift, the sand


L








will bypass the inlet around the tip of the jetties, through deeper depths,

as shown in Fig. 3 (b). The length of the inlet is effectively increased

and waves no longer penetrate as before. The throat section will respond

to these changes, its area will probably increase and its position will

shift, possibly seaward. The inlet is stabilized. If the jetties are in-

effective, sand will enter the inlet, in which case the stability criterion

may be assumed to be applicable. In Fig. 3 (c) we note that in those cases

where the littoral drift is significant in both directions, even though the.

inlet may not migrate as in Fig. 1, at will:be constricted if the sand

enters from both sides as shown.


Example 1-2

Consider Sebastian Inlet on the Atlantic Coast of Florida, (Mehta and

Adams, 1975). After several apparently unsuccessful attempts beginning in

1886, this inlet was finally opened in 1924, with two short jetties flanking

the entrance. The inlet was shallow, and the jetties could not prevent a

gradual shoaling up and eventual closure in the mid-ninteen forties. The

inlet was reopened in 1948-49.with a new alignment. Jetty improvement and ex-

tensions were carried out in 1955, 1959 and 1969-70. A channel was dredged in

1962. The throat cross-section in Fig. 4 reflects the history of the inlet.

A stable section appears to have been attained.



II. LONG-TERM STABILITY CRITERIA


Prism-Area Relationship

The tidal prism is the volume of water that enters the bay during flood

and leaves during ebb. Following the original observation by O'Brien (1931)






























4000








3000








2000








1000








0


"o

- 4

-z

-m
-o

-4
m
z
0
m
o


m
-tn
o M



m z
Sm

r-

z
z

z
--I


1920 25 30 35 40 45 50 55 60 65 70 75


YEAR


Fig. 4. History of Sebastian Inlet as Reflected by the Throat Section.








and others later, empirical relationships between the prism Pm (cubic feet)

on the mean range of tide and throat cross-sectional area, A (square feet),
3
below mean water level may be expressed as


P
-= 5.3 x 104 ft. (for unimproved inlets) (2-1)
Ac

S= 5.0 x 103 .10 (for one and two jettied (2-2)
Ac m inlets)


Eqs. (2-1) and (2-2) are plotted in Fig. 5. Eq. (2-2) is due to Johnson

(1973). They are valid, strictly speaking, for stable inlets, i.e., those

that are in non-silting, non-scouring sedimentary equilibrium. If the actual

Pm/Ac at a given inlet is substantially different from the curves of Fig. 4,

the following two possibilities exist:

1. Pm/Ac is much smaller. This is the case of an inlet in which the

throat section is larger than the equilibrium size, and therefore

the inlet will contract until equilibrium is established according

to Eq. (2-1) or (2-2). Example a newly cut inlet.

2. P /A is much larger. In this case A is too small. The inlet in

this case could go either way, i.e., expand until equilibrium is

attained, or contract further until a probable closure. To determine

which of these two courses the inlet will follow, the following comp-

utations must be made.




3Add the product of surface width times one-half the mean tide range in the
inlet or vicinity, to convert cross-section below mean low water to mean
water level.




















* -, 4v-i,-,I


-~~1 -I-----


S I-
>12.4 i ~
-. 4.


4-141 '22--l
4 41:


-. in-
:7<:H.j!. IlU l.124


.' : .. .. .. .
. ..- I -- I _
-t
,,i: -.7. -- ._ -
-- !.'-e_~~~"1-. 1,0
T Ii -l

:1 iiiti-:; H i~


I -f-'--.---i--t ---T--- ---- T I
b V"6--" .. ..I--0 6 WT.f I: -. .- _'- ..... ... -
'-'-ti L-A ir. rit
^ tr;'- .... ... "' l'- ....... .1 -.... -' .... ;;it'" :"i" "o..n.. 1 2 .. -- .. .'- _Lt *-" -L ;- .. -- '-:. z
IFI1--ii T-. r H-' 'Tr r-ti 4-- I '


- t T- I
--=-. "2_L -" I -


4,r- --- l:4-i

I .. -_


4-'_>,. _--f,,I

-CI /i -- !


