# The Interaction between Long and Short Wind-Generated Waves

## Abstract

The interaction of wind-induced short (capillary) and long (gravity) surface waves of disparate scales is analyzed with the use of an expansion procedure accounting for the lowest-order effects of finite short-wave amplitude on the growth of a small-amplitude long wave. Interactions in both water and air are considered. In the water there is transfer of momentum from the short to the long waves arising from the modulation of the short-wave growth rate by the long wave; this may be interpreted as the effect of the shortwave surface-stress modulations in phase with the long-wave surface elevation and is consistent with earlier treatments employing energy considerations. The interaction in the air is treated with an in viscid model. This shows that the modulation of the short-wave Reynolds stresses by the long wave can give rise to a phase shift between long-wave pressure and surface slope which may significantly increase the rate of transfer of momentum from the wind to the long wave.

## Keywords

Short Wave Critical Layer Longe Wave Stoke Drift Wave Slope## Preview

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