WS Ba C GaC ied, 54a KS 77-3
UNS. oe Gag v
Figure
14
11. Due to differences in required boundary conditions between the
various models, and for reasons of economy, the first 17 columns of cells
along the west side of the grids (the interior area) were not used in RCPWAVE,
CURRENT, and the sediment transport model. This area is covered by Model A.
WIFM required the additional cells in the interior area in order to use the
prototype data available there for boundary conditions and to accurately simu-
late the complex tidal currents in the inlet.
The Tidal Simulation Model, WIFM
12. WIFM is a general long wave model which can be used for simulation
of tides, storm surges, tsunamis, etc. It allows flooding and drying of land
cells near the shoreline. It is a depth-averaged model so that variations in
the vertical direction are averaged in the model. It is used in the present
study to determine tidal elevations and velocities in the two horizontal
coordinate directions. The following description of WIFM is extracted from a
report by Leenknecht, Earickson, and Butler (1984).
Equations of motion
13. The hydrodynamics of the numerical model WIFM are derived from the
Navier-Stokes equations in a Cartesian coordinate system (Figure 5). The long
WATER SURFACE
BENCHMARK CATUM
Figure 5. Coordinate system for WIFM
15
wave approximations of small vertical accelerations and a homogenous fluid
yield the following vertically integrated (depth-averaged) two-dimensional
equations of continuity and momentum:
Continuity
an 0 0
ee ee (weal) ay (wel) = (7)
Momentum
YP
du du du a gu 2
= —= —- — - + +
eee ee ge Oa) tala ea VD)
Cid
Zz
2 2
= 6 gu,au cist neh e—iai(Q) (8)
2 2 x
ox oy
1/2
ov OV OV Q) gv 2
— —+y + +e — = a +
are iP Wl rev By fu + g 9 (n n,) Pa (u va)
Cd
Zz
2 2
cae over oy ER Ee (9)
ox oy y
where
nN = water surface elevation above datum
t = time
u,v = velocities in the x- and y-directions
d =n +h, the total water depth
h = local still-water depth
R = rate of water volume change in the system due to rainfall or
evaporation
= Coriolis parameter
g = acceleration due to gravity
Cc = Chezy coefficient for bottom friction
€ = eddy viscosity coefficient
16
The variable is accounts for hydrostatic water elevations due to atmospheric
pressure differences, and Es and By represent external forces such as wind
stress.
Numerical method
14. The alternating-direction-implicit (ADI) method has been used by
Leendertse (1970) and others to solve the two-dimensional equations of motion.
When the advective terms are included in the momentum equations (Equa-
tions 8, 9) the ADI method has encountered stability problems. Weare (1976)
indicates that the problems arise from approximating advective terms with
one-sided differences in time and suggests the use of a centered scheme with
three time-levels. WIFM employs a centered stabilizing-correction (SC) scheme
which is second-order accurate in space and time, and boundary conditions can
be formulated to the same order of accuracy. A brief development of the SC
scheme is presented in the following paragraphs. Note that n and h are
defined at the cell center and u and v _ at the cell faces.
15. The linearized equations of motion can be written in matrix form
as:
Wig AUL BUY = 0 (10)
where
The SC scheme for solving Equation 10 is
17
k-1
k= = oO
(1 + ) U (1 ne 22.) U Ci)
@eaqj) tf emer ee (12)
y y
where
1 At
i iF 2 Ax AS
1 At
A == — BS
SZ BY Oy
The quantities Oy. and 8 are centered difference operators, and the super-
script k indicates time-level. The starred quantities can be considered
intermediate values between the k and k+l time-levels.
16. The first step in the SC procedure computationally sweeps the grid
in the x-direction, with the second step sweeping in the y-direction. Com-
pleting both sweeps constitutes a full time-step, advancing the solution from
the k time-levell’ to the kt! time-level- The form of the difference equa—
tions for the x-sweep is given by
a qe eo we") + xs, 6. GER a) & = S (ta) = 0 (13)
— (ey = oy 2 a= CG = qo) 30 (14)
— Cle eye ts oF GD) = @ (15)
and the y-sweep by
Go eae as 7 ase (16)
ysth oe (17)
18
1 k+l g k+1 k-1
— = * = =
(v ve) + DAy o, (n n ) 0 (18)
17. Noting that v* in Equation 15 is only a function of previously
computed variables at the k-l time-level, its substitution into Equation 18
and the substitution of u* (Equation 17) into Equations 13 and 14 yield the
simplified forms
x—Sweep
se (ne TH) te a a + uh Tay + is s, Go) sO ~ C9)
eee aha Lal lt on Meneame ee
y-sweep
Reena as ae a pace acc mle i ae
eo ie thn i 8, sh gia, 2565
18. The details of applying the SC scheme to Equations 7-9 can be found
in a report by Butler (in preparation). The diffusion terms of Equations 8
and 9 are also represented with time-centered approximations. The inclusion
of diffusion terms contributes to the numerical stability of the scheme
(Vreugdenhil 1973) and serves to somewhat account for turbulent momentum
dissipation at the larger scales. While the resulting finite difference forms
of Equations 7-9 appear cumbersome, they are efficient to solve. Application
of the appropriate equation to one row or column of the grid (the "sweeping"
process) results in a system of linear algebraic equations whose coefficient
matrix is tridiagonal. Tridiagonal matrix problems can be solved directly,
without the cost and effort of matrix inversion.
19. Apart from Courant number considerations, the computational time-
step for the SC scheme in WIFM is largely governed by simple mass and momentum
conservation principles. The maximum time-step for a problem is characterized
by
19
At = v (23)
where V is the largest flow velocity to be encountered at a cell with its
smallest side length AS . The parameter n is of order 1. Therefore, the
time-step is constrained by the smallest cell width which contains the highest
flow velocity. In physical terms, Equation 23 requires that the flow cannot
move substantially farther than one cell width in one time-step.
Boundary conditions
20. WIFM allows a variety of boundary conditions to be specified, which
can be classified into three groups: open boundaries, land-water boundaries,
and thin-wall barriers.
21. Open boundaries. When the edge of the computational grid is
defined as water, such as a seaward boundary or a channel exiting the grid,
either the water elevation or the flow velocities can be specified as an open
boundary-condition. This information can be input to WIFM as tabular data, or
constituent tides can be calculated within the model during the time-stepping
process.
22. Land-water boundaries. WIFM allows land-water boundaries to be
either fixed or variable to account for flooding in low-lying terrain. Fixed
boundaries specify a no-flow condition at the cell face between land and
water. The position of a variable boundary is determined by the relationship
of the water elevation at a "wet" cell to the land elevation at a neighboring
"dry" cell. Once a water elevation rises above the level of adjacent land
height, water is initially moved onto the "dry" cell by using a broad-crested
weir formula (Reid and Bodine 1968). When the water level on the dry cell
exceeds some small value, the boundary face is treated as open, and computa-
tions for n ,u , and v are made at the now "wet" cell. Drying is the
inverse process, and mass is conserved in these procedures.
23. Thin-wall barriers. These barriers are defined along cell faces
and are of three types: exposed, submerged, and overtopping. Exposed
barriers allow no flow across a cell face. Submerged barriers control flow
across a cell face by using a time-dependent friction coefficient. Overtop-
ping barriers are dynamic. They can be completely exposed, completely sub-
merged, or they can act as broad-crested weirs. The barrier character is
determined by its height and the water elevations in the two adjoining cells.
20
The Wave Model, RCPWAVE
24. The RCPWAVE model is a linear short-wave model which considers
transformation of surface gravity waves in shallow water including the pro-
cesses of shoaling, refraction, and diffraction due to bathymetry and allows
for wave breaking and decay within the surf zone (the region shoreward of the
breaker line). Unlike traditional wave-ray tracing methods, the model uses a
rectilinear grid so that model output in the form of wave height, direction,
and wave number is available at the centers of the grid cells. This avail-
ability is highly advantageous since the information can be used directly as
input to the wave-induced current and sediment transport models, and the prob-
lem of caustics due to crossing of wave rays is avoided. The description of
RCPWAVE that follows is extracted from a report by Ebersole, Cialone, and
Prater (1986).
25. Berkhoff (1972 and 1976) derived an elliptic equation approximating
the complete wave transformation process for linear waves over an arbitrary
bathymetry constrained only to have mild bottom slopes (thus the designation
mild slope equation (Smith and Sprinks 1975)). The mild slope equation can be
expressed in the following form:
Oia, Oa 2s fy SON a 2 Te, o
x (cc, at ay (:c, oe Gone ¢=0 (24)
where
¢(x,y) = complex velocity potential
27
Oo = wave angular frequency = rT
T = wave period
c(x,y) = wave celerity =
tam Ke}
= pe, lee
eC) group velocity = ak
k(x,y) = wave number given by the dispersion relation
of = gk tanh(kh) (25)
26. Numerical solution of this equation for the velocity potential
field is an effective means for solving the complete wave propagation problem.
All
The equation can be solved using either finite element (for example, Berkhoff
1972, Houston 1981) or finite difference methods (for example, William,
Darbyshire, and Holmes 1980). Since transmission and reflection boundary con-
ditions are easily implemented into these solution schemes, this approach is a
popular one for modeling tsunami propagation and for solving problems involv-
ing the response of harbors to short and long waves. This method becomes
computationally infeasible for large scale, open coast, short-wave problems
because of its great expense.
27. The model RCPWAVE is an alternative approach for solving the open
coast wave propagation problem. It addresses the processes of refraction and
diffraction and can be applied to a large region quite economically. The
model also contains an algorithm which estimates wave conditions inside the
surf zone. This wave breaking model is an extension of the work of Dally,
Dean, and Dalrymple (1984) to two horizontal dimensions.
Wave transformation outside
the surf zone: theoretical basis
28. The velocity potential function for linear, monochromatic, plane
waves can be represented by the following expression:
¢=ae (26)
where
& H(x,y)
20
a(x,y) = wave amplitude function equal to
H(x,y) = wave height
s(x,y) = wave phase function
Here the velocity potential function describes only the forward scattered wave
field. No considerations are given to wave reflections. By substituting this
expression for the velocity potential into Equation 24 and solving the real
and imaginary parts separately, two equations can be derived (Berkhoff
(1976)), namely,
2 2
coma’ + -— + ay (v2 ° vee,)) oF a - lnalj = 0 (27)
ox dy ace
Ve (a°ce, Vs) = (28)
22
where the symbol V denotes the horizontal gradient operator.
29. Together, these equations describe the combined refraction and
diffraction process. Diffraction is often erroneously described as the
propagation of energy along wave crests which are defined to be perpendicular
to the wave phase function gradient Vs . Equation 28 shows energy is still
propagated in a direction perpendicular to the wave crest. Diffractive
effects do change the phase function as a result of significant gradients and
curvatures of the wave height. These changes cause the local wave direction
to vary. If diffractive effects are neglected, Equations 27 and 28 reduce to
those describing pure refraction in which the wave number represents the mag-
nitude of the phase function gradient.
30. Linear wave theory assumes irrotationality of the wave phase
function gradient. This property can be expressed mathematically as
Vx (Vs) = 0 (29)
The phase function gradient can be written in vector notation as
>
>
Vs = |vs | cos 6@it [Vs | sin 6 j (30)
> >
where i and j are unit vectors in the x- and y-directions, respectively,
and 0(x,y) is the local wave direction. Equations 29 and 30 can be combined
to yield the following expression:
0) 0)
a (|vs| sin 6) - ay (|vs| cos 6) = 0 (31)
If the magnitude of the wave phase function is known, local wave angles can be
calculated from Equation 31. Similarly, Equation 30 can be substituted into
Equation 28 to yield
p) 2 p) 2 .
ae (a cc, |vs| cos 6) + aH (a cc, |Vs| sin 9) = 0 (32)
This form of the energy equation can be solved for the wave amplitude function
a once the wave phase characteristics Vs and 6 are known. The wave
23
height can be determined and is proportional to the amplitude function since
wave frequency is constant.
31. Equations 27, 31, and 32 along with the dispersion relation
describe the combined refraction and diffraction process for linear plane
waves subject to the restrictions that the bottom slopes are small, wave
reflections are negligible, and any energy losses are very small and can be
neglected. These equations are assumed to be valid outside the surf zone.
The numerical solution scheme used to solve these equations is presented in
the next section.
Wave transformation outside
the surf zone: numerical solution
32. The three governing equations (27, 31, and 32) are solved using
numerical methods. Partial derivatives within the equations are approximated
using finite difference operators. Finite difference solution methods require
the construction of a computational grid system or mesh. Solution accuracy is
directly related to resolution within the grid system. Discussions throughout
this section refer only to grid systems comprised of constant sized, rectangu-
lar cells. RCPWAVE is capable of computing solutions on variably sized, rec-
tilinear grid systems.
33. Figure 6 shows nine rectangular cells which make up a small part of
a larger mesh. Each cell has a length equal to Ax in the x-direction and
Ay in the y-direction. The maximum values of i and j are M and N,
respectively. All variables which vary as a function of space are defined at
the cell centers (see Ebersole, Cialone, and Prater (1986) for details of the
finite difference procedure used).
