Turbulent viscosity variability in self-preserving far wake with zero net momentum

Abstract

The profile of the self-preserving far wake with zero net momentum depends on the effective turbulent viscosity coefficient. The current model is based on the assumption of uniform viscosity in the wake cross section. It predicts the self-similar shape of the wake where the width W depends on the distance z from the body as W∝z(1/5) for the axisymmetric case (or z(1/4) for the plane case). The observed wake width, however, demonstrates the dependence W∝z(α) (where α≤1/5). We generalize the model of a self-preserving far wake for the case of the turbulent viscosity coefficient depending on the radius. Additional integrals of motion allow a new family of self-similar profiles with α≤1/5.