Fetch Relations for Wind-Generated Waves as a Function of Wind-Stress Scaling

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Abstract
We present the variation that results when fetch relations for wind-generated wave spectra are sealed by the friction velocity component in the dominant wave direction rather than the magnitude of the friction velocity, using the data collected during the Canadian Atlantic Storms Program (CASP). The effects of three possible drag coefficients are considered. the usual constant drag coefficient, the open-ocean long fetch drag coefficient, and finally, the wave age dependent drag coefficient for growing waves recently measured by Smith and Anderson in HEXOS. Contributions to the correlation coefficients for dimensionless variables due to both scaling variables and dimensional variables are computed. We find that the friction velocity component in the dominant wave direction rather than the friction velocity magnitude should be used as the scaling variable. The self-correlation introduced to the correlation coefficients is then less than that resulting from the friction velocity magnitude. Balance relations among physical fetch relations support this conclusion and imply that the wave age dependent drag coefficient for growing waves is the appropriate drag coefficient to use in scaling variables. We generalize Snyder et al.'s parameterization of the wind input energy and derive a functional form for Phillips’ equilibrium range α-function.

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