Solutions of the Navier-Stokes equation at large Reynolds number

The problem of two-dimensional incompressible laminar flow past a bluff body at large Reynolds number $( R )$ is discussed. The governing equations are the Navier–Stokes equations. For $R = \infty $, the Euler equations are obtained. A solution for R large should be obtained by a perturbation of an Euler solution. However, for given boundary conditions, the Euler solution is not unique. The solution to be perturbed is the relevant Euler solution, namely the one which is the Euler limit of the Navier–Stokes solution with the same boundary conditions. For certain semi-infinite or streamlined bodies, the relevant Euler solution represents potential flow. For flow inside a closed domain a theorem of Prandtl states the relevant Euler solution has constant vorticity in each vortex. In many cases it can be determined by simultaneously considering the boundary layer equations. For flow past a bluff body, the relevant Euler solution is not known, although the free streamline flow for which the free streamline deta...