34. Model input includes values of the deepwater height Hy » direction
on » and period T of waves to be simulated. It also includes specification
of the bottom bathymetry throughout the grid. The wave number, which is
related to the wave period and the local water depth through the dispersion
relation, is computed at every cell. It is used as an initial guess for the
magnitude of the wave phase function gradient. The wave celerity c and the
group velocity e are functions of the wave period, wave number, and water
depth. Therefore these variables can be calculated at each cell.
24
j=1TON y - AXIS
i=1TOM
a
x - AXIS
Figure 6. Definition of coordinate system and grid cell
conventions used in RCPWAVE
35. From Snell's law,
aa waren (88)
where cy is the deepwater wave celerity (defined to be gy, an estimate of
the local wave angle is obtained everywhere. This estimate assumes that the
bottom contours are parallel with the y-axis. If the bottom bathymetric
contours make a known nonzero angle with the y-axis, a better first guess for
the wave angles can be made. The new approximation is
sin(®@ - 6 )
Dee Oe Ce a6 (34)
ZS)
"The local wave angle, deepwater wave
where 6, defines the "contour angle.'
angle, and contour angle follow the angle convention shown in Figure 7. The
contour angle is an input parameter for RCPWAVE.
y- AXIS
POSITIVE 0,
NEGATIVE 6,
6
Necarive| & POSITIVE 5
x - AXIS 6, =DEEPWATER WAVE ANGLE
@ =LOCAL WAVE ANGLE
6, =OFFSHORE CONTOUR ANGLE
Figure 7. Definition of angle conventions used in RCPWAVE
36. Wave heights at each cell are estimated as the product of the deep-
water wave height, a shoaling coefficient we and a refraction coefficient
K , thus
r
H = HK re (35)
where
cos on 1/2
Kr a cos 8 (36)
26
and
1 1/2
K = —— 0.0... .C.C.:.:.:. se _ -
s 2kh
E + sarc | tanh(kh)
(37)
The dispersion relation, Snell's law, and this simple estimator of the wave
height allow an initial guess to be made for the variables of interest
throughout the grid system.
37. The solution scheme implements the following marching procedure
once initial guesses for the variables of interest have been made. Starting
at the offshore row eeionaced by i=M-3 , Equations 31 and 32 are used to
compute wave angles and then heights along the entire row (from j=2 to j=N-1).
Wave height is used interchangeably with amplitude function since one is
directly proportional to the other.
38. Wave angles and heights along a given row are solved for itera-
tively because of the implicit differencing formulation used. Calculations of
the wave angle (actually the sine of the wave angle) and the wave amplitude
function are repeated until the average change (along a row) in each variable
from one iteration to the next is less than some tolerance. These convergence
criteria, 0.0005 for sines of the wave angles and 0.001 ft (or a metric equiv-
alent) for wave heights, are suggested values for prototype applications.
39. This solution considers only refraction since the wave number k
is used as an estimate of the magnitude of the phase function gradient. Equa-
tion 27 is then used to compute the true magnitude of the wave phase gradient.
This "new wave number" accounts for the effects of diffraction. Backwards
differences are used to approximate the x-derivatives because they only re-
quire information which has already been computed. Next, Equations 31 and 32
are again solved in order to compute the wave angles and heights using these
new wave numbers. This procedure is repeated along the row under considera-
tion until the change in new wave number, from one iteration to the next, is
less than 0.5 percent of the newly computed value. This condition must be met
at each cell along the row. As a row of new wave numbers is computed, the
values are filtered in the y-direction using the method of Sheng, Segur, and
Lewellen (1978). This filter removes cell-to-cell oscillations introduced as
a result of the differencing scheme used to compute the new wave numbers.
Row-by-row marching proceeds until solutions are computed along row i=2.
ZA]
40. Lateral boundary conditions for a row are specified at the conclu-
sion of calculations for that row. The value of all variables at cells j=N
and j=l are set equal to their values at cells j=N-l1 and j=2 , respec-
tively. This boundary condition implies that the change in the variable in
the y-direction is zero. The condition is most valid when the bathymetric
contours are nearly straight and parallel to the y-axis. For this reason the
grid is oriented so that the y-axis is nearly parallel to bottom contours
along the lateral boundaries.
41. Boundary conditions along the offshore boundary of the grid are
used to initiate the shoreward marching algorithm. They are computed from
deepwater wave input supplied by the user along with the following assumption.
Bottom contours extending from the offshore grid row (i=M) out to deep water
are assumed to be straight and parallel to a line making an angle of 00 with
the y-axis. In other words, Snell's law is assumed to be valid from deep
water to the outer boundary of the grid system. No inshore boundary condi-
tions (along row i=l) are required because of the forward marching solution
scheme.
Wave transformation
inside the surf zone
42. Waves approaching the very nearshore zone tend to steepen and
eventually break because of decreasing water depths. Shoreward of this break-
ing point dissipative energy losses due to turbulence strongly influence the
wave height. Linear theory does not allow for prediction of the breaker loca-
tion nor for wave transformation across the surf zone. Instead, empirical and
approximate methods must be used to describe the breaking process.
43. The first aspect to consider in surf zone transformation of waves
is incipient wave breaking. RCPWAVE uses the following criterion of Weggel
(1972):
H, = ——— (38)
where
Hy = breaking wave height
28
1.56
fs te
@ a ee)
m = bottom slope
hy = water depth at breaking
A018. @oor™)
because it accounts for bottom slope and wave period.
44. Once the incipient breaking point is defined, a mechanism is needed
to transform the breaking wave across the surf zone. The transformation
algorithm selected for use in RCPWAVE (Dally, Dean, and Dalrymple 1984) uses
an energy flux basis. Through analogy with energy loss in a hydraulic jump in
a channel, the following equation is postulated for one-dimensional transfor-
mation of waves advancing in the -x direction:
acre ss
Goo i fee, m Gey) | on
where
Ec_ = energy flux associated with the breaking wave
K = rate of energy dissipation coefficient (set equal to 0.2 in
RCPWAVE)
(Ec_) = stable level of energy flux that the transformation process
8 s seeks to attain
The right side of Equation 39 is simply a dissipation term. The subscript s
is used to denote the stable level of a variable. Substituting the linear
wave theory estimate for E (E = 0.125 a) into Equation 39 results in the
following expression:
2
d(H c_)
Be Ee cu He
dx hl? sg (x a) (40)
45. Various field (Thornton and Guza 1982) and laboratory (Horikawa and
Kuo 1966) experiments have shown that, well into the surf zone, the wave
height tends toward a stable value which is proportional to the local water
depth. This relationship can be expressed as
29
H_ = Th (41)
where
ia
I
stable wave height
T = proportionality coefficient (set equal to 0.4 in RCPWAVE)
Equation 40 can now be rewritten as
K 2 2. 2
=-|]Hec - Pla & =D 42
h g ( a oe
46. This surf zone wave transformation model, extended to two dimen-
sions, can be incorporated into the conservation of wave energy equation
(Equation 28) by simply adding a dissipation term D to the right side. The
function D must now represent dissipation in the direction of wave prop-
agation. Also for dimensional consistency, the term D must be multiplied by
the wave celerity and the magnitude of the wave phase gradient, and the wave
height must be replaced by the wave amplitude function. In vector notation,
the energy equation becomes
Vw (ace, Vs) = = ace, |Vs| - (&) rh? ce, |¥5| 5 (43)
This equation can be thought of as being valid both inside and outside the
surf zone. Outside, the coefficient k is zero, and the equation reduces to
Equation 28.
47. All discussion relating to wave transformation within the surf zone
up to this point has addressed the problem of determining wave heights. The
problem of wave phase must be addressed also. Diffraction effects are assumed
to be negligible inside the surf zone. Therefore, the wave number k is as-
sumed to accurately represent the magnitude of the wave phase function gradi-
ent. The linear wave theory assumption that the waves are irrotational also
will be assumed to remain valid inside the surf zone. Consequently, wave
angles are computed in the same manner as outside the surf zone. Details con-
cerning the numerical solution inside the surf zone can be found in Ebersole,
Cialone, and Prater (1986).
30
The Wave-Induced Current Model, CURRENT
48. When waves break and decay in the surf zone, in general they induce
currents in the longshore and cross-shore directions and changes in the mean
water level. These currents play a major role in the movement of sediment in
the nearshore. They are computed using the model CURRENT.
Equations of motion
49, The hydrodynamic equations used in the model for wave-induced
currents may be derived from the Navier-Stokes equations (for details, see
Phillips 1969 and Ebersole 1980). It is assumed in the derivation that the
fluid is homogeneous and incompressible, and the vertical accelerations are
negligible so that the pressure distribution is hydrostatic. By vertically
integrating the three-dimensional form of the equations and applying appropri-
ate boundary conditions, the depth-averaged two-dimensional form of the equa-
tions of motion and continuity are obtained. These equations are derived by
time-averaging over a time interval corresponding to the period of the waves.
Referring to a Cartesian coordinate scheme (Figure 8), these are:
Momentum
= chs) 0s OT
OW a g§ Magy Beg Mos g “ul x, Sy) a 0 (44)
ot ox oy ox od bx od ox oy oy
= 3s os oT
oV OV aV an 1 1 x y 1 xy
+U—+V— —+= = -- =
ot u ox M oy wi oy i pd "by ne od ( ox i oy p Ox ¢ (2)
Continuity
an , 2 3 =
: + ax (Ud) + Dy (Vd) = 0 (46)
where
U and V = depth-averaged horizontal velocity components at
time t in the x- and y-directions,
respectively, ft/sec
n = displacement of the mean free surface with
respect to the still-water level, ft
p = mass density of seawater, silmaayizee
31
Au
i}
n + h = total water depth, ft
€ and T = bottom friction stresses in the x- and
bx by 2
y-directions, respectively, lb/ft
S 5 8 » and $ = radiation stresses which arise because of the
xx xy Ws/
excess momentum flux due to waves (refer to
Longuet-Higgins and Stewart (1964) for their
significance), lb/ft
T = lateral shear stress due to turbulent mixing,
1b/£t2
2S)/
a. CROSS-SECTION A-A
OCEAN fe Breaker LINE
BOUNDARY
STILL-
LINE / ee pee
V. =
A m A
{ / 6 >o0h — a {
[ D
> (@) ap aD
Sm
4
: :
| \ 2 -*— SET-UP LINE
b. PLAN
Figure 8. Definition sketch for an irregular beach
(swl = still-water level)
32
The condition yn > 0 is known as setup, and n <0 is called setdown.
50. Bottom friction. At present, the numerical model uses a linear
formulation for friction (Longuet-Higgins 1970). Thus
Te 2oc <|(M |= U (47)
Thy =Hoe <[uyepl? V (48)
where c is a drag coefficient (of the order of 0.01) and <|u is the
>
eras
time average, over one wave period, of the absolute value of the wave orbital
velocity at the bottom. From linear wave theory
2H
<|u ~ WP gin Tan
|>
(49)
orb
Equations 47 and 48 are based on the assumption that the velocity components
U and V of the current are small compared with the wave orbital velocity,
6
| Be
51. Radiation stresses. The radiation stresses are of major importance
since they furnish the main forces for creating wave-induced currents. Refer-
ring to Longuet-Higgins (1970), for monochromatic waves, they are defined in
terms of the local wave climate as follows:
Seeeene | (x -5) eos Q + (n - ) eine | (50)
E n cos 9 sin 9 (51)
S
xy
S E (2n - +) ster @t+(n- ib Boaa fs) (52)
yy 2 2
where
okh
( Sein an (53)
Nie
33
(n is the ratio of wave group celerity to phase celerity), 9 is the local
wave direction (defined as shown in Figure 8), and E is the wave energy
density. The values of H, k, and @ are obtained from RCPWAVE.
52. Lateral shear. In the numerical model, the coordinate scheme is
chosen such that x is positive in the offshore direction and y is approxi-
mately in the alongshore direction. An eddy viscosity formulation is chosen
for the lateral shear. The eddy viscosity is assumed to be anisotropic.
Denoting - and ey as the eddy viscosities in x- and y-directions, respec—
tively, in general, - is assumed to be a function of x and y and ¢ a
y
constant. Accordingly,
= Bae &
Txy o(c, ay fi x =) ee)
For field applications, the eddy viscosity Ey is chosen according to the
following relation given by Jonsson, Skovgaard, and Jacobsen (1974):
2
_, ele is 2
€ 7 os 0 (55)
4n h
x
This represents twice the value used by Thornton (1970). The value of ¢
was, in general, taken to be equal to the value of . at the deepest part
(usually near the offshore boundary) of the numerical grid.
Method of solution
53. In view of the similarity among Equations 44-46 and the equations
for long waves (Equations 7-9), CURRENT was developed by modifying WIFM. Thus
CURRENT also is an implicit finite difference model and uses the SC scheme
described previously. Details of the method of solution can be found in
Vemulakonda (1984).
Initial and boundary conditions
54. In order to solve the problem under consideration, appropriate
initial and boundary conditions must be specified. Usually an initial condi-
tion of rest is chosen so that n » U , and V are zero at the start of the
calculations. To avoid shock, the radiation stress gradients are gradually
built up to their full values over a number of time-steps. The numerical
computation is stopped when a steady state is deemed to have been reached.