-- 17-


' I I I I


4 I


2 T


-T I


/L --i i - 1 ---- T-

I-~-
- :- .. -I : I -- 1 ---

^i_^;_p_ ~~t~^r


. i .
_*rI_4_;"-- L- -. I.lT,- T


- -, .. .
..... .-- .,-4 -

" ,. .i [ .7' ;:;
---" i -


1 I ,-1
:-T1114
ff;


- .1:


-I-

L t~lii


I 'I


--~--,--.-t-. ---f--- I





S :I- I
I:--',-7 :-i-_, : --7 -: ---


that .1~ 'I-i- -


I- J_ L . : -- ',+ '-. '


1, t- t


* i'.- t !- =P ..
, .. .} ^ :t; .. ...


TIDAL PRISM Pm ON THE MEAN RANGE (ft3)


Fig. 5. Prism-Area Relationships for Inlets in Sedimentary Equilibrium.


L~~ILL~IL~ I I IL I~__ I _lill__ I I


;1


' _


I-I -


~ ':'i"iji : i:''ii; t -r~-l-i:l


I


i !J


I !


! 1 -


_7









Critical Cross-sectional Area

Escoffier (1940), and later Dean (1971a)and O'Brien and Dean (1972) noted

that the hydraulics of an inlet-bay system determines a critical throat cross-

section, Ac given the inlet-bay geometry, ocean tide characteristics and

head losses in the inlet. If the actual Ac > Ac the inlet is stable, and if

Ac < Ac, the inlet will be unstable.

Under the assumption that the flow through the inlet results from the

head difference between the ocean and the bay, and that the rise and fall of

the water level in the bay is in phase, i.e., the bay water level remains

horizontal at all times, a relationship is obtained (see Part I) between the

maximum velocity Vmax through throat cross-section of the inlet and the re-

pletion coefficient K (Keulegan, 1967), defined here according to O'Brien and

Clark (1973) as,

A 2ga
K T c o Ao (2-3)
27ra0 B


where

T = tidal period,

2a = ocean tide range,

A = throat cross-sectional area below mean water level,

F = impedance.

The impedance F reflects a summation of all the head losses through

the inlet. F may be obtained from

fL
F = 1 + c (2-4)
4Rc


-11-








Here,

f = Darcy-Weisbach friction factor,

R = hydraulic radius at the throat,

L = equivalent channel length, as defined in Part I.


In Fig. 6, Keulegan's solution of the dimensionless maximum velocity,

Vax, where,

A
V T c V (2-5)
max 2nra AB max


as a function of the repletion coefficient K is presented. The application

of this curve for determining a critical throat cross-section will be il-

lustrated by an example.


Example 2-1

Consider the case of a pilot channel which is being excavated across a

barrier island to a bay of particular size. Assume the following values of

the relevant parameters (Dean, 1971a):


2a = 3.0 ft.
o
AB = 108 ft2

f = 0.03 (a reasonable value)

L = 2500 ft. (equal to barrier width)

Wc = A/Rc = 20 Rc (2-6)

T = 44640 sec.

where W is the width at the throat of this wide channel and is assumed to

be twenty times the hydraulic radius. This yields,
-4
4.66 x 104 A
K c (2-7)
1 + 83.85

c


-12-























0
0.6
E






E


0.4

0 0


S0.2






0.1 0.2 0.3 0.4 0.5 0.7 1 2 35 4 5 7 10

Repletion Coefficient, K























---t-


-..-.4i ---


.4.i::i:


- ---f--i--i
....I!
I I .


-4---


______ __________________ -v...--t .-
_:------ -4--~ _I-i
-.---- it! ---- -i-- ----i- ------i

/ -i- -- --i I- i- 1-- j I-... i

t ~ I -
I. .:. I-..~ i- ;:::: ----- C-- -I_. ~ _
-t .... I.:1--. I....4. ..:..i
-~~~., .---- -t.-.--.-------- +- --:---.---i -~

-1.. .~.. ;-i I-.
----!'----; L -'-- '
1. .: -- .i_....
.:i:: :: _-:-

S- -'--- I -tl-:.4.- :

---'--I ...-:-- T...-.


