A Simple Statistical Treatment of Highly Turbulent Couette Flow

Abstract

From the integral conditions for momentum and kinetic energy balance in the state of fully developed turbulence, it is found possible to estimate the bulk statistical properties of highly turbulent Couette flow as functions of the Reynolds number. The average boundary shear, boundary layer thickness, and average momentum transport through the ?constant flux? layer are determined to within the value of a single non-dimensional constant. The conclusions of this analysis are in quantitative agreement with laboratory measurements and are consistent with empirical formulas for the Reynolds stress over smooth surfaces. The significance of the results is discussed with specific reference to the problem of ?parameterizing? the statistical effects of turbulent momentum transport in terms of the large-scale average motion of the atmosphere.