SELF-CONSISTENCY BETWEEN WIND STRESS, WAVE SPECTRUM, AND WIND-INDUCED WAVE GROWTH FOR FULLY ROUGH AIR-SEA INTERFACE

When the flow at the air-sea interface is aerodynamically rough (i.e., for wind speeds above 7.5 m s-1, typically), then form drag on the roughness elements accounts for virtually all the stress. Assuming such a situation, we seek a self-consistent solution for the wind stress in the sense that the wind stress entering the models of sea spectrum and wind-induced growth rate is constrained to be equal to the wind stress obtained through integration of form drag over the wavenumber space. Using the models by Donelan and Pierson (1987) for both fully developed sea spectrum and short-scale wind-induced wave growth rate, we find self-consistent, firmly constrained solutions with roughness lengths in good agreement with Charnock's formulation (namely, z0 proportional to u*2), with a constant of proportionality which is of a magnitude very close to experimental values reported in the literature. Thus it appears that there is consistency between our knowledge of the surface stress, wind input, and spectral shape. In contrast, when the short-scale wind-induced growth rate is replaced by the one proposed by Plant (1982), the roughness length z0 is found to become extremely sensitive to small fluctuations of either wind-induced growth rate or sea-wave spectral level. A poorly constrained and highly fluctuating rather than deterministic value of Charnock's coefficient would then be expected at full development. Numerous confirmations of Charnock's relationship performed in the field at or near full development tend to support Donelan and Pierson's approach for wind-induced growth rate at short scales. The model was also tested in versions in which the viscous drag was tentatively parameterized, and the conclusions reported here were qualitatively unaffected.