A New Empirical Formula for the Aerodynamic Roughness of Water Surface Waves

Abstract

A new empirical formula for the aerodynamic roughness of water surface waves has been derived from laboratory experimental results using dimensional analysis. The formula has different forms according to wind speed: at moderate wind speeds the formula is a function of the friction velocity of wind, the surface tension, the water density, the kinematic viscosity of water and the acceleration of gravity; at strong winds the formula is expressed by the Charnock relation. The aerodynamic roughness does not depend on such wave state parameters as the spectral peak frequency or the steepness of waves, unlike almost all parameterizations that have been proposed to date. The drag coefficient at moderate winds depends on the surface tension of water and the water temperature through the temperature dependence of the kinematic viscosity of water.