On the Relation between the Growth Rate of Water Waves and Wind Speed

Abstract

Various wind velocities u, Uλ/2, Uλ and U₁₀ are correlated to the measured growth rate of water waves β, where u is the friction velocity of the wind, and Uλ/2, Uλ and U₁₀ are the wind speeds respectively at the heights λ/2, A and 10m above sea surface (λ: wave length). It is shown that within a range of the dimensionless wind speed, 0.1<u/C<0.6, there are no appreciable differences in the correlations, where C is the phase velocity of water waves. The present relation between β and Uλ shows qualitatively similar properties as the one obtained by Al'Zanaidi and Hui (1984): the growth rate for waves with rough surface is larger than that with smooth surface. However, our present relations give, for the both waves with different surface roughness, larger values by factors 1.7-1.8 than those given by Al'Zanaidi and Hui's relation.