Unforced Oscillation of Rip-Current Vortex Cells

Abstract

Abstract A numerical simulation of a monochromatic surface gravity wave–driven flow over an alongshore quasi-periodic rip-channeled beach using the wave-resolving model Funwave is used to investigate coherent, very low-frequency (VLF) motions with characteristic frequencies f < 4.0 mHz inside of the surf zone generated by wave breaking. These oscillations of the nearshore cellular vorticity pattern occur for shore-normal waves over a wide range of amplitudes of the incident wave field and occur despite the wave forcing being essentially constant. The oscillations occur at the lower end of the VLF spectrum or around fp = 0.55 mHz. For small incident wave amplitudes, an equilibrium state consisting of a staggered counterrotating vortex array generates a net weak alongshore current that is also seen in drifter trajectories observed in the field. Using a simpler pseudospectral vorticity model of a single dipole generated by a smooth, stationary in time forcing function sb, this study shows show that the Strouhal number of the vortex shedding process responsible for the oscillation is dependent on the circulation strength of the vortices in the dipole, as well as the bottom friction parameter. This process includes the pinching off, advection, and eventual regeneration of the vortex in the dipole. A simple scaling argument shows good agreement with the frequencies observed in the simulations.