5 Longshore Current Model
Introduction
The longshore current is determined by solving the longshore momentum
equation under the assumption of alongshore uniformity. Kraus and Larson
(1991) discuss the governing equation employed in NMLong together with
underlying assumptions and limitations. In NMLong-CW, the same
differential equation as in the original model is solved to calculate the cross-
shore distribution of the longshore current, with the difference that wave
properties are described in a relative frame of reference. Another difference
compared to NMLong is the possibility of specifying an arbitrary current in
NMLong-CW that might be generated, for example, by tidal motion. In the
following, the governing equation is reviewed with emphasis on the changes
made. Reference is made to Kraus and Larson (1991) for more complete
discussion.
Longshore Momentum Equation
In NMLong-CW, after the wave transformation calculations described in
Chapter 3 have been performed, the longshore current is computed from the
alongshore momentum equation including lateral mixing, bottom friction,
and external forcing. The equation is,
d dV
1 dSxy
- fby =
- Rw - Rlc
εh
(34)
ρ dx
dx dx
where
V = longshore current velocity (total current
originating from waves, tide, and external current)
ε = lateral mixing coefficient
directed alongshore
Rw and Rlc = forcing associated with wind and an external current
(e.g., tide), respectively.
The lateral mixing coefficient is parameterized as (Kraus and Larson 1991),
ε = ΛHum
(35)
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Chapter 5 Longshore Current Model
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