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Two-layer geostrophic vortex dynamics. II: Alignment and two-layer V- states. (English) Zbl 0722.76093
Summary: [For part I see, the author, N. J. Zabusky and G. R. Flierl, ibid. 205, 215-242 (1989; Zbl 0676.76093).]
The process of alignment, a new fundamental interaction between vortices in a stratified and rapidly rotating fluid, is defined and studied in detail in the context of the two-layer quasi-geostrophic model. Alignment occurs when two vortices in different density layers coalesce by reducing their horizontal separation. It is found that only vortices whose radii are comparable with or larger than the Rossby deformation radius can align. In the same way as the merger process (in a single two-dimensional layer) is related to the reverse energy cascade of two-dimensional turbulence, geostrophical potential vorticity alignment is related the barotropic-to-baroclinic energy cascade of geostrophic turbulence in two layers. It is also shown how alignment is intimately connected with the existence of two-layer doubly connected geostrophic potential vorticity equilibria (V-states), for which the analysis of the geometry of the stream function in the corotating frame is found to be a crucial diagnostic. The finite-area analogues of the hetons of N. G. Hogg and H. M. Stommel [Proc. R. Soc. Lond., Ser. A 397, 1-20 (1985; Zbl 0571.76017)] are also determined: they consist of a propagating pair of opposite-signed potential vorticity patches located in different layers.

MSC:
76V05 Reaction effects in flows
76U05 General theory of rotating fluids
76B47 Vortex flows for incompressible inviscid fluids
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References:
[1] Polvani, Geophys. Astrophys. Fluid Dyn. 51 pp 87– (1989)
[2] DOI: 10.1017/S0022112088002435 · Zbl 0653.76020
[3] DOI: 10.1016/0377-0265(80)90009-3
[4] Fliebl, J. Fluid Mech. 97 pp 349– (1988)
[5] DOI: 10.1017/S0022112088003088 · Zbl 0645.76024
[6] DOI: 10.1016/0021-9991(88)90165-9 · Zbl 0642.76025
[7] DOI: 10.1017/S0022112085002324 · Zbl 0574.76026
[8] DOI: 10.1103/PhysRevLett.40.859
[9] DOI: 10.1175/1520-0469(1971)028 2.0.CO;2
[10] DOI: 10.1088/0305-4470/21/5/018
[11] DOI: 10.1017/S0022112087002684
[12] Zabusky, Ann. NY Acad. Sci. 373 pp 160– (1981)
[13] DOI: 10.1017/S0022112087001150 · Zbl 0633.76023
[14] DOI: 10.1017/S0022112089000108
[15] DOI: 10.1017/S0022112084001750 · Zbl 0561.76059
[16] DOI: 10.1088/0034-4885/43/5/001
[17] DOI: 10.1175/1520-0469(1986)043 2.0.CO;2
[18] Hogg, Proc. R. Soc. Lond. 397 pp 1– (1985)
[19] DOI: 10.1175/1520-0469(1980)037 2.0.CO;2
[20] DOI: 10.1017/S0022112088003271 · Zbl 0658.76102
[21] Gryanick, Izv. Acad. Nauk SSSR Atmos. Ocean. Phys. 9 pp 171– (1983)
[22] DOI: 10.1017/S0022112086001246
[23] DOI: 10.1016/0021-9991(84)90051-2 · Zbl 0524.76029
[24] DOI: 10.1063/1.857647
[25] Saffman, Phys. Fluids 23 pp 171– (1979)
[26] DOI: 10.1146/annurev.fl.11.010179.002153
[27] Pullin, J. Fluid Mech. 209 pp 359– (1989)
[28] Polvani, J. Fluid Mech. 205 pp 215– (1989)
[29] DOI: 10.1063/1.857485
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