Time-Averaged Forms of the Nonlinear Stress Law

Abstract

On the assumption that the mean velocity and the probability distribution of the higher frequency fluctuating motions are known, an expression for the mean surface stress is given. For the case of isotropic background variations, the mean stress is shown to be a simple nonlinear function of the mean velocity and the standard deviation of the fluctuations. Results should be useful in studies concerning the stress at the bottom of either the ocean or the atmosphere. For use in the oceanic case, a constant drag coefficient is considered. For the atmospheric case, the drag coefficient is a function of wind speed. Results are compared for several previously proposed forms of this functional dependence.