34
55. The numerical model permits various types of boundary conditions
among which are the following:
a. "No flow" (wall). This type of boundary condition is used at
FF closed boundaries such as the still-water line on beaches and
at impermeable structures. The normal velocity is set to zero
in this case.
Io
Uniform flux. In this type of open boundary condition, the
flux at a boundary cell is made equal to that at the next
interior cell. Thus the condition assumes 9(Ud)/ax = 0 or
9(Vd)/d3y = 0 at the boundary. This type of condition is used
for the lateral boundaries since it is a passive condition.
c. Radiation. This open boundary condition requires that any
transients developed initially inside the numerical grid should
propagate out of the grid as gravity waves. It is of the form
dn/ot + c(dn/dx) = 0 where c is the phase speed of a surface
disturbance n(x,t) . It is often used by the wave-induced
current model at the offshore boundary and is found preferable
to a wall or constant elevation condition there. Both of the
latter conditions are highly reflective, and, as a result, the
transients tend to bounce back and forth between the offshore
and nearshore boundaries and take a long time to damp out. On
the other hand, the radiation condition seems to work quite
well, allowing the transients to propagate out of the grid and
permitting the setdown at the offshore boundary to assume an
appropriate value.
56. The boundary conditions frequently used in the wave-induced current
model are illustrated in Figure 9.
57. At present, the model allows for subgrid (thin-wal1) barriers such
as jetties, provided they are impermeable and nonovertopping. The program
essentially sets to zero the velocity component normal to the appropriate cell
face.
The Sediment Transport Model
58. The sediment transport model predicts the transport, deposition,
and erosion of noncohesive sediments such as sands in open coast areas as well
as in the vicinity of tidal inlets. It accounts for both tides and wave ac-
tion by using for input the results of WIFM, RCPWAVE, and CURRENT in terms of
tidal elevations and currents, wave climate information, wave-induced cur-
rents, and setups at the centers of grid cells. The model computes transport
separately for straight open coast areas and areas in the vicinity of tidal
inlets. In the case of the former, transports inside and outside the surf
zone are treated separately.
35
SHORELINE: NO FLOW (WALL)
T SW
Y
X
UNIFORM
FLUX
Vid, = Voda
UNIFORM
FLUX
V3d3 = Vada
OFFSHORE: RADIATION CONDITION
On 3 On =
me! Or 8
Figure 9. Boundary conditions used in numerical model CURRENT
Transport inside the surf zone
59. Inside the surf zone it is the wave breaking process that is
primarily responsible for the transport of sediment. This process is quite
complex and not well understood. There is even considerable disagreement on
the primary mode (bed load or suspended load) of sediment transport in the
surf zone (Komar 1978). Thus a model that determines transport in the surf
zone must be empirical, to some degree, in its formulation.
60. The surf zone transport model used in this study is based upon an
energetics concept developed by Bagnold (1963) who reasoned that the wave
orbital motion provides a stress that moves sediment back and forth in an
amount proportional to the local rate of energy dissipation. Although there
is no net transport as a result of this motion, the sediment is in a dispersed
and suspended state so that a steady current of arbitrary strength will trans—
port the sediment. Thus breaking waves provide the power to support sand in a
dispersed state (bed and suspended load), while a superimposed current (litto-
ral, rip, tidal) produces net sand transport.
61. The total littoral transport rate I, (vertically integrated and
parallel to the shoreline) within the surf zone can be related to the wave
conditions at the breaker line by
36
I = ie) sin cos a, (56)
b
where
I = immersed weight sand transport rate (1b/sec)
K = empirical coefficient
On = breaker angle
and the subscript b is used to denote conditions at the breaker line.
62. Following Komar (1977), the local (vertically integrated) immersed
weight longshore transport rate, per unit width in the cross-shore direction,
may be written as
tk, 2
a Mee (0.5f£) ogy hv, (57)
where
ky = coefficient to be determined
f = drag coefficient
y= : = breaker index
Moons local longshore velocity
63. By integrating i, across the width of the surf zone Xp
*b
I) = f i, dx (58)
0
or
“b
tk 2
< 1 H
I, Sea, (0.5f£) oo J h v, dx (59)
under the assumption that the coefficients ky and f are constants for a
particular field site. Since the values of H , ) >» and h are known,
being input to the sediment model, the integral on the right side of Equa-
tion 59 may be determined numerically. For example, using the trapezoidal
rule,
37
2
ae i Ha te y So | ay i Bg, Yee oy
2 = Hee Ae
0
where IMAX corresponds to the number of water cells within the surf zone.
Equation 60 allows for a gradual variation in cell size Ax . The velocity
Vo is taken as the magnitude of the resultant of the total velocity
components u, and v,, in the x- and y-directions. Thus
T T
Viens uw, + vs (61)
where
up =u +U (62)
AE cals +V (63)
For each computational grid line from the shoreline to the breaker line for
each time-step, the value of I, is used to determine the unknown coefficient
k, from Equations 56 and 59:
2
KH “e, sin Oh cos os
iS ie we I, ()
The value of K is taken to be 0.39 if significant wave heights are used as
in this study (Shore Protection Manual (SPM) 1984).
64. Once kK is known, the local transport rate i, may be determined
from Equation 57 and hence the local volumetric sediment transport rate dy >
as in the following equation:
2
mk, foy hv,
> ey oy & se)
where
0 = mass density of solids
2.65 9 for sand
ir
jah)
u
ratio of volume of solids to total volume of sediment
0.6 for sand
38
It is not necessary to know the value of f in order to solve for de in the
above procedure. Once de is known, the local volumetric sediment transport
rates q, and Ge for the cell may be determined by multiplying dp by
Up/V» and ValVo >» respectively.
Transport beyond the surf zone
65. Beyond the surf zone, waves are not breaking. Currents (tidal,
littoral, and rip) still transport sediment, but the sediment load is much
smaller than the load in the surf zone. Waves still assist in providing power
to support sand in a dispersed state. However, there is little turbulent en-
ergy dissipation, and frictional energy dissipated on the bottom represents
most of the energy dissipation. Bed load is the primary mode of sediment
transport beyond the surf zone according to Thornton (1972).
66. Since beyond the surf zone it is the tractive forces of currents
(including wave orbital velocity currents) that produce sediment movement, a
sediment transport by currents approach is taken. Again, since the complete
physics of the problem is not completely understood, a semiempirical approach
must be taken. In this model, the approach of Ackers and White (1973) is
followed after appropriate modification for the influence of waves.
67. Ackers and White (1973) studied sediment transport due to currents.
They used the results of 925 individual sediment transport experiments to
establish various empirical coefficients. The approach considers both
suspended load and bed load. It is assumed that the rate of suspended load
transport is dependent upon the total shear on the bed. Therefore, the shear
velocity v, is the important velocity for suspended load transport. Bed
load transport, however, is assumed to depend upon the actual shear stress on
individual sediment grains. Ackers and White (1973) assume that this stress
is comparable with the shear stress that would occur on a plane granular sur-
face bed with the same mean stream velocity. Thus the mean velocity of flow
v is the important velocity for bedload transport.
68. Considering only currents (not waves), Ackers and White (1973)
derived sediment transport rate in a dimensionless form. For convenience in
practical application, this may be written as
pele) Ses (66)
39
where
q = total volumetric sediment transport rate per unit width normal to
the current (vertically integrated combined bed and suspended
sediment load CEES ECOTIES)
Pp = porosity of sediment = 1 - a'
D = sediment diameter which is exceeded in size by 65 percent (by
weight) of the total sample
n, = 1.0 - 0.2432 In Y (67)
1/3
Y=D [ees (68)
v
s = specific gravity of sediment
y = kinematic viscosity of fluid
C = exp [2-86 In Y - 0.4343 (In x)? - 8.128] (69)
fra 22s n@ant 1)
1/2:
Y¢
_ 9.66
m= + 1.34 (71)
okval n-l
v() (22 10s 224)
Fe Ne (72)
Re om?
Equations 67, 69, 70, and 71 apply for 1 < Y < 60 (transition sediments).
For values of Y greater than 60 (coarse sediments), C, n, , m, , and A
1 1
have the values of 0.025, 0, 1.5 and 0.17, respectively.
69. Beyond the surf zone, both currents and nonbreaking waves exist.
So the Ackers and White formulation derived originally for currents only must
be modified for the presence of waves. The waves do not increase the level of
turbulence since turbulence is confined to a narrow boundary layer by the
oscillating wave orbital velocities. Since the shear velocity is dependent
upon the intensity of turbulence and thus the total energy degradation rather
than the net traction on individual sediment grains, the shear velocity is not
changed by wave action. With the wave-induced turbulence confined to a narrow
boundary layer and the waves propagating essentially without energy loss, the
40
effect of waves is to increase the traction on individual grains by increasing
the mean velocity felt by the grains. Thus the mean velocity of flow must be
increased, but the shear velocity must remain unchanged. The mean velocity of
flow is increased by using the following equation developed by Bijker (1967)
and modified by Swart (1974):
a 2
(v) = (v) i¢eig = (73)
wave and current current 2 2;
where
2) 1/2
Eo = Cy ea (74)
x 10h
Cc, = 18 log (4 ) (75)
fw. = Jonsson's (1966) friction factor with D as bed roughness
us = wave orbital velocity
= <|| |>
u
orb
Thus Equation 66 becomes
2 TY \ ah
tho
vil +=\F. — m
poate iV ANY _G 1
qusaa—= 5 D v, = (F - A) (76)
1
A
with
1-n
af 1/2 1 : ae
lee (es) H(z tos 2)
2ZONGZL IN: * D
Loe Lier oe ee Alco (77)
[g(s - 1)D]
41
Equations 76 and 77 are used for calculating sediment transport beyond the
surf zone. In these equations, v is interpreted as the total velocity Vo
due to currents = te + v5 and Vi is obtained from the relation
2
Ps BVe
%=V es [> (78)
(e) C2
VA
where Pe is the bed shear stress and Cc. is the Chezy coefficient. From
q , the local transport rates qe and a are obtained as before.
Transport in the vicinity of inlets
70. The flow and sediment transport in the vicinity of tidal inlets
differ markedly from the flow and sediment transport in the surf zone for a
straight open coast. The bathymetry in the inlet area is highly irregular
with the presence of channels, bars, and shoals. The breaker line is gener-
ally shifted farther offshore and is irregular. Breaking and decay of waves
and wave-induced currents are the major mechanisms for transport of sediment
in the surf zone near straight coasts, with tidal currents being of secondary
importance. Generally Up is much less than Vr: In the vicinity of
inlets, tidal currents are a major mechanism comparable to wave-induced cur-
rents. Moreover, Un and Vp may be comparable. We are primarily inter-
ested in the transport and deposition of sediment in the navigation channel.
There is no guidance in the open literature as to how sediment transport in
this area should be handled. In view of the factors mentioned previously, the
model uses the Ackers and White formulation modified for the presence of waves
(Equations 76 and 77) in this area. From previous experience (Vemulakonda
et al. 1985), this approach was found to yield satisfactory results.
Erosion and deposition
71. In the case of noncohesive sediments, once the transport rates of
sediment qd, and ay are known, changes in bed elevation can be determined
from the continuity equation
Si LS (79)
42
where & is the bed elevation. Equation 79 indicates that if more material
enters a cell than leaves it, ¢ will increase (there will be deposition),
and if more material leaves than enters, ¢ will decrease (there will be
erosion). Equation 79 is applied in a finite difference form to all the grid
cells at the end of each time-step to determine erosion and deposition. Note
that an increase in ¢ means a decrease in still-water depth h and vice
versa. Therefore, the values of h are updated simultaneously.
43
PART III: VERIFICATION AND BASE CONDITION TESTS
Tides
72. Astronomical tides are the primary driving force for currents
within St. Marys Inlet; they also contribute significantly to the ocean cur-
rents in the study area. WIFM is used to compute the currents for an average
tide range in order to supply the sediment transport model with a time-series
of depth-averaged horizontal velocity fields covering one tidal cycle
(12.42 hr for the semidiurnal tide at Kings Bay).
Verification
73. Bathymetry. Most of the bathymetry and topography information used
to define the grid cell elevations in Grid 1 (Figure 3) came from NOS nautical
charts 11488, 11502, and 11503. Detailed soundings taken by the US Army Engi-
neer District, Jacksonville (CESAJ), in June 1982 provided bathymetry for the
navigation channels. All depths in the grid were referenced to mlw, and a
datum difference of 3.0 ft between mlw and mean sea level (msl) was used. The
maximum water depth in Grid 1 was 66 ft mlw.
74. Prototype data. The prototype tide data used to calibrate and
verify WIFM in this study consisted of tidal elevations and currents. Fig-
ure 10 shows the locations of the tide and velocity gages deployed in the
Kings Bay study area. Tide data were collected by the United States Geologi-
cal Survey (USGS) and CEWES between September and December 1982. Currents
were measured along ranges 1-4 (Figure 10) on 10 November 1982, and along
ranges 5-7 on 12 November 1982. These surveys recorded approximately one
tidal cycle. At each range, currents were measured at three stations: A, B,
and C. At each station, velocities were measured at the surface, middepth,
and close to the bottom. Only ranges 1-4 lay within the bounds of the compu-
tational grids, so ranges 5-7 were not used in this report. These current
measurements were accurate and error-free, so they were used by WIFM in veri-
fication. The details of the prototype tide and current data collection
effort are reported by Granat et al. (in preparation).
