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A row of counter-rotating vortices. (English) Zbl 0778.76022

Summary: In 1967, 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:

76D05 Navier-Stokes equations for incompressible viscous fluids

Citations:

Zbl 0152.454
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References:

[1] DOI: 10.1017/S0022112067000941 · Zbl 0152.45403
[2] DOI: 10.1017/S0022112082000044 · Zbl 0479.76056
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