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Title: Inviscid two dimensional vortex dynamics and a soliton expansion of the sinh-Poisson equation
Authors: Chow, K. W.
Ko, N. W. M.
Leung, R. C. K.
Tang, Shiu-keung
Subjects: Vortices
Issue Date: May-1998
Publisher: American Institute of Physics
Source: Physics of fluids, May 1998, v. 10, no. 5, p. 1111-1119.
Abstract: The dynamics of inviscid, steady, two dimensional flows is examined for the case of a hyperbolic sine functional relation between the vorticity and the stream function. The 2-soliton solution of the sinh-Poisson equation with complex wavenumbers will reproduce the Mallier-Maslowe pattern, a row of counter-rotating vortices. A special 4-soliton solution is derived and the corresponding flow configuration is studied. By choosing special wavenumbers complex flows bounded by two rigid walls can result. A conjecture regarding the number of recirculation regions and the wavenumber of the soliton expansion is offered. The validity of the new solution is verified independently by direct differentiation with a computer algebra software. The circulation and the vorticity of these novel flow patterns are finite and are expressed in terms of well defined integrals. The questions of the linear stability and the nonlinear evolution of a finite amplitude disturbance of these steady vortices are left for future studies.
Rights: © 1998 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in K. W. Chow et al., Physics of Fluids 10, 1111 (1998) and may be found at
Type: Journal/Magazine Article
DOI: 10.1063/1.869636
ISSN: 1070-6631 (print)
1089-7666 (online)
Appears in Collections:BSE Journal/Magazine Articles

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