75. Plates 1-4 show the measured tides at Gages 1-4 of Figure 10 for
November 1982. The mean long-term tide ranges, as given by the 1982 NOS Tide
Tables, vary between 5.8 ft (St. Marys Entrance, north jetty) and 6.0 ft
(Fernandina Beach, Amelia River). The measured tide data for the range survey
44
“J Tes =
Re NG
STATE PARK = an f
<2 i | Limits
°7g/ACRAB!
NeISLAND)
VA,
| 2
| vee
| = =
| F i OCEAN
| |
LEGEND SCALES |
| © FRESHWATER INFLOW PROTOTYPE. a ra |
| se TIDE GAGE enn 4 0 4 8 12 16 20 FT |
| 2 STATION NO.
|
| |
|
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| VERIFICATION STATION |
LOCATION MAP |!
L MEADEAY. 10-12 NOVEMBER 1982 SURVEY |
Figure 10. Locations of field gages
45
date of 10 November 1982 agreed with these mean ranges and so represented an
average tide for the study area. Since the prototype tides measured on
10 November 1982 represented an average tide range, these tidal elevation sig-
nals were used as boundary conditions in WIFM. The prototype range current
data were used to verify the velocity computations.
76. Plate 5 shows the prototype tide records for 10 November 1982. The
sampling rate for the records was 5 min, and these data were spline filtered
to remove high-frequency noise. Tides measured at Gages 2, 3, and 4 served as
boundary conditions to the Amelia River, St. Marys River, and Cumberland Sound
boundaries of the model. The signal from Gage 1, located at the south jetty
of the inlet (Figure 10), was used as the boundary condition at the eastern
edge of the computational grids. However, the travel time for a gravity wave
between the eastern boundary and the actual location of Gage 1 is 25 min, so
the boundary condition was phase shifted 25 min to account for this distance.
The lateral ocean boundary conditions were interpolated between this offshore
signal and the tide signal at the inlet (Gage 1). The boundary condition at
St. Marys River (Gage 2) was also phase shifted 7 min to account for gravity
wave travel time between the mouth of the river (the grid boundary) and the
site of the prototype gage farther upstream.
77. The zero datum shown in Plate 5 represents the mean for each
measured tide record rather than a geophysical datum such as the National
Geodetic Vertical Datum (NGVD) of 1929 . The elevations of the tide recorders
used in this study were not referenced to a benchmark, so the relationships
between the gage means are not known. The lack of a common datum caused
numerous problems during calibration, since WIFM requires all elevations to be
measured from a common datum. Since the tide gages were all fairly close to
one another (less than 2 miles apart), even minor changes in elevations caused
gradients great enough to change the flow patterns within the study area.
These elevation adjustments were determined during the model calibration.
78. Permeability of jetties. Since both jetties at St. Marys Entrance
are awash at high tide and known to be permeable, the tidal model has to prop-
erly simulate this effect on the velocity patterns. From field measurements
taken by Florida Coastal Engineers in 1975, "it was estimated that up to
28 percent of the total [tidal] flood flow enters [the inlet] through the per-
meable jetties rather than at the ocean terminus of the structures." (Parchure
1982, p. 27). Since the widths of the jetties are small compared with grid
46
cell dimensions, they can be modeled in WIFM as flow barriers placed at grid
cell faces. The hydrodynamics of flow over these barriers is computed by the
broad-crested weir formula (Chow 1959). The parameters of barrier submergence
(head across the weir) and Manning's n in the formula dictate the flow rate
or "permeability" across a barrier in WIFM. The permeable jetties at St. Marys
Entrance were therefore simulated with submerged barriers in the tidal current
model.
79. An ad hoc method determined barrier "permeability" parameters for
WIFM. Two initial assumptions were made to reduce the number of variables
involved in parameter estimations. First, the crest of the submerged barriers
used in WIFM was arbitrarily set to -4 ft msl. This depth ensured that the
barriers would not become exposed during low tide. Second, it was assumed
that the bottom friction in the study area, below -10 ft msl, could be
approximated with a set Manning's n of 0.025. These assumptions reduce the
variables affecting permeability to: (a) water velocity over the barrier,
(b) water depth surrounding the barrier, and (c) the Manning's n of the bar-
rier. The relationships between these variables were determined by a simple
computational experiment.
80. A horizontal flume with length scales of the same magnitude as
St. Marys Inlet was modeled by WIFM. The flume is 16,000 ft long and 2,400 ft
wide, and it has a submerged barrier obstructing half the channel width at the
center of the flume. Plate 6 illustrates the plan view of the layout, and the
velocity pattern for a typical computation. WIFM was run for 128 different
combinations of flow velocity (1, 2, 3, and 4 fps), water depth (10, 20, and
30 ft), and barrier Manning's n (varied from 0.025 to 0.050). Discharges
per unit width were measured at the inflow and over the barrier for each run,
and the permeability for the given conditions was computed as the percentage
ratio of the latter to the former. It was determined that permeability was
not a function of the flow velocity.
81. Figure 11 shows the family of curves plotted from this experiment.
To set a desired permeability for a jetty barrier in the tidal current model,
the water depth at the jetty section is noted, and the appropriate Manning's
n is determined by interpolating between isobath curves in Figure 11. The
Manning's n values needed to simulate a 28 percent jetty permeability were
determined for each barrier segment in this fashion.
47
JETTY
PERMEABILITY
PERCENT PERMEABILITY
a
fo)
20
10
0
1 2 3 4 5 6 1 8 9 10
" BARRIER
CHANNEL
Figure 11. The relationship of barrier permeability to depth and
Manning's n
82. Calibration of the tidal model required the adjustment of WIFM
boundary conditions until the computed elevations at tide Gage 1 matched the
prototype data for 10 November 1982. The model was then verified for
correctness by successfully reproducing the velocities measured at ranges l,
3, and 4. The WIFM boundary conditions were adjusted during calibration by
adjusting the datums for the prototype tide signals and accounting for the
phase differences in the signals due to their placements in the grid as input
conditions. All of the datum adjustments were less than 2 in. Note that WIFM
used a time-step of 60 sec for all the computations.
83. Plate 7 shows where numerical gages were placed in Grids 1 and 2 in
order to measure the computed velocities for the base and plane conditions in
St. Marys Entrance. The gage sites in Plate 7 all correspond to either loca-
tions where prototype data were collected during the survey of 10 November
1982, or to important locations in the navigation channel. Table 1 equates
the gage numbers in Plate 7 with the gage names used subsequently. The
48
missing numbers in the sequence correspond to gages outside the grid segment
shown in Plate 7.
84. Plate 8 shows the match between the computed and prototype tide for
10 November 1982 at the four gage locations. The computed signals at
Gages 2-4 are merely the prototype tide with the datum adjustments added,
since these gages are boundary conditions in the model. Computations for tide
Gage 1, in the inlet, match the prototype data.
85. Plates 9-13 compare the model computations of tidal currents to the
prototype surface and middepth velocities at ranges 1, 3, and 4. (Solid
curves represent numerical results and dashed curves prototype data.) Varia-
tions with time of both velocity magnitude and phase are shown over a tidal
cycle. Since the numerical model is depth-averaged, in general its results
would match the middepth measurements more closely. The agreement between the
computations and the prototype data at the inlet (range 1) is excellent, both
in magnitude and phase. The ability of the tidal current model to simulate
the inlet velocities is crucial to the other aspects of this study, and the
model performs this task well. In the case of ranges 3 and 4 (Plates 10-13)
the numerical results represent the whole range. The computed and prototype
velocities at range 4 (Cumberland Sound) also agree well. The velocity com-
parisons at range 3 (St. Marys River) agree in magnitude but differ slightly
in phase. This phenomenon is probably due to the drainage characteristics of
large marsh areas around St. Marys River which lie outside the boundaries of
the tidal model.
86. Plates 14 and 15 show the computed velocity patterns in St. Marys
Entrance for the peak flows of ebb and flood tide. The dashed portions of the
barriers represent the permeable sections of the inlet jetties. The flow
across the jetties can be seen on these Plates, and it appears that the flow
is more pronounced across the south jetty.
87. In summary, the tide model used prototype gage elevation data for
forcing boundary conditions. The measured tidal elevation at the south jetty
of the inlet was reproduced in the numerical model. There was good agreement
of numerical results with measured velocity data at range 1 in the inlet and
satisfactory agreement at interior velocity ranges. Where the flows are
influenced by other features in the region interior to the inlet, such as
marshes which are not included in the tide model of Model B, close agreement
is not expected. This lack of agreement should not cause concern since the
49
interior flows are studied by Model A and since the main purpose of Model B is
to study coastal processes in the region mostly exterior to the inlet. There-
fore, the calibration and verification of the tide model are complete and
successful.
88. Since the channel bathymetry and geometry used in verification
tests are close to existing (base) condition and the tide of 10 November 1982
is representative of the mean tide, the results of WIFM from verification
tests were also taken to be those for base condition. They were used accord-
ingly in the sediment transport model. The reader should note that the tidal
conditions of 10 November 1982 were used in Model A also for base condition.
The tide model generated a data file, consisting of tidal elevations and
velocities, for each grid cell for each half hour of an approximated semi-
diurnal period of 12.50 hr for later use in the sediment model.
Waves and Wave-Induced Currents
89. The hydrodynamic models RCPWAVE and CURRENT were extensively tested
and compared with analytic solutions, laboratory data, and available field
data during their development (Ebersole, Cialone, and Prater 1986 and
Vemulakonda 1984). Considerable experience has been gained previously at WES
in field application of these models (Vemulakonda et al. 1985). So reliance
can be placed on the results of these models. The models do not require site-
specific calibration. Because synoptic field data on waves and wave—induced
currents were unavailable for the project area, no separate verification tests
were performed for these models except indirectly through sediment model veri-
fication. The models were run for the base condition using the same bathyme-
try and channel geometry as in the tidal model. The results of the models
were used in verification and base tests of the sediment transport model.
Wave climate
90. One of the primary objectives of the wave and wave-induced current
model runs is to furnish input to the sediment transport model. In the case
of the sediment transport model, the interest is in sediment transport and
yearly shoaling rates in the navigation channel under an average year's wave
climate, including normal storms but excluding extreme storms such as hurri-
canes and other tropical storms. So the wave climate for an average year
at the project site was obtained from the WES Wave Information Study (WESWIS)
50
based on 20-year hindcast. This information was in the form of frequency of
occurrence of waves in terms of predominant direction, significant wave
height, and period bands in a depth of 60 ft mlw. Table 2 shows a sample of
WESWIS data for St. Marys Inlet. The wave approach angle notation in this
table is different from that used in the rest of this report. Angles in the
table are measured with respect to the shoreline. Consider waves with an ap-
proach angle of 70.0 to 79.9 deg and significant wave heights in the band 0.0
to 0.49 m. They are distributed in period bands between 0.0 to 11.0 sec and
greater. The total frequency of occurrence of these waves summed over all the
period bands is 3.515 percent (3,515 + 1,000) or 0.03515. Similarly, WESWIS
provides wave information in direction bands of 10 deg from 0 to 180 deg for
all the wave height bands (0 to 5.00 m and greater).
91. In this study, these data were further consolidated into 79 differ-
ent incident wave conditions (combinations of significant wave height, period,
and direction) to run the wave and wave-induced current models. For conve-
nience in running the sediment transport model, wave condition 80 was defined
as a null wave condition when there was no significant wave activity. These
combinations are listed in Table 3 which shows the percentage of occurrence of
each condition. The directions represent angles in degrees measured from azi-
muth 87.5 deg (approximate shore normal direction). Negative angles signify
waves coming from directions south of the normal; positive anglés signify
waves coming from directions north of the normal. The wave combinations shown
in Table 3 are obtained from Table 2. Consider the example from Table 2
again. Since the wave approach angle is between 70.0 and 79.9 deg, the aver-
age value of 75.0 deg is taken. In terms of the notation of Table 3, the wave
direction becomes -12.5 deg. Since the wave height band is from 0.0 to
0.49 m, the mean value of 0.25 m or 0.82 ft is taken for the significant wave
height. As for period, on the basis of the distribution of Table 2, a mean
period of 8.0 sec is taken. These are the values shown for wave 28 in
Table 3.
Jetties
92. To account for diffraction of waves due to the two jetties of
St. Marys Inlet, a special subroutine was developed. It used the diffraction
solution of Penney and Price (1952). The wave model was first run without
accounting for the presence of the jetties. The diffraction subroutine took
the solution near the jetties as input and modified it to allow for
51
diffraction around the jetties. For this, the actual layout of the jetties is
used. The procedure was somewhat similar to that of Perlin and Dean (1983).
During the development of the subroutine and the procedure, several tests were
performed including comparison of its results to the laboratory data of Hales
(1980) for a single structure case, and to two physical hydraulic model tests
conducted at CEWES for the two jetty case. In each case, the results of the
subroutine compared favorably with laboratory data. In the grid for CURRENT,
the jetties were represented in a stair-step fashion similar to that in WIFM.
CURRENT treated them as thin-walled nonovertopping impermeable barriers.
