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Zbl 0778.76022
Mallier, R.; Maslowe, S.A.
A row of counter-rotating vortices. (English)
[J] Phys. Fluids, A 5, No.4, 1074-1075 (1993). ISSN 0899-8213

Summary: In 1967, {\it J. T. Stuart} [J. Fluid Mech. 29, 417-440 (1967; Zbl 0152.454)] found an exact nonliner solution of the inviscid, incompressible two-dimensional Navier-Stokes equations, representing an infinite row of identical vortices which are now known as Stuart vortices. In this paper, the corresponding result for an infinite row of counter-rotating vortices, i.e., a row of vortices of alternating sign, is presented. While for Stuart's solution, the streamfunction satisfied Liouville's equation, the streamfunction presented here satisfies the sinh-Gordon equation. The connection with Stuart's solution is discussed.

MSC 2000:: *76D05 Navier-Stokes equations (fluid dynamics)

Keywords: Stuart vortices; streamfunction; Liouville's equation; sinh-Gordon equation

Citations: Zbl 0152.454

Cited in: Zbl 1065.76125 Zbl 0830.76035

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