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.

We study the influence of turbulent viscosity variability on the properties of self-propelled body wake model. In addition to the already known integrals of motion obtained with constant turbulent viscosity, we obtain new ones. The presence of new integrals of motion leads, in particular, to changes in the behavior of the width and profile of the wake leading to its conservation.