On theories dealing with the interaction of surface waves and ocean circulation

The classic theory for the interaction of surface gravity waves and the general ocean circulation entails the so-called wave radiation stress terms in the phase-averaged momentum equation. The equations of motion are for the combined Eulerian current and Stokes drift. On the other hand, a more recent approach includes the so-called vortex force term in the momentum equation wherein the only wave property is Stokes drift. The equations of motion are for the Eulerian current. The idea has gained traction in the ocean science community, a fact that motivates this paper. A question is: can both theories be correct? This paper answers the question in the negative and presents arguments in favor of the wave radiation theory. The vortex force approach stems from an interesting mathematical construct, but it does stand up to physical or mathematical scrutiny as described in this paper. Although not the primary focus of the paper, some discussion of Langmuir circulation is included since the vortex force was first introduced as the basis of this oceanic cellular phenomenon. Finaly the paper explains the difference in the derivation of the radiation stress theory and the vortex force theory: the later theory entails errors related to its use of curl and reverse-curl [or uncurl] processes.