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6.2 Including Wave Reflection
The author has made unsuccessful attempts to include wave reflection in the model.
Kirby (1986) used coupled equations governing the interaction of a forward and a backward
(reflected) propagating wave that are coupled through a slope interaction. He was able to
obtain the reflection and transmission coefficients over submerged breakwaters that agree
well with the experiments of Seelig (1980). Once the arrays of the complex amplitudes of
the two waves is determined, the radiation stress terms can be determined from equations
that have been derived following the same procedure as used by Mei (1972) but defining
as being comprised of two components. In fact this procedure can also be used to obtain
the radiation stress terms for any number of components. The only limit being the amount
of computation required as the number of components increases.
Smith (1987) following the work of Miles (1967) for wave reflection and transmission
over a step derived equations for the complex reflection and transmission from a submerged
plane barrier. An attempt was made using this formulation to obtain the circulation and
wave pattern from a submerged breakwater represented as a plane impermeable barrier.
However problems of numerical stability were encountered. It is suspected that the sharp
gradients between the region with the presence of the reflected wave and regions of its
absence adjacent to the barrier produced unrealistic gradients in the radiation stress terms.
An attempt was made to include the reflected wave for the case of an emerged plane barrier
with the same unstable result. This is a topic for further investigation.
6.3 Extending the Model to Include Sediment Transport
The model as it currently stands can be extended to include sediment transport. The
wave model can be slightly amended to retain wave energy dissipation as an array. If a
formulation of sediment entrainment can be made in terms of the wave energy dissipation
and the bottom shear stress, everything else is in place to accomplish the sediment transport
model. A simple numerical mechanism would be to assume steady state conditions for
certain time intervals and solve for the wave and current field and the sediment concentration