0.2 0.3 0.4 0.5 0.7


2 3 4 5


Repletion Coefficient, K

Fig. 6. Dimensionless Maximum Velocity, V'max as a Function of Keulegans Repletion
maxCoefficient.
Coefficient.


0.6






0.4


7 10








For a range of A values, Eq. (2-7) gives the corresponding K, Fig. 5

yields V'x and Eq. (2-5) gives V Fig. 7 shows the plot of Vmax versus
max max max
A The value of A (= 2000 ft2) at the peak Vmax of 5 ft/sec is defined as

A For any A > A a reduction AA in A due to sand deposition will in-

crease the maximum velocity Vmax by AVmax, thus increasing the scouring

capability of the flow and therefore the deposited sand will be flushed out.

Likewise, any increase AAc will result in a reduction AVc in the velocity,

thus aiding in the shoaling of the throat, until the throat-section returns

to Ac. This is the case of a stable inlet. For any A < Ac, a reduction

AA will mean a corresponding reduction AVmax and will enhance the possibility

of further sand deposition. Thus the inlet in this case is unstable.

In the case of a stable inlet, the actual value of A is determined by

the sedimentary equilibrium relationship, i.e., Eq. (2-1) or (2-2).

Assume that this example is one of an unimproved inlet. Note that the

tidal prism Pm may be expressed as (See Part I):

V maxAc T
S= max c (2-8)
m IC
K

where CK = 0.86. Combining Eq. (2-8) with (2-1) gives,

5.3 x 104 rCK
V Kmax (2-9)
max T


which gives


Vmax = 3.21 ft/sec (2-10)


This value of V occurs along the stable part of the curve of Fig. 6 at
max
A = 7000 ft2, which isthe hydraulically stable throat cross-section under
c


-14-


L


















i 4----,-- i-4 ------
U)
Vmax 3.21 ft/sec






-J n
>2






+Ac '
2 I ^ ----------- -1^-1 __ _------




100 o A/ 4 A6
THROAT CROSS SECTION Ac
Fig. 7. Relationship between Vmax and A ; Determination of Critical Qross-section.








sedimentary equilibrium.


Note that if the cross-section of the new pilot channel is between 2000

and 7000 ft2, sedimentary equilibrium requirement will cause the channel to

enlarge to 7000 ft2. Likewise, an initial cut larger than 7000 ft will
2
contract to that value. If however, the initial cut is less than 2000 ft2

it will be hydraulically unstable, and therefore will contract indefinitely.


A Semi-empirical Approach

One of the limitations of the hydraulic computations described above is

that they do not explicitly involve the effect of wave intensity on stability.

Clearly, high energy waves generate more littoral drift, which in turn will

cause greater stability problems for an inlet (Bruun, 1966; O'Brien, 1971;

Johnson, 1973). Recognizing the opposing roles of the waves and of tidal

flow through 'the inlet in establishing the long-term stability regime, the

following dimensionless coefficient M has been introduced as a stability

criterion (Mehta, 1975),

PT
M a (2-11)
2yAc W

where

Pa = annual average longshore wave power,

y = unit weight of ocean water (64 lbs/ft3).

and

T/2
W = VcS dt (2-12)




4Dean(1971b) and Mehta and Brooks (1973) have applied the method described
in this section to long lagoons with three inlets.


-16-


I









where

t = time,

V = velocity at the throat,

S = slope of the energy grade line in the inlet of cross-section Ac
and hydraulic radius R .

The numerator of Eq. (2-11) is the longshore wave energy over the tidal

period per unit length of the shoreline. The denomenator is the flow energy

over a tidal cycle, per unit length of the inlet. Note that yV A S is the

power per unit length available in the flow in the channel. We assume a

sinusoidal variation of V


Vc = Vmax sin at (2-13)

where a = 27/T. S is related to the Chezy discharge coeffieicnt C through

V2
S = c (2-14)
C2R
c

Substitution of Eqs. (2-13) and (2-14) into (2-12), integration, and finally,

elimination of Vmax using Eq. (2-8) leads to

P 3
W = 4.2 C2RmT2 3 (2-15)


Eq. (2-15) defines W for computing M in Eq. (2-11). The Chezy coefficient

C may be obtained from Fig. 9 of Part I. The straight line shown there may

be expressed as,


log C = 1.40 + 4 x 10-4 Ls/Rc (2-16)


-17-









Where Ls has been defined in Fig. 10 of Part I as the distance be-

tween the outer bar and the junction of the channel near the inner shoal.

The longshore wave power Pa is related to the rate of littoral drift

QL according to


Pa = 0.48 QL (2-17)


where Pa is in foot-pound per foot per hour and QL is in cubic yards per

year. In view of the possibility of sand entering the inlet from both

sides, as shown in Fig. 3 (c), Pa should be based on the "gross" rate of drift,

i.e., the sum of the drift from the left and from the right.

Mehta (1975) has computed M for a number of inlets and has defined regions

of good, intermediate and poor long-term stability in a plot of M versus P ,

by classifying known stability condition of each of the inlets into these

three categories. The stability regions are indicated in Fig. 9.


Example 2-2

Consider John's Pass and Blind Pass, Florida, both of which connect north

Boca Ciega Bay to the Gulf of Mexico (Mehta and Adams, 1975). In the past

approximately 100 years, John's Pass has widened and is a stable inlet at the

present time. Blind Pass, on the other hand, has contracted and has poor

stability. This change has been brought about, to a great extent, by the

reduction in the surface area of north Boca Ciega Bay due to the construction

of dredge fill islands, some of which are particularly close to Blind Pass.

Fig. 8 shows this reduction. Throat characteristics of the two inlets are

given below.


-18-











































1890 1910 1930


1950


1970


YEAR


Fig. 8. Reduction in North Boca Ciega Bay Area (after Mehta and Adams, 1975).


3.0


M-
CO
0
x

W


w
CO

mr


2.2





2.0


1870













Year John's Pass Year Blind Pass
Ac W A Wc

(ft2) (ft) (ft2) (ft)


1873 5100 425 1873 5790 510

1883 4640 370 1883 5340 540

1926 5720 445 1926 2250 355

1941 6850 510 1936 2420 510

1952 9140 600 1952 1690 195

1974 9500 590 1974 440 85




We will assume here that the ratio Pm/Ac obtained from recent measurements

is applicable at all times in the past. The Chezy coefficient C will be as-

sumed to be constant and equal to values obtained from recent measurements.

The annual average longshore wave power Pa has been derived from handcast

wave statistics, and will also be assumed to be the same over the years.

The tidal period T = 12 hours will be assumed. Numerical values of the

parameters for the two inlets are as follows:


-20-









Parameter John's Pass Blind Pass

P /Ac (ft) 3.79 x 104 4.98 x 104

A (ft2) variable variable

Pa (ft-lb/ft/hr) 1.04 x 105 1.04 x 105
T (hr) 12 12
Rc = W /Ac (ft) variable variable

C (ftl/2/sec) 32 37

y (Ib/ft3) 64 64




The prism Pm is obtained by multiplying Pm/Ac by the Ac at the given

year. M values are computed through Eqs. (2-15) and (2-11).


