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Some steady vortex flows past a circular cylinder

Published online by Cambridge University Press:  25 April 2000

ALAN ELCRAT
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA
BENGT FORNBERG
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
MARK HORN
Affiliation:
Intergraph, Huntsville, AL 35894, USA
KENNETH MILLER
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA

Abstract

Steady vortex flows past a circular cylinder are obtained numerically as solutions of the partial differential equation Δψ = f(ψ), f(ψ) = ω(1 − H(ω − α)), where H is the Heaviside function. Only symmetric solutions are considered so the flow may be thought of as that past a semicircular bump in a half-plane. The flow is transplanted by the complex logarithm to a semi-infinite strip. This strip is truncated at a finite height, a numerical boundary condition is used on the top, and the difference equations resulting from the five-point discretization for the Laplacian on a uniform grid are solved using Fourier methods and an iteration for the nonlinear equation. If the area of the vortex region is prescribed the magnitude of the vorticity ω is adjusted in an inner iteration to satisfy this area constraint.

Three types of solutions are discussed: vortices attached to the cylinder, vortex patches standing off from the cylinder and strips of vorticity extending to infinity. Three families of each type of solution have been found. Equilibrium positions for point vortices, including the Föppl pair, are related to these families by continuation.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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