| Abstract: Surface wave equations appropriate
to three-dimensional ocean models apparently have not been presented in
the literature. It is the intent of this paper to correct that
deficiency. Thus, expressions for vertically dependent radiation
stresses and a definition of the Doppler velocity for a vertically
dependent current field are obtained. Other quantities such as
vertically dependent surface pressure forcing are derived for inclusion
in the momentum and wave energy equations. The equations include terms
that represent the production of turbulence energy by currents and
waves. These results are a necessary precursor for three-dimensional
ocean models that handle surface waves together with wind- and
buoyancy-driven currents. Although the third dimension has been added
here, the analysis is based on the assumption that the depth dependence
of wave motions is provided by linear theory, an assumption that is the
basis of much of the wave literature. |