Optimal coordinates for squire's jet

The existence of optimal coordinates is examined in relation to the problem of a laminar round jet without swirl, issuing into an infinite fluid at rest. Flow is assumed to be steady and incompressible. A paraboloidal coordinate system is selected and the method of inner and outer expansions is applied to the Navier-Stokes equations written in the system. An optimal solution is obtained and the optimal coordinate system coincides with the stream-surface coordinate system of the outer entrained flow.