Solutions for the turbulent classical wake using Lie symmetry methods

We investigate the turbulent planar classical wake and derive the governing equations using the eddy viscosity closure model. The Lie point symmetry associated with the elementary conserved vector is used to generate the invariant solution. We first consider the case where the eddy viscosity depends only on the distance along the wake. We then relax this condition to include the dependence of the eddy viscosity on the perpendicular distance from the axis of the wake. The profiles of the mean velocity show that the role of the eddy viscosity is to increase the effective width of the wake and decrease the magnitude of the maximum mean velocity deficit.