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.

中文翻译：

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在没有产生或消散的情况下，短重力波在较长波峰附近的非稳态陡峭化

波浪作用方程式提供了一个通用框架，该框架已应用于短和长表面波之间的保守流体动力相互作用。迄今为止，仅研究了有限范围的解决方案。在这里，我们表明波动函数方程预测在长单色波上传播的短波组是不稳定的。我们从理论和数值上证明了一种新的棘轮型不稳定性，由于相速度和作用波动之间的相关性，这种不稳定性逐渐将短波作用凝聚在长波峰周围。这种不稳定性特别令人关注，因为它可能导致在主波方向的±35度以内的方向传播的短波发生破裂的可能性更高。