An Exact Solution for Decay of Grid Produced-Turbulence: Part 1

Abstract

A new approach to the exact solution for decy of grid-produced turbulence in the final period has been proposed.   The governing equations are the two-point and three-point velocity correlation equations in which the quartic correlations are neglected as the closure assumption, and the pressure-veocity correlations are neglected tentatively.   Without recourse to the isotropic conditions, theseequations are found to be separable into a pair of Oseen (type) equations.   As a result, the double- and triple-correlations are solved analytically as an initial value problem.  The effect of the triple correlation adds a correction term proportional to x-⁴ to the well knowndecay law x^-5/2 for the turbulent energy in the final period: <( u)²>=Ax^-5/2+ Bx^-4 , where <( u)²> is the turbulent energy, A and B are contants determined by the initial conditions, and x is the streamwise coordinate.