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.
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Research Article|
May 01 1998
Inviscid two dimensional vortex dynamics and a soliton expansion of the sinh-Poisson equation Available to Purchase
K. W. Chow;
K. W. Chow
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
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N. W. M. Ko;
N. W. M. Ko
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
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R. C. K. Leung;
R. C. K. Leung
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
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S. K. Tang
S. K. Tang
Department of Building Services Engineering, Hong Kong Polytechnic University, Hunghom, Hong Kong
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K. W. Chow
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
N. W. M. Ko
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
R. C. K. Leung
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
S. K. Tang
Department of Building Services Engineering, Hong Kong Polytechnic University, Hunghom, Hong Kong
Physics of Fluids 10, 1111–1119 (1998)
Article history
Received:
September 02 1997
Accepted:
January 23 1998
Citation
K. W. Chow, N. W. M. Ko, R. C. K. Leung, S. K. Tang; Inviscid two dimensional vortex dynamics and a soliton expansion of the sinh-Poisson equation. Physics of Fluids 1 May 1998; 10 (5): 1111–1119. https://doi.org/10.1063/1.869636
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