PAPER 2 – A Two-Parameter Model of Turbulence, and its Application to Free Jets

A model of turbulence is investigated in which the Reynolds stress appearing in the momentum equation is calculated from the expression u′v′¯  =  kL(∂U/∂y); the kinetic energy, k, and the length scale, L, of turbulence are determined from differential transport equations for these quantities. These equations are solved for various free-jet situations, and the empirical constants involved are adjusted so as to give best agreement between predictions and experimental results. The plane mixing layer, the plane jet and the radial jet can be predicted with a single set of constants; for the round jet a different set has to be used. This suggests a dependence of the otherwise universal constants on the ratio of L to the radius r. Comparisons are presented of predicted and measured rates of spread, profiles for U, k and u′v′¯, and energy balances. For most cases the agreement is within the experimental accuracy.