Duration- and fetch-limited growth functions of wind-generated waves parameterized with three different scaling wind velocities

Abstract

Under steady wind forcing, wave development follows the duration- and fetch-limited growth laws. These growth functions are used extensively to obtain the sea state information when only limited observations of the environmental variables are available. Validation and verification of wave models also employ numerical experiments of duration- and fetch-limited wave growth as benchmark tests. The reference wind speed reported in most of the wave-growth data is the equivalent neutral wind speed at 10 m elevation, U10. It is generally believed that a more suitable scaling wind speed is either the wind friction velocity, u*, or the wind speed at an elevation proportional to the wavelength of the ocean surface fluctuation, Uλ/2. The connection among the growth functions using different velocity scales is the drag coefficient of the ocean surface. In this paper, the similarity relation of the drag coefficient based on wavelength scaling is applied to the conversion of the wave growth functions from U10 to Uλ/2 and u* scaling. The results are in good agreement with field measurements that include direct u* measurements. Comparisons with numerical model output are also described.