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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