93. Because of the highly variable nature of the computational grid,
the wave model was run on a uniform grid with 500-ft by 500-ft cells, and its
results were interpolated to the variable grid. The wave and wave-induced
current models were run for each of the 79 wave conditions. There are no
waves or wave-induced currents corresponding to wave 80. Each of the wave
conditions represented the offshore boundary condition for the wave model.
The model was run for the condition, and its results were stored in the form
of wave height, direction, and wave number at each grid cell. They were next
used as input to CURRENT which computed and stored on a file the setup nN and
the two velocity components U and V for each grid cell for each wave. For
convenience the corresponding wave information for each cell was also stored
on the same file. Note that in general CURRENT used a time-step of 50 sec and
in each run calculations were continued until an approximate steady-state con-
dition was reached by the current field.
Results
94. For convenience, results for only three typical cases out of the 79
listed in Table 3 will be presented here. They have been selected so that
they represent waves coming from south and north of the shore-normal direction
and approximately along the shore-normal direction. It is convenient to pre-
sent the results from the wave and wave-induced current models in terms of the
uniform grid in the computational plane rather than the variable grid (Fig-
ure 3). One advantage of this type of display is that the results for the
entire grid can be shown on an 8-1/2-in. by 1l-in. sheet of paper. However,
there is a disadvantage in that cell centers are not at the proper distances
relative to each other. Thus, boundary cells appear much closer to the center
than they really are. Moreover, the cell dimensions are distorted. Cells
close to the inlet, the barrier islands, and the navigation channel appear to
52
be relatively larger; and as one moves away from this region (for example,
closer to the lateral and offshore boundaries) the cells appear to be rela-
tively smaller than they really are. In what follows, for convenience, the
results will be shown on the uniform grid.
95. Figure 12 shows the region covered by the 50- by 73-cell uniform
grid in the computational plane. The grid is 50 cells wide in the alongshore
75
N
70
|
AMELIA NY . AZIMUTH
ISLAND
65
60
55
50
45
40
35
30
25
0 8 16 24 32 40 48
Figure 12. Uniform grid and bathymetry in
computational plane
direction and 73 cells long in the onshore/offshore direction. The figure
shows Amelia and Cumberland Islands, the navigation channel, the locations of
the two jetties on St. Marys Inlet (the jetties are stair-stepped for the CUR-
RENT model), and bathymetric contours with elevations referenced to msl (mlw
plus 3 ft). The offshore boundary of the grid is at an approximate depth of
63 ft msl. Note the shoals offshore, south of the south jetty, and north of
the north jetty. For convenience, these will be referred to hereafter as the
offshore, south, and north shoals, respectively.
53
96. Figures 13, 15, and 17 display the results of the wave model, at
cell centers, corresponding to waves coming from three different directions.
These are waves 22, 45, and 59 from Table 3. These three conditions will be
referred to as cases A, B, and C, respectively. For all three cases, the
significant wave height in 63-ft depth of water msl is identical and equal to'
7.4 £t. The period is roughly the same. The wave directions are quite
different. In each of the figures, the length of an arrow (vector) is
proportional to the wave height (a scale is shown), and the direction of the
arrow indicates the direction in which the waves are progressing. For
clarity, only vectors for alternate cells in each coordinate direction are
plotted.
97. Figures 14, 16, and 18 present the wave-induced currents at grid
cell centers corresponding to cases A, B, and C. In these figures, the length
of an arrow is proportional to the magnitude of the current (a scale is shown),
and the direction of the arrow indicates the direction of the current. The
currents are depth-averaged. For convenience and clarity, only vectors in
alternate cells in each coordinate direction are plotted.
98. Figure 13 corresponds to a wave of period 7.2 sec coming from
azimuth 120 deg in 63-ft depth msl (Case A). The waves respond to the off-
shore shoal. The wave height increases, and the wave direction changes as the
waves go over the shoal. The wave height decreases, and the waves resume
their original direction once the waves pass the shoal. The waves converge on
the south shoal due to refraction, move parallel to the jetty, and break on
the shoal. Because of the sheltering effect of the south jetty, very little
of the incident wave energy goes past the jetty tips into the inlet. Note
also the sheltering effect behind the north jetty resulting in very little
wave action there. The waves converge on the north shoal, and the wave energy
spreads out (diverges) due to a "bay" effect as the waves reach the shoreline
of Cumberland Island. Near the approximately straight shorelines of both bar-
rier islands, the wave height decreases because of wave breaking and decay.
99. Figure 14 shows the wave-induced currents corresponding to Case A.
Near the straight part of the shorelines of Amelia and Cumberland Islands, the
currents are mainly parallel to the shore and move to the north. However,
near the south shoal, because of wave refraction and breaking, the currents
tend to move in a westerly direction. The net result is the counterclockwise
circulation we see over the shoal. The currents are the largest in this
54
PLOY OF WAVE DIRECTIONS AMD WAVE HEIGHTS (KBUUV2e2)
AMELIA
i b CUMBERLAND
{} .
ISLAND ua
C ISLAND
U
Ve
hii,
* iyi,
YY
: Me
ues 2 Be
Bl = 74 Be, 1S 762 S85 35 Yt
Azimuth = 120 deg YY “n
Liat
ey
Hy,
HE
40 48
PLOT OF VELOCITY (KBUCee3) i
AMELIA ay CUMBERLAND
ISLAND | or ISLAND
Figure 14. Wave-induced
currents for Case A
G
\>!
a
a
i St wy Oe 1 a
52)
PLOY OF UAVE DIRECTIONS AND VAVE HEIGHTS (KBUUU4ED
U
NOW ean
Sf
%
AMELIA
ISLAND
CUMBERLAND
ISLAND
65
! i a
R
60 if UY a!
Art
| ay 3 1! In Y
50 ‘5 | \ al 4
\N fi a4
45 hk
\ Ni
40 R
x
35 4 4 | x
el Ke
25 i Hf ¢ &
20 Fe [ L
BY
15
10
5
0
Oo § 16 «24 32 40 48
PLOT OF VELOCITY (KBUC4S3)
AMELIA
ISLAND
c&
7
?
a
zat,
Arie
Soy
Figure 16. Wave-induced
currents for Case B
Iyveyeourr
eda eaoa tee
Somes
ay Pee ee
vs
>> bee
NN
R
i
t
a
\e
A
\'
‘
iret
|
|
ad
Ig C2 Add IG
aG>v72x2424vaasa awa
FIM ITT eacy/! 9 rary fay 4
> La at oe St ee
44a
») 9
Tt
2 SI a
ey a a
> 2 2
> ? 2
? > >
> > >
> > >
Figure 15.
Wave heights
and directions for Case B,
BS 74 aes WS Pos SGC5
Azimuth = 80 deg
SFT/SEC
toeaageyvvuvvyvwvy
awvwyvrvwrwvwvvevvvwevwvw vwv vv v
2
CUMBERLAND
ISLAND
PLOT OF UAVE DIRECTIONS AND VAVE HEIGHTS (KBUUUG9)
Pomme cee a
esti z iS ISLAND
a> > al y
| Hs 4
Tt ag ARS
* h aN \
Figure 17. Wave heights ‘\ ea XA ¥
pel hecton Fore > = ER ANSE
Aeaencn = 80 den ANA He
cr
: ARRAN VAAN
ARS
oe
: RAR
0 8 16) 2h 2 a
70 AMELIA
65 |. ISLAND
60
55
2 Figure 18. Wave-induced
40 sis currents for Case C
30 +
Pea ee ea .
tl InP > VY pnw part anrAanarhee
57
region. Currents are strong on the inside of the north jetty because waves
advance and break along the jetty. These currents have a westerly direction
and advance into the inlet. Because of diffraction, currents are very weak
behind the north jetty.
100. Figure 15 corresponds to a wave of period 7.8 sec coming from
azimuth 80 deg in 63-ft depth of water msl (Case B). In this case, since the
waves are approximately normal to the shoreline and the offshore contours,
there is not much refraction of the waves offshore or even near the straight
line portion of the shoreline. The waves converge on the south shoal, because
of refraction, resulting in higher wave heights on the shoal. There is a
similar convergence on the north shoal and a small divergence of wave energy
near Cumberland Island. The incident wave direction is such that there is
very little sheltering due to the two jetties. As a result the waves propa-
gate straight and far into the inlet because the depth contours are approxi-
mately straight and parallel to the waves inside the jetties. The wave
heights are large between the jetties.
101. Figure 16 displays the wave-induced currents for Case B. In this
case, because the incident waves are approximately normal to the shoreline,
there are no noticeable currents along the straight portions of the shoreline.
Because of wave convergence and breaking, the currents are strong over the
south shoal. A circulation pattern may be observed on the shoal. As the
waves propagate straight and unchanged between the jetties without breaking or
decaying, there are no noticeable wave-induced currents in this region. Cur-
rents may be observed on the north shoal because of wave convergence, break-
ing, and decay there. These currents are smaller than those observed on the
south shoal.
102. Figure 17 corresponds to a wave of period 6.9 sec and azimuth
60 deg in 63-ft depth of water msl (Case C). The waves refract on the off-
shore shoal. They refract and converge strongly on the north and south
shoals, resulting in higher wave heights on both shoals. Since the waves are
aligned approximately parallel to the two jetties, there is very little
sheltering due to the jetties so that the waves propagate deep into the area
between the jetties. They break and decay near the straight portions of the
shoreline.
103. Figure 18 represents the wave-induced currents for Case C. Near
the straight reaches of the shoreline the currents are parallel to the shore
58
and in the southerly direction, as one would expect. The currents are strong
over the north and south shoals because of wave breaking and decay. The pat-
tern of the currents is complicated. Currents move in an easterly direction
along the interior of the north jetty and westerly direction along the
interior of the south jetty.
104. In summary, the overall results of the wave and wave-induced cur-
rent models used for verification and base conditions are reasonable and
behave in a manner one would expect, given the complicated bathymetry of
St. Marys Inlet region and the two jetties on the inlet. The incident waves
respond differently to the bathymetry, the shoals and the jetties, depending
on their direction of incidence. The wave-induced currents depend on the
bathymetry, the waves everywhere in the grid, and whether or not the waves
break and decay in a given region of the grid.
Sediment Transport
Verification tests
105. In order to make a strict verification of the sediment transport
model, it is necessary to have either long-term (several years long) informa-
tion on shoaling rates in the navigation channel and bathymetric changes in
the general area or actual wave measurements made simultaneously with measure-
ments on shoaling rates and bathymetric changes over a shorter time period (a
few months). The latter type of data are not available for the project area.
As for the former, examination surveys are available for the channel. As men-
tioned previously, the approach used by the sediment transport model does not
account for extreme storms. So the prototype data selected should not include
periods of such storms. As for dredging, it is possible to simulate dredging
in the numerical model provided detailed information is available on the loca-
tions and durations of dredging and the amounts of material dredged at each
location. Usually, such detailed information in terms of computational grid
cells is not available from dredging records. Therefore the prototype data
should not include periods of dredging. In the case of St. Marys Inlet, the
navigation channel was deepened to the existing condition (40-ft project
depth) in 1978 and 1979 so only 5 to 6 years of prototype data are available.
The channel still has not stabilized after the deepening. Sediment transport
and other processes continue to be in a state of transition. Out of the
59
available information on examination surveys for the navigation channel, we
were able to locate only one set of examination surveys covering a period of
approximately 1 year (1980 through 1981) which was free from the effects of
dredging and severe storms. The duration of this data set is too short for
the data set to be used for strict verification of Model B results which are
based on 20-year hindcast wave data. Therefore, a strict verification of
Model B results with the data set is not possible. Instead, the average
yearly erosion/deposition rates along the channel obtained from the data set
will be compared with Model B results to see if the numerical model results
are reasonable and agree with the trends and shoaling magnitudes exhibited by
the field data.
106. Prototype data. The field data set consisted of seven examination
surveys conducted by CESAJ during 1980 and 1981 between sta -80+00 and
sta 325+00 (Figure 19). For convenience, this pre-1985 CESAJ stationing will
be used throughout this report. The locations and dates of the surveys are
oy
s/
ma
399+73.92
325+00
201+00 (APPROXIMATE LOCATION
OF JETTY TIPS)
130+00
-80+00
PLAN 1 EXTENSION se -97+76
!
Figure 19. Pre-1985 CESAJ stationing
60
shown in Table 4. On the basis of several tests, it was determined the datum
used in survey 2 was in error by 0.5 ft. This is not surprising since the
reach of channel surveyed was far away from the tide gages used to locate the
datum. The datum for this survey was adjusted accordingly.
107. The field data were examined in two ways. First, surveys l, 2,
and 7 were used to determine average yearly erosion/deposition rates. At each
of the 35 locations along the channel corresponding to computational grid cell
centers, depths across the width of the channel were averaged, and the
erosion/deposition rates were computed and extrapolated to feet/year values.
(Following a similar procedure, but computing the average depth for each cell
from 16 spatially distributed points in the cell, yielded results that were
close to the results obtained from averaging the cross-section depths). Next,
the total period was broken down into three separate periods of approximately
4, 2, and 6 months, based on the survey dates. At each of the 35 locations,
the erosion/deposition rates obtained for these periods were converted to
feet/year values, and the extreme values at each location were determined.
