Group Invariant Solution and Conservation Law for a Free Laminar Two-Dimensional Jet

A group invariant solution for a steady two-dimensional jet is derived by considering a linear combination of the Lie point symmetries of Prandtl’s boundary layer equations for the jet. Only two Lie point symmetries contribute to the solution and the ratio of the constants in the linear combination is determined from conservation of total momentum flux in the downstream direction. A conservation law for the differential equation for the stream function is derived and it is shown that the Lie point symmetry associated with the conservation law is the same as that which generates the group invariant solution. This establishes a connection between the conservation law and conservation of total momentum flux.