Conservation laws and conserved quantities of the governing equations for the laminar wake flow behind a small hump on a solid wall boundary

The conservation laws and conserved quantities for the governing equations of the two-dimensional laminar wake flow behind a hump on a flat plate are derived. The multiplier method is applied to the linearised governing equations for small humps and a basis of conserved vectors is constructed. Since, in general, the problem contains an unknown non-homogeneous boundary condition, each conserved vector needs to be carefully chosen and additional restrictions need to be applied to ensure that each conserved quantity, which is obtained by integrating the corresponding conservation law across the wake and imposing the relevant boundary conditions, has a finite value. Four non-trivial conserved quantities are found; three of which have only now been identified. The four conserved quantities relate to the conservation of mass, drag and the first and second moments of the momentum deficit. For each case the existence of a solution that satisfies the governing equations, boundary conditions and a finite valued conserved quantity is discussed.