The Depth-Dependent Current and Wave Interaction Equations: A Revision

Abstract

AbstractThis is a revision of a previous paper dealing with three-dimensional wave-current interactions. It is shown that the continuity and momentum equations in the absence of surface waves can include waves after the addition of three-dimensional radiation stress terms, a fairly simple alteration for numerical ocean circulation models. The velocity that varies on time and space scales, which are large compared to inverse wave frequency and wavenumber, is denoted by ûα and, by convention, is called the “current.” The Stokes drift is labeled uSα and the mean velocity is Uα ≡ ûα + uSα. When vertically integrated, the results here are in agreement with past literature.Surface wind stress is empirical, but transfer of the stress into the water column is a function derived in this paper. The wave energy equation is derived, and terms such as the advective wave velocity are weighted vertical integrals of the mean velocity. The wave action equation is not an appropriate substitute for the wave energy equation when the mean velocity is depth dependent.