ϕ = incident angle of the wind (see Figure 1 for a definition of this angle).
The drag coefficient is given by the expression proposed by the WAMDI
Group (1988):
CD = 1.2875 10-3 W < 7.5 m/sec
(29)
CD = (0.8 + 0.065 W ) 10-3 W ≥ 7.5 m/sec
In this formulation the depth-averaged steady cross-shore current (Uc = U
cos δ) is assumed to be zero, implying that the nonlinear advective terms and
the lateral mixing term are zero as well (Kraus and Larson 1991). For the
situation of wind and waves generating a current on a beach that is uniform
alongshore (assumed here), a circulation pattern is established through the
contribution is small compared to the other terms and may be neglected.
The simplest approach for including an external current (e.g., ebb jet) in
the cross-shore momentum equation is to assume that there is no interaction
between the mechanism that generates the large-scale current and the
modification of the waves and wind on the mean water level in the nearshore.
Thus, Equation 28 can still be employed to determine η, if the wave
properties in a relative frame of reference are used, implying that Sxx is given
by:
Cgr
1
1
Sxx = ρgH 2
(cos2 α + 1) -
(30)
Cr
2
8
Any other formulation of the cross-shore momentum equation to include the
external current would necessarily involve describing the generation of this
current by adding terms in the momentum equation (e.g., driving forces,
inertia and bottom friction terms). Although this might be desirable in some
situations, in the present version of NMLong-CW it was considered outside
the scope of the modeling effort to develop such a general flow model, and
the simplified approach outlined here was taken. For the longshore
momentum equation, a somewhat different approach was taken to include the
external current, as described in Chapter 5.
Modeling the Roller
Observations from the laboratory and field have indicated that the peaks
in the distributions of the setup/setdown and longshore current are typically
translated shoreward compared to what numerical models such as NMLong
predict (e.g., Visser 1982, 1984; Smith, Larson, and Kraus 1993). Several
theories have been proposed to explain this behavior, most of them
hypothesizing that the momentum lost through wave breaking is not
immediately available for driving the longshore current (or for changing the
mean water level), but there is an intermediate step where a roller, or breaker-
induced turbulence, generates a momentum flux before the energy dissipation
eventually occurs. Dally and Brown (1995) developed a model to describe
the mass and momentum flux in the roller. Thus, by combining this model
with NMLong-CW, the aforementioned translation in the peaks is better
simulated.
21
Chapter 3 Wave Model
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