7 Summary and Conclusions
This study enhanced the capability of NMLong to simulate the cross-
shore distribution of the wave height, mean water level, and longshore
current in the nearshore by taking into account the interactions between
currents and waves. Also, a model of the momentum transport in the roller
generated by the wave breaking was included to simulate the shoreward
translation in the forcing commonly observed in measurements as a shift in
the location of the longshore current and mean water level peaks. The new
model is denoted NMLong-CW, where CW stands for interaction between
currents and waves.
The wave action flux conservation equation was implemented to account
for the interaction between currents and waves. The dispersion relation and
Snell's law were formulated to include a current of arbitrary magnitude and
direction. A critical element in the wave transformation calculations is
estimation of the energy dissipation produced by wave breaking, and an
algorithm was implemented that is applicable to any water depth and
describing both depth- and steepness-limited wave breaking. Wave blocking
may occur in a situation with an opposing current, and a routine was added in
NMLong-CW to check for this. The roller model by Dally and Brown (1995)
was also implemented in NMLong-CW to represent the transport of
momentum by wave rollers in the surf zone.
NMLong-CW was evaluated with several high-quality data sets involving
measurements of wave height, mean water level, and longshore current for
both monochromatic and random waves. The wave module was verified, in
particular, for situations where waves propagated against a current
experiencing breaking, dissipation, and blocking on a current. Agreement
with measurements was good in shallow water, where NMLong-CW is
expected to be applied, whereas some discrepancy was observed for deep
water concerning the energy dissipation. However, even in the comparisons
with measurements for deep water, the model displayed a robust behavior
and predicted the shoaling phase and maximum wave height well and the
location of wave blocking to an acceptable degree.
Chawla and Kirby (1998, 2002) observed in their laboratory experiments
that blocking occurred at greater wave celerity than predicted by linear wave
theory. To improve the agreement between model calculations and
measurements, they applied the dispersion relation from third-order Stokes
theory instead of from linear wave theory. In the present study, this option
was explored, but the decision was made not to employ a higher-order wave
theory for the dispersion relation for the following reasons:
a. To develop a theoretically consistent model, other wave quantities
besides the wave speed and wavelength should be described by
higher-order wave theory, which substantially complicates the model
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Chapter 7 Summary and Conclusions
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