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 has a strong impact on cross‐ and down‐wind slope statistics and thus air‐sea exchanges and remote sensing. Plain Language Summary Short waves riding on long waves tend to focus their energy near the crest of the long waves. This focusing is most pronounced for short waves propagating within 35 degrees of the long wave direction, and may lead to a preferential breaking of short waves. This effect may explain the relatively low energy observed in short waves that propagate near the direction of the long waves. Key Points Wave trains linearly modulated by longer waves are unstable This instability leads to a progressive steepening on the crest of the longer waves