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On the alignment and axisymmetrization of a vertically tilted geostrophic vortex

Published online by Cambridge University Press:  26 April 2006

F. Viera
F. Viera
Affiliation:
The School of Mathematics and Statistics, The University of Sydney, NSW, 2006, Australia
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Abstract

We investigate the evolution of a vertically tilted geostrophic vortex of cylindrical shape and circular horizontal cross-section using the recently developed method of boundary surface dynamics. The vortex consists of a finite volume of constant potential vorticity immersed in a spatially unbounded fluid of uniform density stratification. The fully nonlinear three-dimensional problem is then reduced to the calculation of the Lagrangian evolution of the boundary surface of the vortex region, thus decreasing the dimensionality by one. In the numerical simulations presented here, the vortex shows a general tendency to attain vertical alignment and a horizontal axisymmetrical shape by wobbling about its centre and going through three basic stages of evolution: (a) the circular horizontal cross-sections of the upper and lower parts of the vortex distort and become elongated; (b) the upper and lower sections then become vertically aligned by reducing their horizontal intercentroid distances; and (c) the distorted horizontal cross-sections relax towards axisymmetry, often through the process of filamentation. For a given vortex height, if the horizontal scale of the flow is close to the internal radius of deformation, or equivalently, the density stratification is not too strong, the processes of filamentation and vertical alignment are enhanced. However, for stronger stratifications, both filamentation and vertical alignment are found to be greatly inhibited. For relatively small initial inclination angles, filamentation only occurs in the upper and lower sections of the vortex. Increasing the angle of tilt also increases the tendency of the surface to steepen and filament in the middle sections of the vortex. For a fixed value of the ratio of horizontal scale of the flow to the deformation radius, taller vortices have an increased tendency to align and axisymmetrize than shorter vortices of equal inclination angle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 29 - 50
Copyright
© 1995 Cambridge University Press

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References

Charney, J. G. 1963 Numerical experiment in atmospheric hydrodynamics. Proc. Symp. Appl. Math., Am. Math. Soc. 15, 289–310.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
McWilliams, J. C. 1989 Statistical properties of decaying geostrophic turbulence. J. Fluid Mech. 198, 199–230.Google Scholar
McWilliams, J. C. 1990 The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361–385.Google Scholar
Melander, M. V., McWilliams, J. C. & Zabusky, N. J. 1987 Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech. 178, 137–159.Google Scholar
Melander, M. V., Zabusky, N. J. & McWilliams, J. C. 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid mech. 195, 303–340.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics, chap. 6. Springer.
Polvani, L. M. 1991 Two-layer geostrophic dynamics. Part 2. Alignment and two-layer V-states. J. Fluid Mech. 225, 241–270.Google Scholar
Polvani, L. M., Zabusky, N. J. & Flierl, G. R. 1989 Two-layer geostrophic dynamics. Part 1. Upper-layer V-states and merger. J. Fluid Mech. 205, 215–242.Google Scholar
Rhines, P. B. 1977 The dynamics of unsteady currents. In The Sea, vol. 6, pp. 189–318. Wiley.
Rhines, P. B. 1979 Geostrophic Turbulence. Ann. Rev. Fluid Mech. 11, 401–441.Google Scholar
Viera, F. 1994a Boundary Surface Dynamics: An algorithm for stratified geostrophic flows. J. Comput. Phys. 111, 336–346.Google Scholar
Viera, F. 1994b The evolution of cylindrical geostrophic vortices. Proceedings: Computational Techniques and Applications: CTAC-93, pp. 462–469. World Scientific.
Viera, F. 1994c The dynamics of stratified geostrophic vortices. Part 1. Combined merger/alignment simulations. Res. Rep. 94–12. School of Mathematics and Statistics, The University of Sydney.