Vorticity selection with multiple eddies in two-dimensional steady flow at high Reynolds number (Q2706094)

The authors revisit the old classical Prandtl-Batchelor problem [see \textit{G. K. Batchelor}, J. Fluid Mech. 1, 177-190 (1956; Zbl 0070.42004)] for steady two-dimensional flows in the presence of multiple eddies. In particular, the authors investigate how to select the limiting vorticities for the corresponding Euler flow as the Reynolds number tends to infinity. A perturbed symmetric eddy problem is considered, where the Navier-Stokes solution is close to the Euler flow, and linear theory may be used to describe the boundary layers. Using a series solution, the authors obtain an extension of the Feynman-Lagerstrom formula, and compare their results with finite-difference simulations in a rectangle at Reynolds numbers 500, 1000, and 2000.