Abstract
We study the effect of atmospheric stability on the growth of surface gravity waves. To that end we numerically solved the Taylor-Goldstein equation for wind profiles which deviate from a logarithmic one because stratification affects the turbulent momentum transport. Using Charnock’s relation for the friction height z of the wind profile it is argued that the growth rate of the wave depends on the dimensionless phase velocity c/u* (where u* is the friction velocity) and a measure of the effect of atmospheric stability, namely the dimensionless Obukhov length gL/u * 2 , whereas it only depends weakly on gzt/u * 2 (where zt is the friction height of the temperature profile). We find that for given u*, the growth rate as a function of c/u* is larger for stable stratification (L>o) than for an unstable stratification (L<o). If one, on the other hand, considers the growth rate as a function of c/U10 (where U10 is the windspeed at 10 meters) the situation reverses and unstable growth is larger over most of the frequency range. We explain these features in a qualitative way.
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