Lie symmetry methods applied to the turbulent wake of a symmetric self-propelled body

We investigate the equations governing the turbulent planar wake behind a slender symmetric self-propelled body. The eddy viscosity closure model is used to complete the system of equations. The Lie point symmetry associated with the conserved vector is derived in order to generate the invariant solution. We consider the cases where the eddy viscosity depends only on the distance along the wake in the form of a power law and when a modified version of Prandtl's hypothesis is satisfied. We examine the effect of neglecting the kinematic viscosity. We then discuss the issues that arise when we consider the eddy viscosity to also depend on the perpendicular distance from the axis of the wake. Mean velocity profiles reveal that the eddy viscosity increases the boundary layer thickness of the wake and decreases the magnitude of the maximum mean velocity.