Skip to main content Accessibility help

Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states

  • L. M. Polvani (a1) (a2)


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, geostrophic 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 Hogg & Stommel (1985) are also determined: they consist of a propagating pair of opposite-signed potential vorticity patches located in different layers.



Hide All
Babiano, A., Basdevant, C., Legbrs, B. & Sadourny, R., 1986 Vorticity and passive scalar dynamics in two-dimensional turbulence. J. Fluid Mech. 183, 379397.
Benzi, R., Paternello, S. & Santangelo, P., 1988 Self-similar coherent structures in two-dimensional decaying turbulence. J. Phys A 21, 12211237.
Charney, J. C.: 1971 Geostrophic turbulence. J. Atmos. Sci. 28, 10871095.
Deem, G. S. & Zabusky, N. J., 1978 Stationary V-states: interactions, recurrence and breaking. Phys. Rev. Lett. 40, 859.
Dbitschel, D. G.: 1985 The stability and energetics of corotating uniform vortices. J. Fluid Mech. 157, 95134.
Dritschel, D. G.: 1988a Contour surgery: a contour dynamics method for long time behavior of two-dimensional, inviscid, rotational flow. J. Comput. Phys. 77, 240266.
Dbitschel, D. G.: 1988b The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194, 511532.
Fliebl, G. R.: 1988 On the instability of geostrophic vortices. J. Fluid Mech. 97, 349388.
Fliebl, G. R., Larichev, V. D., McWilllams, J. C. & Reznik, G. M., 1980 The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Ocean 5, 141.
Griffiths, R. W. & Hopfinger, E. J., 1986 Experiments with baroclinic vortex pairs in a rotating fluid. J. Fluid Mech. 173, 501518.
Gryanick, V. M.: 1983 Dynamics of singular geostrophic vortices in a two-level model of the atmosphere (or the ocean). Izv. Acad. Nauk SSSR Atmos. Ocean. Phys. 9, 171179.
Helfrich, K. & Send, U., 1988 Finite amplitude evolution of two-layer geostrophic vortices. J. Fluid Mech. 197, 331348.
Herring, J. R.: 1980 Statistical theory of quasigeostrophic turbulence. J. Atmos. Sci. 37, 969977.
Hogg, N. & Stommel, H., 1985 The heton, an elementary interaction between discrete baroclinic geostrophic vortices and its implication concerning eddy heat-flow. Proc. R. Soc. Lond. A 397, 120.
Hua, L. B. & Haidvogel, D. B., 1986 Numerical simulation of the vertical structure of quasigeostrophic turbulence. J. Atmos. Sci. 43, 29232936.
Kraichnan, R. H. & Montgomery, D., 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547619.
McWilllams, J. C.: 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.
McWilliams, J. C.: 1989 Statistical properties of decaying geostrophic turbulence. J. Fluid Mech. 198, 199230.
Melander, M. V., McWilllams, J. C. & Zabusky, N. J., 1987 Axisymmetrization and vorticity gradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech. 178, 137159.
Melander, M. V., Zabusky, N. J. & McWilllams, J. C., 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303340.
Polvani, L. M.: 1988 Geostrophic vortex dynamics. Ph.D. thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, WHOI-88-48.
Polvani, L. M. & Carton, X. J., 1989 The tripole: a new coherent vortex structure of incompressible two-dimensional flows. Geophys. Astrophys. Fluid Dyn. 51, 87102.
Polvani, L. M., Flierl, G. R. & Zabusky, N. J., 1989b Filamentation of coherent vortex structures via separatrix crossing: a quantitative estimate of onset time. Phys. Fluids A 1, 181184.
Polvani, L. M., Zabusky, N. J. & Flierl, G. R., 1989a Two-layer geostrophic vortex dynamics. Part 1. Upper-layer V-states and merger. J. Fluid Mech. 205, 215242.
Pullin, D. I., Jacobs, P. A., Grimshaw, R. H. J. & Saffman, P. G. 1989 Stability and filamentation of finite-amplitude waves on vortex layers of finite thickness. J. Fluid Mech. 209, 359384.
Rhines, P. B.: 1979 Geostrophic turbulence. Ann. Rev. Fluid Mech. 11, 401441.
Saffman, P. G. & Szeto, R., 1979 Equilibrium shapes of a pair equal uniform vortices. Phys. Fluids 23, 171185.
Verron, J., Hopfinger, E. J. & McWilllams, J. C., 1990 Sensitivity to initial conditions in the merging of two-layer baroclinic vortices. Phys. Fluids A 2, 886889.
Wu, H. M., Overman, E. A. & Zabusky, N. J., 1984 Steady state solutions of the Euler equations in two dimensions. Rotating and translating V-states with limiting cases. I. Numerical algorithms and results. J. Comput. Phys. 53, 4271.
Zabusky, N. J.: 1981 Recent developments in contour dynamics for the Euler equations. Ann. NY Acad. Sci. 373, 160170.
MathJax is a JavaScript display engine for mathematics. For more information see

Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states

  • L. M. Polvani (a1) (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed