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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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