Rederivation of the Saturation Range in the Frequency Spectrum of Wind-Generated Gravity Waves

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  • 1 Department of Oceanography, Naval Postgraduate School, Monterey, Calif. 93940
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Abstract

The saturation range in the frequency spectrum of wind-generated waves is rederived. Laboratory and theoretical work show that wave breaking is the result of kinematic instability, suggesting that wave celerity is the governing parameter in the saturation range. Using similarity arguments, a general formulation is rederived giving the wave profile spectrum Sη(ω) ∝ ω−5 in deep water as derived by Phillips and Sη(ω) ∝ ω−3 in shallow water. The velocity spectrum in the saturation range is derived using linear wave theory as a spectral transfer function. In both deep and shallow water the horizontal velocity spectrum Su(ω) ∝ ω−3. Wave and velocity measurements made in deep and shallow water are presented showing agreement with theory.

Abstract

The saturation range in the frequency spectrum of wind-generated waves is rederived. Laboratory and theoretical work show that wave breaking is the result of kinematic instability, suggesting that wave celerity is the governing parameter in the saturation range. Using similarity arguments, a general formulation is rederived giving the wave profile spectrum Sη(ω) ∝ ω−5 in deep water as derived by Phillips and Sη(ω) ∝ ω−3 in shallow water. The velocity spectrum in the saturation range is derived using linear wave theory as a spectral transfer function. In both deep and shallow water the horizontal velocity spectrum Su(ω) ∝ ω−3. Wave and velocity measurements made in deep and shallow water are presented showing agreement with theory.

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