Another phenomenon that could occur, if a current opposing the waves is

present, is that energy is transported offshore although the waves propagate

onshore. The limit for this situation to occur is given by:

cos α

=-

(27)

cos δ

This condition corresponds to the solution of the dispersion relation for the

higher wave number (see Figure 2). Although it is not likely that such

conditions would occur in model applications for the nearshore, a check is

still included in NMLong-CW because the user is free to specify an arbitrary

external current.

In NMLong-CW, the cross-shore momentum equation is employed to

determine changes in the mean water level (setup/setdown) induced by wave

and wind. The model includes the possibility of specifying an external

(large-scale) current and determining the effect of this current on the wave

transformation, as well as the interaction with currents calculated by

NMLong-CW (e.g., currents generated by waves and wind). In the wave

action equation (Equation 1), the inclusion of the current is straightforward

and independent of the mechanisms that are generating the current.

However, for the momentum equations, it less obvious as to how to account

for the external current, especially for the cross-shore momentum equation.

For example, one type of external flow that might be of interest to

incorporate in applying NMLong-CW is the ebb jet from a tidal inlet.

Effectively, this type of flow is generated by a momentum source (the inlet)

generating a jet that is discharged offshore under the influence of turbulent

mixing, inertia, and bottom friction. Measurements of the jet flow or simple

models employing jet theory might be accessed to estimate the velocity field,

which, in turn, could be the input for the external current to NMLong-CW.

However, in applying the cross-shore momentum equation to determine the

waves, questions arise as to how to treat the external current in such

calculations. In this context, it should be pointed out that NMLong-CW is

based upon alongshore uniformity, which could be in contradiction to the

complex and often highly 2-D flow field at an inlet. However, applied with

care, there are many situations at an inlet where applications of the model are

theoretically justified, and satisfactory results will be obtained. Because of

the alongshore uniformity assumption, considerations should always be made

with regard to the possible variation in quantities alongshore, including the

current. Such considerations involve the relationship between the spatial

scale of the current and wave motion.

In NMLong and NMLong-CW, the mean water level η is determined

using the following cross-shore momentum equation,

= - xx - *C*Dρa W W cos ϕ

ρ*gd*

(28)

20

Chapter 3 Wave Model

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