On the instability leading to rip currents due to wave–current interaction

Abstract

We examine the instability leading to depth-averaged circulations, which are related to rip currents in the surf zone, due to wave–current interactions. Our intention is to clarify some issues which are critical to the determination of instability properties, as yet unresolved from previous studies. Those issues are also of interest for hydrodynamic instability problems in general. Attention is restricted to normally incident waves and the region inside, and just offshore of, the surf zone where linearized shallow-water waves are applied. The coupling of waves and circulations is modelled using the concept of wave radiation stresses and the classical ray theory. The instability properties, in terms of the neutral modes, the most unstable mode and the corresponding maximum growth rate, are examined in the domain of parameters which represent the effects of offshore wave height and bottom friction dissipation. Comparisons with observations of natural rip currents are made, and qualitative agreements are achieved.