Prandtl-Batchelor flows with corners #

Michael Vynnycky

11:10 Wednesday in 3E11.

Part of the Applied fluid dynamics session.

Abstract #

The Prandtl–Batchelor theorem states that the vorticity in a steady laminar high Reynolds number flow containing closed streamlines should be constant; however, apart from the simple case of circular streamlines, in which case there can be an analytical solution, very little is known about how to determine this constant. This talk extends earlier work for flow driven by a surrounding smooth moving boundary to the case where the enclosing boundary has corners; for this purpose, a benchmark example from the literature for flow inside a semi-circle is considered. Asymptotic analysis for high Reynolds numbers, involving an inviscid core flow, viscous boundary layers and corner regions, and computations of the full Navier–Stokes equations for high Reynolds numbers, are considered. Reasonable agreement is obtained for the value of constant core vorticity, and possible future directions for improving the agreement are discussed.