ϕ = incident angle of the wind (see Figure 1 for a definition of this angle).

Group (1988):

(29)

In this formulation the depth-averaged steady cross-shore current (*U*c = *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 *S*xx is given

by:

*C*gr

1

1

(cos2 α + 1) -

(30)

*C*r

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.

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