Statistical Derivation of Kolmogorov’s −5⁄3 Power Law by Turbulent-Viscosity Approach

Abstract

Kolmogorov’s −5⁄3 power law is derived by a statistical approach based on turbulent viscosity. A crucial point in this analysis is that no use is made of the response (Green’s) function which may lead to a divergence at lowest wave numbers. An equation is found for the two-time velocity covariance by using turbulent viscosity to be determined as a part of the solution. Convection effect of big eddies upon small ones is uniquely removed from the equation for small time separation. As the result, Kolmogorov’s law are derived with a good estimate of Kolmogorov’s constant.