Conservation laws and conserved quantities for the two-dimensional laminar wake

Abstract

A systematic and unified method is presented for the derivation of the conserved quantities for the laminar classical wake and the wake of a self-propelled body. The multiplier method for the derivation of conservation laws is applied to the far downstream wake equations expressed in terms of the velocity components which gives rise to a second-order system of two partial differential equations, and in terms of the stream function which results in one third-order partial differential equation. Once the corresponding conservation laws are obtained, they are integrated across the wake and upon imposing the boundary conditions and the condition that the drag on a self-propelled body is zero, the conserved quantities for the classical wake and the wake of a self-propelled body are derived. In addition, this method results in the discovery of a new laminar wake which may have physical significance.