-21-


Year John's Pass Year Blind Pass
m M Pm M
(ft3) (ft3)

1873 1.93 x 108 0.19 1873 2.88 x 108 0.094
1883 1.76 x 108 0.22 1883 2.67 x 108 0.089

1926 2.17 x 108 0.18 1926 1.12 x 108 0.14
1941 2.60 x 108 0.16 1936 1.21 x 108 0.094

1952 3.46 x 108 0.14 1952 8.42 x 107 0.25
1974 3.60 x 108 0.14 1974 2.19 x 107 0.58









M versus P from the above table are plotted in Fig. 9. The trajectory

of the data for John's Pass shows that in the 100 year period covered, this

inlet has improved its stability, moving from a state of intermediate to

good stability during 1880's. Conversely, Blind Pass, which was a stable

inlet up until the early 1920's became rapidly unstable from then on, in

direct response to dredge fill operations near its bayward end, as indicated

by the overall reduction in the bay area in Fig. 8.


-22-













STABILITY COEFFICIENT M
o


--4





rri ___iiit_:- -o- _
I ____


-"I -j -- -------- -o---^
S0 .
. ..... .










-4_ -------
-, --
-'" 0 i (A




mo

" r :d::::: :::: 0
(DC.0 2":':":-': *..- '.--



gD --- -- -J-- -4 ^----- -
V' "i:I: i i: : i. i-,
-_O V. ii : .i: i ii:i:i: ::;:;: 0
,, -. r --.-...----- ^ ^ ^ ^__________ __;

: ---- \:: i *-







(. t.

L__:
3lu :~:l~~!!i iii!i ~iiii ~ :i .

:o :::








REFERENCES


Bruun, P., Tidal Inlets and Littoral Drift, Universitetsforlaget,
Trondheim, Norway, 1966.

Dean, R. G., "Hydraulics of Tidal Inlets," Unpublished Notes, Coastal and
Oceanographic Engineering Laboratory, University of Florida, 1971a.

Dean, R. G., "Coastal Engineering Study of Proposed Navarre Pass," Coastal
and Oceanographic Engineering Laboratory Report No. UFL/COEL-73/006,
University of Florida, Gainesville, Florida, 1971b.

Escoffier, F. F., "The Stability of Tidal Inlets," Shore and Beach, Journal
of the American Shore and Beach Preservation Association, Vol.8,
No. 4, 1940, pp. 114-115.

Johnson, J. W., "Characteristics and Behavior of Pacific Coast Tidal Inlets,"
Journal of the Waterways, Harbors and Coastal Engineering Division,
ASCE, Vol. 99, No. WW3, Proc. Paper 9927, August, 1973, pp. 325-339.

Keulegan, G. H., "Tidal Flow in Entrances: Water Level Fluctuations of
Basins in Communication with the Seas," Committee on Tidal Hydraulics
Technical Bulletin No. 14, U.S. Army Engineers Waterways Experiment
Station, Vicksburg, Mississippi, July, 1967.

Mehta, A. J., "A Long-term Stability Criterion for Inlets on Sandy Coasts,"
Coastal and Oceanographic Engineering Laboratory Report UFL/COEL-75/015,
University of Florida, August, 1975.

Mehta, A. J., and Brooks, H. K., "Mosquito Lagoon Barrier Beach Study,"
Shore and Beach, Journal of the American Shore and Beach Preservation
Association, Vol. 41, No. 2, October, 1973, pp. 26-34.

Mehta, A. J., and Adams, Wm. D., "Glossary of Inlets Report John's Pass
and Blind Pass," Sea Grant Publication (in Press), University of
Florida, August, 1975.

Mehta, A. J., and Adams, Wm. D., "Glossary of Inlets Report Sebastian
Inlet," Sea Grant Publication (in Press), University of Florida,
December, 1975.

O'Brien, M. P., "Estuary Tidal Prisms Related to Entrance Area," Civil
Engineering, ASCE, Vol. 1, No. 8, 1931, pp. 738-739.

O'Brien, M. P., "Notes on Tidal Inlets on Sandy Shores," Hydraulic Engineering
Laboratory Report No. HEL-24-5, University of California, Berkeley,
California, May, 1971.

O'Brien, M. P., and Dean, R. G., "Hydraulic and Sedimentary Stability of
Coastal Inlets," Proceedings of the 13th Coastal Engineering Conference,
ASCE, Vol. II, Vancouver, Canada, July, 1972, pp. 761-780.


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