Figure 20 is a plot of the average and extreme values from the prototype data
-15 LEGEND nN
— PROTOTYPE AVERAGE / \ A
- ! \
——— PROTOTYPE EXTREMA gw / MI VIM
4
on
EROSION ~<+* DEPOSITION
RATE, FT/YEAR
(a)
—
f=)
15
-100 -50 0 SO pan Ome O0ie a 200Ria250e S00 350
DISTANCE, 100 FT
Figure 20. Prototype data on erosion/deposition rates
61
at different stations along the channel. The sign convention that erosion
rates are positive and deposition rates are negative is used hereafter.
108. Testing procedure. At the start, the sediment model used the
bathymetric information from field surveys 1 and 2 for the channel. Outside
the channel, the bathymetry used was identical to that used by the tide, wave,
and wave-induced current models for base condition since better detailed
information was not available.
109. To generate a wave sequence for 1 year for the verification and
base tests of the sediment model from the waves given in Table 3, the follow-
ing procedure was used. Each wave event in the sequence was assumed to be
steady with a duration of 4 hr. This is a reasonable assumption from field
experience and measurements, provided extreme storms are ruled out as done
here. Each wave condition (1 to 80) of Table 3 was identified with a fre-
quency of occurrence. During the running of the sediment model, wave condi-
tions were selected such that each of the 80 conditions occurred at the
frequency shown in Table 2. Thus, the waves used by the sediment model re-
flected nature in terms of wave statistics provided by WESWIS. The same waves
were used for base and Plan 1 tests.
110. The sediment model used a time-step of 1 hr. This value was
considered optimum on the basis of testing and previous experience. The
computational sequence employed by the sediment model consisted of the fol-
lowing steps:
a. Read in the local bathymetry.
b. Pick the first wave condition.
c. Read in the corresponding wave information (wave height,
angle, period, wave-induced velocities, and setups/setdowns).
. Read in the first hour of the tide data (tidal velocities and
elevations).
- Combine the above quantities to obtain a total velocity field,
wave field, and local depth.
f£. Compute sediment transport quantities and the associated ero-
sion and deposition rates.
g- Repeat steps d, e, and f at 1l-hr intervals for a total of
4 hr.
h. Pick the next wave condition and continue steps c through g,
Gie@o
As indicated previously, the local still-water depth h for each cell was
updated at each time-step based on the erosion or deposition in the cell. The
62
total local depth, which is the sum of h , ", and 1 , was also updated.
The total velocity components Up and Vr were adjusted on the basis of sim-
ple continuity to account for the change in bed elevation of the cell. It was
observed from running the sediment transport model that model results in terms
of erosion/deposition rates (ft/year) along the channel became approximately
constant after the model was run for 150 to 180 prototype days. There were
minor variations from run to run as the total time was increased, but the
trends and magnitudes stabilized. Therefore, the above sequence was performed
for 180 instead of 365 prototype days to compare with field data for
verification.
111. Results. Based on the trends exhibited by the prototype data, the
reach of the channel between sta -—80+00 and sta 325+00 was divided into
seven zones for verification (Figure 21). A similar approach was used for
Model A verification. Four to six computational grid cells were in each zone.
The value assigned to a zone is the average of the values for the cells in the
zone. A comparison of the prototype average erosion/deposition rates with
results of Model B is shown by zones in Figure 22. Also shown in the figure
are prototype extrema based on 1 year of prototype data. Model B results show
the same trends as the prototype average results and are in approximate
quantitative agreement in zones 1-4 (between sta -80+00 and sta 241+56). It
is not surprising that they do not match quite as well between sta 241+56 and
sta 325+00. This is a highly dynamic region, especially outside the jetty
tips (sta 251+00) and is very much dependent on the actual (rather than aver-
age) wave climate that existed between surveys. This can be seen in the large
spread between prototype extrema. There is movement of material from the off-
shore bar and shoals into the channel. As was pointed out previously, proto-
type data of 1 year's duration are not necessarily representative of a 20-year
average. On the whole, Model B results are reasonable and in agreement with
field data.
Base tests
112. The only difference in the bathymetries used at the start of veri-
fication and base tests was in the navigation channel. The sediment model
used the channel bathymetry from the CESAJ survey of June 1982 for the base
tests because the same bathymetry was used in all the other models for base
condition.
63
DISTANCE, 100 ft
Figure 21. Zone numbers assigned to channel reaches for verification tests
EROSION +> DEPOSITION
RATE, FT/YEAR
a LEGEND oa
| oleae PROTOTYPE AVERAGE a \
ne a —-« PROTOTYPE EXTREMA, a
o—o \
by MODEL B vy)
25
0
25
5.0
78
-100 -50 0 S000 SOR e e008 e250 eS SOC hearS50
DISTANCE, 100 FT
Figure 22. Comparison of prototype data with Model B results
for verification
64
113. At the time Model B computations were made, up-to-date field sur-
vey information was not available on channel bathymetry between sta 325+00 and
sta 399+74, nor was up-to-date bathymetric information available for areas on
either side of the channel. Model B used the best available information,
which usually was CESAJ construction dredging survey information and the
bathymetric information from NOS charts. Unfortunately, this information does
not seem to represent the current bathymetry for the reach of the channel be-
tween sta 325+00 and sta 399+74 and the areas of either side of the channel in
this reach, according to the latest CESAJ surveys. These surveys seem to
indicate that the depths may be greater (by 5 ft or more) in this reach. For
this reach of the channel, the information available to us at the time of com-
putations indicated the depths were greater than the existing project depth of
40 ft and that the channel seemed to be in a state of erosion; therefore it
did not require maintenance dredging. There was no quantitative information
available on erosion/deposition rates for this reach.
114. The sediment transport model followed the same testing procedure
as it did for verification. The model was run for 200 prototype days, and its
results were converted to channel erosion/deposition rates (ft/year). For
base tests, the entire length of channel offshore of sta 399+74 was consid-
ered. The channel was divided into ten zones (zones 1 to 10 in Figure 23).
Figure 24 shows the erosion/deposition rates by zone for base. When the
results for verification and base are compared (Figures 22 and 25), it is
observed that there is similarity in the trends and magnitudes. This is not
surprising since the channel bathymetry in the two cases is not that much
-100 -50 0 SO 1000 150i 2002500 300) 350400
DISTANCE, 100 ft
Figure 23. Zone numbers assigned to channel reaches for
base and Plan 1 results
65
different inside the jetties and the forcing functions (tides, waves, and
wave-induced currents) are the same for both cases. In both cases, there is
deposition outside the jetty tips (sta 251+00). It changes to erosion inte-
rior to the jetty tips because of circulation due to wave-induced currents.
The heaviest deposition rates are observed near the jetty tips. This is the
area where the channel cuts through the offshore bar and material from the bar
tends to move into the channel and deposit there.
-100 -50 0 50 100 150 200 250 300 350 400
DISTANCE, 100 ft
Figure 24. Erosion/deposition rates (ft/year) for base condition
from Model B (+ = erosion, - = deposition)
66
EROSION ~+e DEPOSITION
RATE, FT/YEAR
oS
0
Figure 25.
90 =6 100 = 150 3 200 3s 250~S 300
DISTANCE, 100 FT
Erosion/deposition rates for base
67
350
400
PART IV: PLAN CONDITION TESTS
Paltaniwel!
115. Model B tested only one plan condition which will be referred to
hereafter as "Plan 1." The plan is to (a) widen the navigation channel to
500 ft, with the widening taking place on the north side of the present
entrance and offshore channels; (b) extend the channel on the ocean side, with
the extension being at an angle 20 deg south of the present channel center
line at sta -97+76 approximately; and (c) deepen the channel to -49 ft mlw
(46-ft project depth plus 3-ft advance maintenance). The channel is to have a
trapezoidal cross section with side slopes of 3H:1V. Figure 26 shows details
of the planned channel layout and cross section. As requested by the Officer
In Charge of Construction (OICC), TRIDENT, the plan tested assumes also that
the landward 1,000 ft of the south jetty will be made sand-tight
simultaneously.
116. In view of the urgent need expressed by OICC for Plan 1 results
from Model B for design of the entrance and offshore channels, the wave and
wave-induced current models were not rerun for the Plan 1 condition as origi-
nally planned. Running the models again would have delayed the results con-
siderably. Moreover, since the changes from base to Plan 1 condition of the
navigation channel were reflected mainly in the cell size and bathymetry for
one row of cells in the computational grid, it was felt the effect of channel
modification on waves and wave-induced currents would be minor compared to its
effect on tides and sediment transport.
Computational Grid
117. As indicated previously in Part II, the computational grid for
Plan 1 (Grid 2) retained the major features (overall dimensions, orientation,
number of cells, etc.) of the grid for base (Grid 1). The only difference
between the two grids lies in the mapping of the row of cells corresponding to
the navigation channel. These cells were made 500 ft wide by minor adjust-
ments of the cells on either side. In view of the rectilinear nature of the
grid, the navigation channel was represented in a stair-step fashion where it
turned south. It was assumed that dredging for the navigation channel
68
Teuueyo [T uetTg Jo s{TrTe,eq
NOILOAS SSOYD
Le =0
‘oz ean8ty
l
SATIN IWOIILNWN
fanvisi
Ae day :
| VITA
anv yaa)
oN
‘ B
69
extension stopped wherever the natural ocean depth became equal to or greater
than 49 ft mlw. (This location of the oceanward entrance of the navigation
channel would be determined in the field from the latest bathymetric surveys
for the final channel design.) In the navigation channel itself, the planned
channel depths were used. The bathymetry used outside the channel was the
same as that for base condition.
Tides
118. To properly model the sand-tightened section of the south jetty in
the numerical model, the crests of the barriers simulating this jetty section
were raised to the prototype jetty elevation of +3 ft msl; and the Manning's
n values governing flows over the barriers were changed appropriately.
119. Plates 16-19 compare the computed base and Plan 1 velocities
(magnitudes and phases) at seven sites in the inlet (refer to Table 1 and
Plate 7 for locations of these sites). All of the changes in tidal currents
are due to sand-tightening of the south jetty. The peak velocity at tide
Gage 1 (Plate 16) has increased by approximately 10 percent between base and.
Plan 1 due to sealing of a section of the south jetty. The gages at the
throat of the inlet (Endeco velocity Gage 2, range survey Gages 1-A, 1-B, and
1-C, and Fort Clinch) (Plates 16-19) show negligible change in velocity. The
velocity at the ocean end of jetties (Plate 18) increases by about 10 percent
in both ebb and flood for Plan 1 and shows a slight phase shift.
120. Plates 20-21 show the tidal current patterns near the inlet for
maximum ebb and flood for Plan 1. For clarity, the plotting of velocities
below 0.1 fps is suppressed in these figures. These two plates can be com-
pared to the base condition patterns of Plates 14-15, but few differences are
apparent in a visual examination. For convenience the vector differences
between Plan 1 and base condition velocities are shown in Plates 22-23 for the
same region near the inlet, for maximum ebb and flood, respectively. Note the
change in velocity scale. The plotting of velocity differences below 0.05 fps
is suppressed in these figures. Both figures indicate that sealing the south
jetty exerts local changes on tidal currents. The large difference vectors at
the landward end of the south jetty represent a decrease in velocities between
base and Plan 1 since flows in this area are stopped by sealing the jetty. No
other significant changes in the current patterns were noted within the study
70
area for Plan 1. The extension of the navigation channel at the seaward end
produced almost no effect upon the current patterns.
Sediment Transport
Testing procedure
121. The testing procedure used was similar to that for base conditions
except the computations were performed with Grid 2, and the bathymetry at the
start of computations corresponded to Plan 1 conditions. The sediment trans-
port model used the results of the tide model for Plan 1 and the results of
the wave and wave-induced current models for base conditions. As for the base
test, computations were performed for 200 days of prototype time, and the
results were used to estimate yearly erosion/deposition rates along the
channel.
Results
122. The channel was divided into 11 zones for Plan 1 (Figure 23). The
exact offshore limit of zone 1A was yet to be determined from field surveys.
Figure 27 shows the erosion/deposition rates by zone for Plan 1. A comparison
of base and Plan 1 results is plotted in Figure 28. The model predicts an
increase in both deposition rates and erosion rates between sta -—9/7+76 and
sta 325+00 from base to Plan 1. Zone 1A is not shown in the figure. This
zone indicates on the average a slight erosional tendency with rates of the
order of 0.1 ft/ year or less. The model predicts deposition in zones 8 and 9
(sta 323402 to sta 374+94) for both base and Plan 1. For Plan 1, the deposi-
tion rates are of the order of 1.0 to 1.4 ft/year. Model B predicts large
erosion rates in zone 10 (sta 374+94 to sta 399+74). Since there is no quan-
titative field information on sedimentation rates in zones 8-10, it is diffi-
cult to comment on Model B predictions for this reach. It is suspected that
since the bathymetric information used for this channel reach and adjacent
areas was not up-to-date, it might have caused deviation of Model B results
from field experience. Another contributory factor might be the grain sizes
found in this reach, which are much larger than elsewhere in the study area.
The model assumes the same grain size distribution throughout the study area.
