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equations. This assumption implies that vertical fluctuations of the flow which are zero in
the time average can be ignored. Many details of the flow may be missed by this assumption
of purely horizontal flow. Of course reducing the problem to a two-dimensional flow has
the distinct advantage of reducing an essentially intractable problem to a simpler tractable
form.
Some of the terms in Eqs. (2.1-2.3) also involve certain assumptions. These terms
are the bottom friction, the surface wind stress and the lateral mixing. These are all
phenomenon that are not completely understood so that assumptions are made concerning
the complex forces that are represented. These assumptions usually involve the use of
empirical coefficients. In this study the wind forces are ignored so the assumptions involved
with the surface stress will not be discussed in detail here. It would be a relatively simple
task, though, to add a wind surface stress to the model, using a quadratic shear stress as
formulated by Birkemeier and Dairymple (1976) and also used by Ebersole and Dedrymple
(1979) following the work of Van Dorn (1953) in determining the value of the empirical
coefficient.
The interaction of an oscillatory fluid flow with a real bottom is very complex. Many
physical phenomena may be at work. With sand bottoms there can be percolation into the
sand and frictional effects resulting in wave energy dissipation. With mud bottoms where
the mud is essentially a dense fluid layer there can be damping and internal waves along
the mud-water interface. Wave energy losses due to bottom effects are not included in the
model but can easily be incorporated into the wave dissipation subroutine. Resuspension
and settling of particles also constitutes a complex phenomenon with density changes and
momentum transfers. All of these effects are glossed over in the model by assuming a rigid
impermeable bottom. As with all of the models discussed above the bottom friction term is
represented in the quadratic form. Noda et al. (1974), Birkemeier and Dalrymple (1976) and
Vemulakonda (1984) all used the weak current formulation as proposed by Longuet-Higgins