2.1. Morphologic Model with 1-D Hydrodynamic Forcing
The classical depth-averaged 1-D inlet hydrodynamics equations of Keulegan
(1967) are implemented. These are the momentum equation,
⎛
2c f L ⎞ U U
∂U
g
(η
)+⎜K
=0,
- ηO
+
+ K ex +
(3)
⎟
⎝
⎠
B
en
∂t
L
RH
2L
and the continuity equation,
dη B
,
(4)
ACU = AB
dt
in which U = depth-averaged and inlet-length integrated current velocity, AC =
breach or inlet channel cross-sectional area below mean sea level (msl), t = time,
the bay and in the ocean, respectively, Ken and Kex = entrance and exit losses,
c f = gn / h in which n = Mannings coefficient typically set as 0.025 s/m1/3,
2
1/ 3
RH = hydraulic radius of the inlet, and AB = surface area of the bay. The
assumptions of an idealized Keulegan inlet apply, such as vertical walls in the
bay, and sufficiently small bay area to allow the bay surface to move up and
down uniformly in response to tidal flow. In the breach model, the breach
cross-sectional area expressed in Eq. (4) is time dependent. Eqs (3) and (4) are
solved for U and η B , respectively.
For the situation of multiple inlets and breaches, if the openings do not
directly interact (with the other Keulegan assumptions still holding), U in
Eq. (3) can be replaced by Ui and AC by (AC)i for the ith opening among N total.
Eq. (4) generalizes to:
dηB
N
∑
.
( Ac )i U i = AB
(5)
dt
i =1
If waves are present, in addition to increasing the bottom shear stress,
breaking waves produce set up, calculated in the model by standard equations.
2.2. Sediment Transport
The sediment transport rate at the bottom is calculated by total load formula
given by Watanabe et al. (1991),
4
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