The local deviation of grain sizes might have resulted in the prediction of
larger erosion and deposition rates locally. There is reason to believe the
effect of these factors is restricted to Model B predictions for zones 8-10
7A
EROSION ~+* DEPOSITION
RATE, FT/YEAR
-50 0 50 100 150 200 250) 300 350) ~ 400
DISTANCE, 100 ft
Figure 27. Erosion/deposition rates (ft/year) for Plan 1 condition
from Model B (+ = erosion, - = deposition)
LEGEND
ae ea F BASE ee
TAN
-530 0 SOP OO SOR 200250 S00 S50 400
DISTANCE, 100 FT
Figure 28. Comparison by zones of erosion/deposition rates
for base and Plan 1
72
and does not extend to the model results for the rest of the study area.
123. In terms of yearly shoaling volumes, if the reach of channel from
sta -80+00 to sta 325+00 is considered, the results translate to approximately
475,000 cu yd/year for base and 788,000 cu yd/year for Plan 1 allowing for the
wider Plan 1 channel, or an increase of approximately 66 percent from base to
Plan 1. The base volume is of the same order as the maintenance dredging vol-
umes recorded in CESAJ dredging logs.
73
PART V: MODELING LIMITATIONS
124. The numerical models used in this study were the most advanced
models available at the time the study was undertaken. However, they do have
certain limitations which must be kept in mind in order to view the results
obtained from this study in proper perspective. As previously indicated,
numerical models represent an approximation to the physical processes. The
degree of approximation depends on the physics in the formulation of the indi-
vidual models, the resolution of the computational grid, and the time-step
used in computation. The assumptions made in the models and the limitations
of the models have been given previously along with the description of the
models in Part II. In this study, the computational grid resolution and the
computational time-steps used have been chosen, on the basis of experience and
testing, such that the results obtained would be reasonably accurate for engi-
neering purposes and, yet, the computational costs would not be prohibitive.
125. Generally, the hydrodynamic models are more exact than the sedi-
ment transport model because more insight into the hydrodynamics is available
and more experience has been gained in modeling the hydrodynamics numerically.
With proper calibration and verification, tidal hydrodynamic models such as
WIFM can predict tidal elevations very accurately and tidal currents fairly
accurately. Monochromatic wave models such as RCPWAVE are fairly accurate in
open coast areas. Their results near structures and inlets are more approxi-
mate because of the difficulties and expense in modeling diffraction near
structures and wave/current interaction near inlets. As for wave-induced cur-
rent models such as CURRENT, people have less experience with them than with
tidal and wave models. Wave-induced current models are reasonably validated
for open-coast situations. Their results are more approximate near inlets and
jetties because the hydrodynamic processes are more complicated and less
understood, the wave fields are less accurately known, and there is a lack of
field data to validate the models.
126. Sediment transport is the most important aspect of the project for
project design; yet the sediment transport model is the least exact of all the
models, and the uncertainty is the greatest with this model. The uncertainty
exists because sediment transport in general involves complex interactions
between the bed and the flow which are not well understood. Of all types of
sediment transport, sediment transport near inlets under the combined action
74
of waves and currents, as typified by this study, is one of the most compli-
cated and least understood processes. The sediment transport model employed
in this study uses fairly simple empirical formulas which are based on labora-
tory and field data. It reflects the inaccuracies inherent in the formulas as
well as the inaccuracies in the results of the three numerical hydrodynamic
models.
127. In this study, a mean tide, and an average year's wave climate
based on 20-year averaging of wave statistics were used in running the sedi-
ment transport model to estimate the yearly shoaling rates in the navigation
channel. In reality, the tidal cycle is more complex, involving spring and
neap tides; and the wave climate varies from day to day, season to season, and
year to year. Severe storms such as hurricanes, which have a dramatic impact
on sediment transport and channel shoaling, have been excluded from this
study. As a result, sediment transport and channel shoaling rates in any
given year may deviate significantly from the values predicted in this study.
Moreover, short-term rates such as averages over a month or a season may dif-
fer markedly from average rates over a year. Even the nature of sedimentation
at a particular location may change from erosion to deposition and vice versa.
This change is exemplified by the field data on shoaling rates shown in Fig-
ure 20. Therefore, the results of this study will provide reasonable esti-
mates of the long-term yearly average values of sediment transport and channel
shoaling rates, provided severe storms are excluded and the uncertainty in the
results for the reach of channel between sta 325+00 and sta 399+74 is noted.
128. In general, the uncertainty in the predictions of the sediment
transport model is reduced by verifying the model with field data from the
project site. For St. Marys Inlet, field data from navigation channel surveys
were available for about a year (November 1980 to December 1981) and are free
from the effects of extreme storms. The model verification, as shown in Fig-
ure 22, is good. In a sense, the verification shown is an indirect verifica-
tion of the modeling system approach as a whole. The yearly shoaling volumes
predicted by the model for existing conditions are comparable to yearly main-
tenance dredging volumes recorded by CESAJ. In general, with proper verifica-
tion numerical sediment transport models are better at predicting the effect
of a change from one condition to another, such as from base to plan, than at
predicting an absolute condition such as base or plan alone. In view of these
facts, it is estimated that Model B results on sediment transport are accruate
US
to within +25 percent for base and Plan 1 conditions.
129. To keep things in perspective, it should be pointed out that at
present the only possible alternative to a numerical sediment transport model
‘ls a physical movable-bed hydraulic model. Movable-bed coastal models are
fairly complicated and expensive to construct and operate. Such models
require more time than a numerical modeling effort. At present, there is no
universal agreement on the scaling relations to be used. Movable-bed coastal
models involving the combined action of waves and currents near inlets (the
type required by the present study) are the most complicated of all coastal
models and the least understood. Their results are approximate because there
has to be a compromise between scaling relations necessary for waves only and
scaling relations required for currents only. According to established ex-
perts, the accuracy of a coastal movable bed model of this type in the hands
of an expert will be of the order of +50-100 percent. Thus, the results of
the numerical modeling system employed in this study are definitely better
than the alternative.
76
PART VI: RECOMMENDATIONS
Advance Maintenance Dredging
130. The following recommendations on advance maintenance dredging are
based not only on Plan 1 results from Model B but also on all other available
information such as field surveys and field experience. It must be emphasized
that these recommendations are for an average year including normal storms and
do not allow for the effects of abnormal storms such as hurricanes and tropi-
cal storms. Since the Navy wants a minimum clear depth of 46 ft mlw always
and since it plans to dredge the channel only once a year, the deposition
rates by zones as well as the deposition rates predicted by Model B for indi-
vidual cells (Figure 29) have been taken into account in making these
recommendations.
10 LEGEND
—— BASE 7
“5 ———PLAN 1
(S]
EROSION ~+* DEPOSITION
RATE, FT/YEAR
(a>)
—
(=>)
15
-150 -100 -50 0 50 1005 S150 2005 250 3000350 ne 400
DISTANCE, 100 FT
Figure 29. Comparison of computed erosion/deposition rates by cells for
base and Plan 1
131. For reasons previously mentioned, the high local deposition rates
predicted by Model B for base and Plan 1 in some reaches of the channel be-
tween sta 325+00 and sta 399+74 are suspect because up-to-date bathymetric
data were not available for model calculations and there are no corroborating
field data for such high rates. On the other hand, field surveys taken in
April 1984 and December 1984 which covered the channel between these stations
Ud
and which became available after Model B was run, seem to indicate erosion
rates of the order of 0.8 ft/year or less between sta 325+57 and sta 361+74
and deposition rates of the order of 1.4 ft/year or less between sta 361+74
and sta 399+74. In view of the uncertainty on sedimentation rates in the
length of channel between sta 325+00 and sta 399+74, and because the existing
depths in this reach are generally higher than 49 ft mlw, an advance mainte-
mance depth of 3 ft is recommended in this reach.
132. For convenience in dredging, the channel was divided into reaches
of at least 2,000-ft lengths at the suggestion of CESAJ. Table 5 lists the
various reaches of Plan 1 entrance and offshore channels where shoaling is
expected, estimates of deposition rates (rounded to 0.1 ft/year), and recommen-
dations for advance maintenance depths (rounded generally to whole feet). If
the length of channel between sta -97+76 and sta 325+00 is considered and only
the rectangular portion of the planned channel cross section is taken, the
total dredging volume for advance maintenance in accordance with the recommen-
dations shown in Table 5 represents a savings of approximately 630,000 cu yd,
or nearly 27 percent, compared to the dredging volume for a channel with 3-ft
advance maintenance throughout this reach.
133. The recommendations given in Table 5 do not take into account the
long-term economic advantages of providing greater advance maintenance depths
and dredging less frequently than once a year, especially in the offshore
areas, in view of the high cost of mobilization of dredging plant. This issue
should be explored before a final decision is made on advance maintenance
depths.
134. From the geologic sections provided by CESAJ, rock seems to be
present at depths of 40 to 54 ft mlw between sta 234+00 and 260+00. Two of
the reaches where large advance maintenance depths of the order of 7 to 9 ft
have been recommended are in this general area. This is the area just outside
of the jetty tips and just interior to the jetties. Severe deposition prob-
lems have been experienced in this general area at present because of material
moving from the shoals on either side of the channel into the channel. Gener-
ally, the highest deposition rates have been observed in the northernmost
quadrant of the channel. In view of the difficulty and expense of dredging in
rock and problems that may be experienced with large overdepth dredging, it is
suggested that overwidth dredging be explored as an alternative to overdepth
dredging in this area. For instance, in addition to providing a reasonable
78
advance maintenance depth, the channel may be widened by 100 to 125 ft (total
width of channel equals 600 to 625 ft) in this reach. Overwidth dredging may
be considered also as an alternative in other reaches where rock may be
present.
Future Testing
135. Model B results for Plan 1 provided in this report have been ob-
tained by testing a 500-ft-wide channel with a project depth of 46 ft mlw and
advance maintenance depth of 3 ft throughout. Once the channel design is
finalized, it is recommended that the final design be tested in Model B with
the latest available bathymetry in and around the channel so that maintenance
dredging requirements can be determined more accurately corresponding to the
final channel design.
136. Model B has been used in this study to estimate average yearly
erosion/deposition rates in the entrance and offshore channels under average
wave conditions, excluding abnormal storms. These estimates are good for pre-
dicting long-term average maintenance dredging requirements. However, the
effect of severe storms such as hurricanes and tropical storms on shoaling can
be quite dramatic. So it is recommended that shoaling of the planned naviga-
tion channel under severe storm conditions be investigated since estimates of
shoaling volumes can be used in channel design as well as in advance planning
for emergency mobilization of the necessary dredging plant to keep the channel
open. This task can be performed using Model B and the storm surge modeling
capability of WIFM.
79
PART VII: SUMMARY AND CONCLUSIONS
137. To study the effects of proposed modification of the exterior
channels of St. Marys Inlet (the ocean entrance to Kings Bay Naval Submarine
Base) on coastal processes, the CIP system of numerical models of CEWES was
employed. The system included models for tides, waves, wave-induced currents,
and sediment transport. The system together with two computational grids
developed for the study was called Model B.
138. Model B was used to study existing (base) conditions as well as
planned conditions. Plan 1 is to (a) widen the navigation channel by 100 ft
on the north side so the total width becomes 500 ft, (b) deepen the channel to
-49 ft mlw (46-ft project depth plus 3-ft advance maintenance) with side
slopes of 3H:1V, and (c) extend the channel on the ocean side with a 20-deg
bend to the south at sta -97+76. It is assumed also that the landward
1,000 ft of the south jetty is made sand-tight for Plan l.
139. The tidal model was verified using the field data of 10 November
1982. This was achieved by forcing the model with measured tidal elevations
and matching observed velocities at ranges in the inlet, Cumberland Sound, and
St. Marys River. There was good agreement.
140. The average year's wave climate for the study area was obtained
from WESWIS, on the basis of 20-year hindcast data. The data set included
normal storms but not hurricanes and tropical storms. This was used in run-
ning the wave and wave-induced current models.
141. The sediment transport model determined noncohesive sediment
(sand) transport in the study area, under the combined action of tides, waves
and wave-induced currents. It considered a mean tide and the average year's
wave climate.
142. The sediment transport model was verified by comparing computed
erosion/deposition rates in the navigation channel with those obtained from
field surveys taken by CESAJ during 1980-81. There was good agreement with
respect to both trends and magnitudes.
143. While all four models were run for base conditions, only the tide
model and the sediment transport model were run for plan conditions (Plan 1)
to meet the urgent need for model results. (Plan conditions were expected to
influence the tide and sediment transport much more than the waves and
wave-induced currents. )
80
144. The effects of Plan 1 on tidal currents were mainly local and
caused by sand-tightening of the south jetty. Velocities at the end of the
jetties and at tide Gage 1 increased by approximately 10 percent. There were
no significant changes in velocities at the throat of the inlet, including
Range 1 and the Fort Clinch area.
145. Model B predicts an increase in deposition and erosion rates be-
tween sta -97+76 and sta 325+00 from base to Plan 1. For the reach of channel
between sta -—80+00 and sta 325+00, the predicted yearly shoaling volumes are
475,000 and 788,000 cu yd/year for base and Plan 1, respectively, or an in-
crease of 66 percent for Plan 1.
146. On the basis of Model B results and all other available informa-
tion, recommendations on advance maintenance dredging were made for different
reaches of the navigation channel (Table 5).
