Vorticity selection with multiple eddies in two-dimensional steady flow at high Reynolds number

This paper discusses the selection problem for the parameters of the Euler flow in Prandtl-Batchelor (PB) theory of steady two-dimensional flow, in cases where multiple eddies occur. In particular we treat a perturbed symmetric eddy problem where the Navier-Stokes solution is close to an Euler flow and linear theory may be used to describe the boundary layers. Extensions of the Feynman-Lagerstrom formula are then obtained. We compare our results with numerical calculations in a rectangle at Reynolds numbers 500, 1000, and 2000.