A NOTE ON THE GENERATION AND NARROWNESS OF PERIODIC RIP CURRENTS

Periodic rip currents on a wide planar beach are generated in the laboratory by shoaling water waves that are periodic in time and in two spatial directions: one normal (x direction) and one parallel (y direction) to the shoreline. These short-crested waves propagate in water of uniform depth with nearly permanent form. They are described analytically by a family of solutions of the Kadomtsev-Petviashvili (KP) equation (KP solutions of genus 2). During shoaling, genus 2 waves retain their spatial pattern past breaking, and they quickly generate periodic rip currents along the beach with a spacing of one-half the y wavelength of the incident waves. KP theory also provides a plausible explanation and prediction for the narrow widths, relative to their longshore spacing, of rip currents generated in this manner. An estimate of their widths is one-half the x wavelength of the incident waves.