The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow

Steady, inviscid, incompressible, two‐dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right‐angled corner. Nonlinear integral equations...

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Bibliographic Details
Published in:The Physics of fluids (1958) 1988-05, Vol.31 (5), p.978-990
Main Authors: Moore, D. W., Saffman, P. G., Tanveer, S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Rotational flow and vorticity
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Summary:Steady, inviscid, incompressible, two‐dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right‐angled corner. Nonlinear integral equations are derived for the shape of the bounding vortex sheet which are solved numerically. Two different formulations are employed to check the results. Previous results by Sadovskii [Appl. Math. Mech. 3 5, 773 (1971)] and Chernyshenko (Royal Aircraft Establishment library translations Report No. 2133, 1983) for specific values of the parameters are confirmed. Only symmetrical solutions are found to exist.
ISSN:0031-9171
2163-4998
DOI:10.1063/1.866718