Mechanism for Modulating the Growth Rate
of Turbulent-Wind-driven Short Surface Waves by Ripples

Yu. I. Troitskaya

Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhnii Novgorod, 603600 Russia

Received March 21, 1995; in final form, November 24, 1995

Abstract—A mechanism is proposed for modulating the growth rate of short capillary–gravity waves in the
presence of a long wave whose steepness is small compared to the limiting steepness. The long wave on the
water surface induces an oscillating velocity component in the air flow. The spatial and temporal periods of
these oscillations are equal to those of the wave. As a result, the growth rate of capillary–gravity waves also
proves to be modulated. Within the framework of a simple model of the turbulent-wind boundary layer with a
constant eddy viscosity and a uniform profile of velocity, growth-rate modulation is calculated, which is used
to study the modulation of the spectrum of short surface waves in the presence of long waves. It is shown that
allowing for growth-rate modulation can lead to a significant increase in spectrum modulation even at moderate
wind velocities.

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