as opposed to conservation of wave energy flux as underlying NMLong, so

that the interaction between the current and waves can be represented.

Alongshore uniformity in hydrodynamic and beach characteristics is still a

requirement, but an arbitrary angle between the current and wave directions

is permitted, so that the wave-current interaction from a cross-shore current

might be simulated. This capability allows NMLNG-CW to calculate wave

transformation, for example, in a narrow inlet for waves arriving with crests

normally incident to the inlet entrance. The dispersion relationship was

modified to include a current, which in turn modifies wave refraction

computed through Snell's law. Wave energy dissipation associated with

depth-limited breaking is described in accordance with the model of Dally,

Dean, and Dalrymple (1985), who postulated that the energy dissipation is

proportional to the wave energy flux over a stable flux given by the water

depth. For waves breaking on a current, a similar formulation is employed,

where the stable flux is obtained based on the limiting wave derived from a

Miche-type criterion. Thus, both depth- and steepness-limited breaking are

included in NMLong-CW, as well as wave decay through energy dissipation.

Wave blocking by an opposing current is also represented in NMLong-CW.

As in NMLong, the longshore current and mean water level are

calculated by the longshore and cross-shore momentum equations,

respectively. The wave properties expressed in a relative frame of reference

(moving with the current) serve as input to compute wave-related quantities

in the momentum equations. In the longshore momentum equation, wind-

generated and external currents are incorporated besides the wave-driven

currents. Thus, NMLong-CW allows for specification of an external current,

for example, large-scale tidal currents or the ebb jet from a tidal entrance.

The user of the model must provide this external current, and it can be based

either on observations or on simulation results from other models, thus being

an input quantity. Integrating such a predefined current into the longshore

and cross-shore momentum equations necessarily requires certain

simplifications, as discussed in the following chapters. Nonlinear friction

and lateral mixing are included in the same manner as for NMLong.

To model the shift in the peak of the longshore current and maximum set-

down observed in laboratory as well as in field data, the roller model

developed by Dally and Brown (1995) was implemented in NMLong-CW.

Thus, a wave energy balance equation for the roller was added in the model

that yields the growth and decay of the roller through the surf zone. The

cross-shore variation in roller mass flux is calculated through this equation,

from which the momentum fluxes in the cross-shore and longshore direction

are obtained. These momentum fluxes are included in the cross-shore and

longshore momentum equations, with the result that the forcing for the

longshore current and mean water level is translated shoreward.

The numerical formulation follows the approach taken in NMLong and

will not be discussed in detail in this report (see Kraus and Larson 1991). A

wave-by-wave description is employed to simulate the random wave field

assuming narrow-bandedness in wave period and direction. Thus, a single

wave period and incident wave angle are sufficient to characterize the wave

field for the time scale of the simulations, and the randomness only enters

through the wave height assumed to be Rayleigh distributed. The driving

forces for the wave-generated current and mean water level change are

expressed in terms of averages based on the calculations carried out for the

ensemble of waves selected. In solving the governing equations, NMLong-

CW employs iterations at several different levels to allow for full interaction

2

Chapter 1 Introduction

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