Abstract
This paper examines the stability of rip currents with shore‐normal wave forcing using numerical stability analyses of nonlinear base flows. Leading order diffraction and wave‐current interaction effects are included, and the effects of depth‐varying currents are also treated in a parameterized manner. Stable and unstable eigenmodes are identified with a variety of forms. For rip currents with strength of O(0.5 m/s), instabilities are seen with a family resemblance to oscillating sinuous jets, as well as more complex forms. For low strength rip currents of O(0.3 m/s), these modes stabilize but are replaced by sinuous and varicose instabilities that extend far offshore and are believed to be convective instabilities made absolutely unstable through wave‐current interaction. Quantitative values for growth rates are found to be strongly dependent on details of the velocity field and on the coefficient of bottom friction. Peak vorticity was found to be a good predictor of oscillation periods for unstable jet modes.
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