ERDC/CHL CETN-IV-25
June 2000
momentum equation, provision for an external (large-scale) current has been incorporated in
addition to the wave- and wind-driven currents. At present, the external current must be
specified as an input, although in the future an option will be added allowing the user to generate
current distributions within NMLong-CW corresponding to, for example, large-scale tidal
currents and ebb jet flows. Additional background information on the current-and-wave
interaction can be found in other CETNs (Smith 1997, 1999) produced under the Coastal Inlets
Research Program (CIRP).
In the following, a summary is given of the equations used in NMLong-CW with focus on the
enhancements made. The procedures for calculating wave transformation, longshore current,
and water level change are discussed separately. Also, a section is included on wave blocking
and the criterion applied to describe this phenomenon. Capabilities of NMLong-CW are
demonstrated by examples. The model is operated through a graphical interface that runs on the
Windows 95/98 and NT platforms for personal computers. NMLong-CW is at the state of the art
in calculation of nearshore waves and currents, and this CETN documents the underlying physics
implemented.
WAVE TRANSFORMATION:
Under the condition of alongshore uniformity, wave
transformation across a nearshore profile is described by the equation for conservation of wave
action flux (e.g., Jonsson 1990):
d ECga cos β ED
=
(1)
ωr
ωr
dx
where E is the wave energy (linear theory used), Cga the absolute wave group speed, β the wave
the wave energy dissipation, and x the cross-shore axis pointing offshore. The presence of a
for Cga and β may be obtained from geometric considerations to yield (see Figure 1 for a
definition sketch):
C ga = (C gr + U 2 + 2C grU cos(δ - α ))
1/ 2
2
(2)
U sin(δ - α )
β = α + arctan
(3)
U cos(δ - α ) + C
gr
where Cgr is the relative group speed, and α the direction of the wave orthogonal.
The
definitions of the angles are 90 ≤ α ≤ 90 and 180 ≤ δ ≤ 180.
2
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