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Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. (English) Zbl 0633.76023
We consider the evolution of an isolated elliptical vortex in a weakly dissipative fluid. It is shown computationally that a spatially smooth vortex relaxes inviscidly towards axisymmetry on a circulation timescale as the result of filament generation. Heuristically, we derive a simple geometrical formula relating the rate of change of the aspect ratio of a particular vorticity contour to its orientation relative to the streamlines (where the orientation is defined through second-order moments).
Computational evidence obtained with diagnostic algorithms validates the formula. By considering streamlines in a corotating frame and applying the new formula, we obtain a detailed kinematic understanding of the vortex’s decay to its final state through a primary and a secondary breaking. The circulation transported into the filaments although a small fraction of the total, breaks the symmetry and is the chief cause of axisymmetrization.

76B47 Vortex flows for incompressible inviscid fluids
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] DOI: 10.1143/JPSJ.50.3517
[2] DOI: 10.1017/S0022112082001372
[3] Haidvogel, J. Phys. Oceanogr none pp none– (1985)
[4] DOI: 10.1016/0021-9991(79)90089-5 · Zbl 0405.76014
[5] Zabusky, Phys. Today 195 pp 77– (1984)
[6] Zabusky, J. Comp. Phys. 195 pp 77– (1982)
[7] Overman, Trans. First Army Conf. on Appl. Maths and Computing. ARO Rep. 25 pp 269– (1984)
[8] DOI: 10.1017/S0022112082000378
[9] DOI: 10.1063/1.863907 · Zbl 0489.76033
[10] Melander, J. Fluid Mech. 167 pp 95– (1986)
[11] DOI: 10.1103/PhysRevLett.53.1222
[12] DOI: 10.1017/S0022112084001750 · Zbl 0561.76059
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