Weakly nonlinear analysis of wind-driven gravity waves

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Abstract
We study the weakly nonlinear development of shear-driven gravity waves induced by the physical mechanism first proposed by Miles, and furthermore investigate the mixing properties of the finite-amplitude solutions. Linear theory predicts that gravity waves are amplified by an influx of energy through the critical layer, where the velocity of the wind equals the wave phase velocity. As the wave becomes of finite amplitude nonlinearities have to be taken into account. In this paper we derive asymptotic solutions of finite-amplitude waves for weak wind and strong gravitation , consistent with Venkataramani's results.

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