Inviscid two dimensional vortex dynamics and a soliton expansion of the sinh-Poisson equation

Physics of Fluids

Volumn 10, Issue 5, 1998, Pages 1111-1119

  Chow, K W ^a   Ko, N W M ^a   Leung, R C K ^a   Tang, S K ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000348772     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869636     Document Type: Article

References (25)

1. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
2. P. G. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, 1992).
3. G. R. Flierl, "Isolated eddy models in geophysics," Annu. Rev. Fluid Mech. 19, 493 (1987).
4. E. J. Hopfinger and G. J. G. Van Heijst, "Vortices in rotating fluids," Annu. Rev. Fluid Mech. 25, 241 (1993).
5. D. Marteau, O. Cardoso, and P. Tabeling, "Equilibrium states of two-dimensional turbulence: An experimental study," Phys. Rev. E 51, 5124 (1995).
6. D. G. Dritschel, "The stability of elliptical vortices in an external straining flow," J. Fluid Mech. 210, 223 (1990).
7. M. R. Dhanak and M. P. Marshall, "Motion of an elliptical vortex under applied periodic strain," Phys. Fluids A 5, 1224 (1993).
8. L. M. Polvani and J. Wisdom, "Chaotic Lagrangian trajectories around an elliptical vortex patch embedded in a constant and uniform background shear flow," Phys. Fluids 2, 123 (1990).
9. V. V. Meleshko and G. J. F. Van Heijst, "On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid," J. Fluid Mech. 272, 157 (1994).
10. J. T. Stuart, "On finite amplitude oscillations in laminar mixing layer," J. Fluid Mech. 29, 417 (1967).
11. R. Mallier and S. A. Maslowe, "A row of counter rotating vortices," Phys. Fluids 5, 1074 (1994).
12. R. A. Pastmanter, "On long lived vortices in 2-D viscous flows, most probable states of inviscid 2-D flows and a soliton equation," Phys. Fluids 6, 1236 (1994).
13. T. Dauxois, S. Fauve, and L. Tuckerman, "Stability of periodic arrays of vortices," Phys. Fluids 8, 487 (1996).
14. J. S. Hesthaven, J. P. Lynov, A. H. Nielsen, J. Juul Rasmussen, M. R. Schmidt, E. G. Shapiro, and S. K. Turitsyn, "Dynamics of a nonlinear dipole vortex," Phys. Fluids 7, 2220 (1995).
15. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981).
16. G. Forrest and D. W. McLaughlin, "Spectral theory of the periodic sine-Gordon equation," J. Math. Phys. 23, 1248 (1982).
17. N. Martinov and N. Vitanov, "New class of running wave sulutions of the (2+1) dimensional sine-Gordon equation," J. Phys. A 27, 4611 (1994).
18. A. C. Ting, H. H. Chen, and Y. C. Lee, "Exact solutions of a nonlinear boundary value problem: the vortices of the two dimensional sinh-Poisson equation," Physica D 26, 36 (1987).
19. K. W. Chow, N. W. M. Ko, and S. K. Tang, "Solitons in (2+0) dimensions and their applications in vortex dynamics," Fluid Dyn. Res. 21, 101 (1997).
20. D. Montgomery and G. Joyce, "Statistical mechanics of negative temperature states," Phys. Fluids 17, 1139 (1974).
21. L. F. Rossi, J. F. Lingevitch, and A. J. Bernoff, "Quasi-steady monopole and tripole attractors for relaxing vortices," Phys. Fluids 9, 2329 (1997).
22. Y. G. Morel and X. J. Carton, "Multipolar vortices in two dimensional incompressible flows," J. Fluid Mech. 267, 23 (1994).
23. J. Sommeria, C. Staquet, and R. Robert, "Final equilibrium state of a two dimensional shear layer," J. Fluid Mech. 233, 661 (1991).
24. D. Montgomery, W. H. Matthaeus, W. T. Stribling, D. Martinez, and S. Oughton, "Relaxation in two dimensions and the sinh Poisson equation," Phys. Fluids 4, 3 (1992).
25. L. Bergström and P. H. Alfredsson, "Symmetry properties of developing three dimensional laminar disturbances in plane Poiseuille flow," Phys. Fluids 6, 1618 (1994).