A vortex force analysis of the interaction of rip currents and surface gravity waves

We use the vortex force formalism to analyze the effect of rip currents on their own wave forcing. The vortex force formalism allows us to decompose the wave forcing into the nonconservative flux of momentum due to wave breaking and the conservative vortex force. Following Yu and Slinn (2003), we consider rip currents initially generated by alongshore variation of wave breaking due to a perturbation of a barred bottom topography. This variation is reduced in magnitude by two current effects on waves: wave ray bending and the flux of wave energy by currents. We compute the change in wave energy caused by these two effects on their own and use this to show that their relative magnitude scales with the square of the ratio of the length to width of the rip current. Both effects increase the wave height over the channels of the longshore bar, which leads to more wave breaking and counterbalances its longshore variation due to bottom refraction. In comparison to wave breaking, the change in the vortex force is negligible. Next, we show how the reduction in wave breaking is similar to an enhanced bottom friction. We then analyze the dependence of this relationship on the breaking parameterization, angle of incidence of the waves, and bottom drag law.