17
rky = y component of the bottom shear stress
t,x = x component of the surface shear stress
t,v = y component of the surface shear stress
and *^xy ^nd Svv are the radiation stress components which arise from the excess
momentum flux due to waves. It should be noted that U and V include the wave induced
mass transport.
These equations are obtained by integrating the local x and y momentum equations and
the continuity equation over the depth of the water column and then time averaging the
results. This is demonstrated in Appendix A, which follows closely the work of Ebersole and
Dalrymple (1979). For greater details of the derivation the reader is referred to Ebersole
and Dalrymple (1979) or Phillips (1969).
These are the same equations that have been used by other modelers such as Birke-
meier and Dalrymple (1976), Ebersole and Dalrymple (1979), Vemulakonda (1984), and
Yan (1987). Birkemeier and Dalrymple used an explicit numerical scheme and neglected
the advective acceleration terms and the lateral mixing. Ebersole and Dalrymple added the
advective acceleration and lateral mixing terms but still used an explicit numerical scheme.
Vemulakonda introduced an implicit numerical formulation for these equations. Each of
these investigators used a refraction wave model based upon the work of Noda et al. (1974)
which solves for the wave height and wave angle at given grid points. Yan (1987) used a
combined refraction-diffraction wave equation to determine the complex wave amplitude
(magnitude and phase) and then solved for the wave angle in terms of the slope of the wa
ter surface. Each of these studies obtained the radiation stress components in terms of the
wave height and wave angle. The present study differs from the previous ones in that the
radiation stress terms are obtained directly from the complex amplitude and its gradients.
This will be discussed in section 2.2.
The use of Eqs. (2.1-2.3) involves many assumptions. The primary assumption is
that the flow field can be represented in two dimensions using depth and time averaged