where
Λ = nondimensional coefficient
H = wave height
um = bottom wave orbital velocity
The velocity V constitutes the alongshore component of U, that is, U =
(V2+Uc2)1/2, where Uc is the mean cross-shore velocity. Lateral mixing as
described here for a depth-averaged model is an approximation to the more
complex process of vertical and horizontal transfer of momentum as derived
by Putrevu and Svendsen (1992).
The forcing associated with a local wind is given by:
ρa
W W sin ϕ
Rw = C D
(36)
ρ
where
by the WAMDI group; see Equation 29)
ρa = density of air
W = wind speed
ϕ = wind direction (W and ϕ defined in the same way as for
the current; see Figure 1)
It is possible to specify an external current, assumed to be associated with
some large-scale circulation not resolved by NMLong-CW. To represent this
current in the model, a forcing is derived from,
Rlc = c f U lc U lc
(37)
component of the external current (Ucs is the cross-shore component of this
current taken to be equal to total cross-shore current Uc, that is, the cross-
shore current is specified and not calculated in NMLong-CW). If no waves
and wind are present, Equation 34 will produce the specified external current
distribution (compare Equations 34 and 37). To represent the roller, an extra
term should be added on the right side of Equation 34 according to
d(MR,l/ρ)/dx, where MR,l = mRCrsin(α) cos(α), as before.
Bottom Friction
The quadratic bottom friction is calculated by means of a rapidly
evaluated square-wave approximation (Nishimura 1988; Kraus and Larson
1991),
w
fby = c f Z + sin 2 α V
(38)
Z
where
42
Chapter 5 Longshore Current Model
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