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Nonlinear instability of a Rossby-wave critical layer. (English) Zbl 0604.76038

The vorticity distribution in a Rossby-wave nonlinear critical layer, given by the Stewartson-Warn-Warn solution, may be strongly modified by the action of shear instability. In a companion paper [P. D. Killworth and M. E. McIntire, ibid. 161, 449-492 (1985)] it was shown, using linear theory, that unstable modes indeed existed. Here, using numerical methods, the nonlinear evolution of unstable disturbances is followed up to the time at which their growth ceases. By such a time there has been considerable redistribution of vorticity in the critical layer.

MSC:

76E30 Nonlinear effects in hydrodynamic stability
76B65 Rossby waves (MSC2010)
76M99 Basic methods in fluid mechanics
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[1] DOI: 10.1175/1520-0469(1978)035 2.0.CO;2 · doi:10.1175/1520-0469(1978)035 2.0.CO;2
[2] DOI: 10.1175/1520-0469(1976)033 2.0.CO;2 · doi:10.1175/1520-0469(1976)033 2.0.CO;2
[3] Warn, Stud. Appl. Math. 59 pp 37– (1978) · Zbl 0415.76020 · doi:10.1002/sapm197859137
[4] DOI: 10.1175/1520-0469(1976)033 2.0.CO;2 · doi:10.1175/1520-0469(1976)033 2.0.CO;2
[5] Stewartson, IMA J. Appl. Math. 27 pp 133– (1981)
[6] DOI: 10.1017/S0022112071001940 · Zbl 0229.76029 · doi:10.1017/S0022112071001940
[7] Stewartson, Geophys. Astrophys. Fluid Dyn. 9 pp 185– (1978)
[8] DOI: 10.1063/1.1692445 · Zbl 0217.25803 · doi:10.1063/1.1692445
[9] Ritchie, Geophys. Astrophys. Fluid Dyn. 9 pp 185– (1985)
[10] Killworth, J. Fluid Mech. 161 pp 449– (1985)
[11] DOI: 10.1175/1520-0469(1970)027 2.0.CO;2 · doi:10.1175/1520-0469(1970)027 2.0.CO;2
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