147. For the length of channel between sta -97+76 and sta 325+00, if
only the rectangular portion of the planned channel cross section is consid-
ered, the total dredging volume for advance maintenance in accordance with
Model B recommendations represents a savings of approximately 630,000 cu yd or
nearly 27 percent compared to the dredging volume for a channel with 3-ft
advance maintenance throughout according to Plan 1.
148. In summary, the study successfully accomplished all the study
objectives, as set forth in paragraph 3, "Purpose," except for the determina-
tion of waves and wave-induced currents under plan conditions. The numerical
models for these processes were not rerun, as originally planned, in order to
meet the urgent needs of the sponsor.
81
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85
Table 1
Numerical Gages Used in WIFM
Numerd caliGageinOe spe ay ete ti men Ly MCCA Sem aries een aan
1 Prototype tide Gage 1 (south spit)
5 Endeco velocity Gage 2 (main channel)
10 Range survey Gage 1-A
iil Range survey Gage 1-B
2, Range survey Gage 1-C
25 Ocean end of jetties—channel
Bi Fort Clinch
28 South channel (Amelia Island)
29 Channel to Cumberland
Table 2
Sample of WESWIS Data for St. Marys Inlet
69.9
60.0 -
CH_ANGLE(DEGREES)
Hi
TOTAL
LONGER
11.0-
9.0- 10.0-
9.9 10.9
F HEIGHT AND PERIOD BY DIRECTION
PERIOD( SECONDS )
HEIGHT( METRES )
WDRASCNMSSOCSO
At ann
Tene
rir
o
eee ree er eee
BS
MOC > © & © © oe oD
a ] Cx)
a)
+r
LALA ord 2 6 6 © © ot)
wu
o
PUAN oro 6 © ot
Ca]
i
OUNTOTFAr © 6 6 ot
ron mmr N
°o
SMAOMO 2 + * +O
On aN +r
N
rm
© NO 6 6 0 © 0 © og)
mor Nu
Cy)
na]
OF 6 6 0 6 0 6 6 o>
oo nR
Ds)
mm
(va) V9 CC CY = 9
wh a
sro
wy
CUM) 6 6 6 0 eo 0 oo ot
ao +
Tt
is4
Ww
=
DADAAAHAAO SL
SS NAN
CORES)
OD0000000 0 Of
COCCCOSOCOCOF-
Nonomonone
Ooo 010 0 000 0
COmANNMMS TiN
TOTAL
79.9
11.0-
-9 LONGER
3.2
70.0 -
-0-
10
10
ANGLE CLASS Z =
OACH_ANGLE( DEGREES)
3.45
F HEIGHT AND PERIOD BY DIRECTION
PERIOD( SECONDS}
LARGEST HS(M)
0.69
AVERAGE HS(M)
HEIGHT(METRES)
ATFOOTFTFNCSCOO
ORSINED «© 6 6 6 ood
Room ca)
on pa
MoMA
AeMMME
Aine
536
AnnormM
ml wot
270
el
HHO 6 6 0 0 0 8 oe Oo
Ss}
fea salealcalcatcalcalsalcalcad- ¢
SEATS ESI
Ce
Oiala lati
DEO COAT Dene Oh
Ooocococoocoor-
MoOMNoMnonona
oe eee eee eee
SORANANMMESIN
TOTAL
89.9
SB Goal
80.0 -
11.0-
9.9 10.9 LONGER
9.0- 10.0-
“OMMOLAD
ANGLE CLASS Z%
OACH_ANGLE(DEGREES )
ZIMUTH
F HEIGHT AND PERIOD BY DIRECTION
3.28
PERIOD( SECONDS )}
LARGEST HS(M)
0.62
AVERAGE HS(M)
HEIGHT( METRES)
ABDODOMAONUHOOS
FAUMOMAM ort «>
MONASH
rion
Ln Ua |
313 3310 2395
AAAAANOR + «
SnOkNNA
De aa)
ric
OLOMSAe
NoOMnmMr
°
°
°
i
NMOMRN
Linc
1491
ANGLE CLASS Z
AAMNCor~
WO tonor
oor Cal
2
0
é
3
0
747 1746
4.32
wy
© COTM © © 6 6 © og
+
na)
LGD © © 6 © 6 © © oh
oO
N
CeCe CCT: «)
r
AAADAAAAGKAO ST
SSS
OO OOOO OO Od
SO IOS SOT
PSO DSU ED UUs US Tes
ooooocoocoooF
NOMNoOMoMNoMNo
OO OO OONONO nO 0
SORANNMMIS SW
12.6
LARGEST HS(M)
0.72
AVERAGE HS(M)
Table 3
Incident Wave Conditions for St. Marys Inlet
DERE EIEN DEES) HEIGST (FT) PERIOD (SECS) FESCENT CUM. FRED. OCCUR.
2. ei 2 043
1 -? 22 3.20 4.31 0434
2 -72.50 2.26 5.39 1,917 06228
3 -72,50 4.40 6.30 235 18463
4 -62.5 82 2.50 2.102 OSE65
5 -52.50 2.46 4.5 £1233 “09793
i -62.50 4.10 6.20 58 30378
? -62.50 5.74 7.09 220 30538
8 -32.50 132 2.40 $1853 32864
9 -22.50 2.46 4°70 11315 13776
10 =59159 4:10 5:70 404 141g
it -=2,50 5.74 5.80 132 gai2
12 -£2.50 7.38 7.40 1032 14404
13 -43/59 182 5120 2.733 117202
14 ~£2,50 2.46 5.50 1.635 19897
15 -42,50 4.10 5.79 444 19344
16 -£2,59 5.74 6.20 116 119457
17 -62,50 7.33 2.20 1 13572
18 -32.59 22 7.20 9.409 263981
19 -22, 2.48 5.30 11235 30376
20 -32,50 4,10 6.00 1456 30232
2. ~52,50 5.24 6.69 iSES 30987
22 -32,59 7.38 7.20 029 131077
23 -22.50 122 4.39 11415 32433
24 -22.50 2.45 4.90 11443 122641
25 -23150 4:10 5.60 377 34013
26 -22.50 5.74 6.50 823 134147
2? -22.59 7.33 7.30 124 24263
23 ~12.50 182 2.00 2.585 137783
29 -12,50 2.45 7.90 2.574 40157
30 -12.59 4:10 6.60 “656 140813
ai “12.50 5.74 2.00 259 41072
3 -12159 7.33 7.50 134 41206
3 -13150 3182 7.40 $99 41305
34 -2.5 32 8.50 5.249 46554
35 -2.50 2146 2.50 4.909 151453
35 -2.50 4:10 3.30 1.349 152912
37 -2.50 5.74 8.00 ‘546 53353
33 -2,50 7.38 2.80 233 133646
33 -2150 9.02 3.30 193 153839
2 -2.50 19.66 3.70 06! 753300
43 7.50 122 2:10 4.197 13097
49 7.50 2,46 6.70 2.5 60629
43 7.50 4.40 6.90 1.075 61704
44 7.50 5.74 2.43 1439 162193
45 7.59 7.33 2,30 132? 162520
46 7.50 9,02 7.69 178 62693
47 7.59 10.66 2.50 065 $2763
43 17.50 182 6.00 2.792 165555
43 17.50 2.46 5.40 1.502 67057
50 17.59 4.10 6.00 761 ‘67818
51 785 3.74 6.60 1327 68145
52 17.5 7.23 7.90 1238 52263
53 17.50 9.02 7.59 153 852i
54 17.59 10.66 7.59 118 69639
55 27.50 132 4.40 1.177 162316
5 27.50 2.46 4,20 1.164 £20380
5 27.59 4,19 5.39 616 75595
53 27.50 3.74 6.20 370 178366
53 27.59 7.38 6.90 25 172220
60 27.30 9:02 7.40 208 72428
61 27.50 10.66 7.50 155 172593
62 37:50 182 2.69 73321
63 37.50 2.46 4.20 11244 174565
64 37.5 4.30 5.30 6 75474
63 37.50 5.74 6.20 1498 175969
65 37.50 7.33 6.90 306 28275
67 37.50 9.02 7.59 149 176424
63 37.50 10.66 7.50 068 76432
63 47.50 82 2:70 997 77383
70 47.50 2.46 4.40 1.225 ‘75614
2 47.50 4.10 5.40 1.088 29202
72 47.50 5.74 6.00 434 3012
73 47.50 7.33 6.70 031 ‘80227
24 57.59 182 4.10 1.706 81933
25 57.50 2.46 5.20 2.106 64039
76 57.50 4.10 5.70 1939 184878
77 57.50 5.74 6.10 070 184948
23 67.59 22 4.90 4.051 22399
? 67.50 2.46 5.79 ‘624 123693
80 ‘00 00 100 «= 10.317 100800
Table 4
Details of CESAJ Examination Surveys
Sue a nLiclustvclDatessaa ln lll ml NiSUrveyedlistattons
1 21-25 Nov 80 130+00 to 325+00
2 8-9 Dec 80 -80+00 to 130+00
3 31 Mar-13 Apr 81 130+00 to 325+00
4 13 Mar-13 Apr 81 -80+00 to 130+00
5 8 Jun 81 130+00 to 325+00
6 8-10 Jun 81 -80+00 to 130+00
7 14-18 Dec 81 -80+00 to 325+00
Reach
Table 5
Recommendations for Advance Maintenance Depths
of Channel
(CESAJ sta)
-97+76
42+38
128+72
181+20
225479
249+03
276+31
325+00
to
to
to
to
to
to
to
to
424+38
128+72
181+20
225+79
249+03
269+85
310+38
399+74
Estimated
Maximum Local
Deposition Rate
ft/year
0.3
0.3
1.8
3od
6.9
8.2
1.5
Recommended
Advance
Maintenance Depth
ft
1.0
1.0
2.0
4.0
7.0
8.5
2.0
3.0
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1962
NOVEMBER
ST MARYS ENTRANCE, SOUTH JETTY
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: For interior resu
Note
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PLATE 23
al J
a
pn
APPENDIX A: NOTATION
Wave amplitude function
Ratio of volume of solids to total volume of sediment
=l-p
Mapping constants for region p in x-direction
Mapping constants for region q in y-direction
Area of cell
Drag coefficient, wave celerity
Coefficient
Wave group velocity
Chezy coefficient
Local total water depth
Sediment diameter exceeded in size by 65 percent (by weight)
of sediment sample, energy dissipation term
Wave energy density = peH-/8
Coriolis parameter, drag coefficient
Terms representing external forces
Wave friction factor with D as bed roughness
Acceleration due to gravity
Local still-water depth
Wave height
Wave height in deep water
Unit vectors in the x- and y-directions
Local immersed weight longshore transport rate
Total immersed weight longshore transport rate
Number of water cells within the surf zone
Wave number
Empirical coefficient
Empirical coefficient
Bottom slope
Maximum values of cell indices for RCPWAVE
Ratio of group velocity to wave celerity = c /c , Manning's
roughness o
Porosity of sediment
Local volumetric sediment transport rate due to currents
Al
Local volumetric sediment transport rate
Local volumetric sediment transport rates in x- and
y-directions
Rate of water volume change due to rainfall or evaporation
Arbitrary variable, mass density of sediment relative to that
of fluid (specific gravity of sediment), wave phase function
Radiation stresses
Time
Wave period
Wave orbital velocity at the bottom
Time average of the absolute value of the wave orbital
velocity at bottom
Tidal velocity components
Velocity components due to wave-induced currents
Total velocity component = u + U
Shear (friction) velocity
Longshore velocity
Total velocity component =v +V
Coordinates in real space
Width of surf zone
Dimensionless grain diameter
Coordinates in computational space
Breaking index = H/h
Proportionality coefficient
Centered difference operators
Time-step
Cell dimensions in real space
Cell dimensions in computational space
Eddy viscosity for tidal model
Eddy viscosities in x- and y-directions
Bed elevation
Tidal elevation above datum
Mean free surface displacement (setup)
Hydrostatic water elevation due to atmospheric pressure
differences
Angle of wave propagation
Wave direction in deep water
A2
6 Contour angle
: Rate of energy dissipation coefficient
kK Refraction coefficient
Se Shoaling coefficient
Ue» n Grid expansion coefficients
v Kinematic viscosity of fluid
T 3.14159...
9) Mass density of sea water
D . Mass density of solids
fo) Wave angular frequency = 21/T
cA Bed shear stress
eee bes, Bottom friction stresses in x- and y-directions
toed Lateral shear stress due to turbulent mixing
> Complex velocity potential for wave
Superscripts
k-1 Previous time level
k Present time level
k+1 Next time level
x Intermediate time level
Subscripts
b At breaking
s Stable level of a variable
ft Partial derivative with respect to time
A3
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USGS
WESWIS
WIFM
APPENDIX B: ABBREVIATIONS AND ACRONYMS
alternating-direction-implicit
Coastal Engineering Research Center
US Army Engineer District, Jacksonville
US Army Engineer Waterways Experiment Station
Coastal and Inlet Processes
Hydraulics Laboratory
mean low water
mean sea level
mean water level
National Geodetic Vertical Datum
National Ocean Service
Officer In Charge of Construction
Regional Coastal Processes Wave Propagation Model
stabilizing-correction
still-water level
United States Geological Survey
WES Wave Information Study
WES Implicit Flooding Model
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