A windy sea surface with Stokes waves

Abstract

Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves ($4-13$ cm) onto a Reynolds number -- wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave, offering insights with broad implications for interfacial pattern-formation and oceanic remote-sensing.