On the Unsteady Steepening of Short Gravity Waves Near the Crests of Longer Waves in the Absence of Generation or Dissipation

The wave action equation provides a general framework that has been applied to the conservative hydrodynamic interactions between short and long surface waves. So far, only a limited range of solutions have been investigated. Here we show that the wave action equation predicts that groups of short waves propagating over long monochromatic waves are unstable. We demonstrate theoretically and numerically a new ratchet-type instability that progressively condenses short wave action around the long wave crests due to the correlation of phase speed and action fluctuations. This instability is of particular interest because it may lead to a higher probability of breaking for short waves propagating in directions within ± 35 degrees of the dominant waves direction. This preferred breaking could have a strong impact on cross-wind and down-wind slope statistics and thus air-sea exchanges and remote sensing.

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