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The stability of vortices in a rotating, stratified fluid

Published online by Cambridge University Press:  20 April 2006

R. W. Griffiths  and
P. F. Linden
R. W. Griffiths
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
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Abstract

Axisymmetric flows with a two-layer density stratification are produced by releasing either a constant flux of fluid from a point source or a constant volume of fluid into a rotating environment with a different density. In both experiments the density interface intersects one horizontal boundary, forming a front. Transition to non-axisym-metric flow is observed and can be described by two parameters: θ, the square of the ratio of the internal Rossby radius of deformation to the horizontal length scale of the flow, and δ, the fraction of the total fluid depth occupied by the layer inside the front. For θ [Lt ] 1 and δ > 10−1 unstable disturbances obtain most of their energy from the potential energy of the flow, whilst for δ < 10−1 extraction of kinetic energy from the basic shear becomes the dominant driving mechanism. When the front intersects the free surface, n = 2 is the minimum azimuthal wavenumber for an unstable disturbance. At large amplitude of the growing waves, baroclinic and barotropic processes combine to form n vortex dipole structures which entrain buoyant fluid from the original vortex and propagate radially over the free surface. Vortices are also produced by the continuous release of fluid from a confined source at its own density level in a region of constant density gradient. As in the two-layer case the axisymmetric vortex grows to a critical size and then becomes unstable to a disturbance with wavenumber n = 2, producing, at large amplitude, two vortex pairs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 283 - 316
Copyright
© 1981 Cambridge University Press

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References

Baker, D. J. 1971 Density gradients in a rotating stratified fluid: experimental evidence for a new instability. Science 172, 1029–1031.Google Scholar
Barcilon, V. 1964 Role of the Ekman layers in the stability of the symmetric regime obtained in a rotating annulus. J. Atmos. Sci. 21, 291–299.Google Scholar
Busse, F. H. 1968 Shear flow instability in rotating systems. J. Fluid Mech. 33, 577–589.Google Scholar
Calman, J. 1977 Experiments on high Richardson number instability of a rotating stratified shear flow. Dyn. Atmos. Oceans 1, 277–297.Google Scholar
Csanady, C. T. 1979 The birth and death of a warm core ring. J. Geophys. Res. 84, 777–780.Google Scholar
Douglas, H. A., Hide, R. & Mason, P. J. 1972 An investigation of the structure of baroclinic waves using three-level streak photography. Quart. J. Roy. Met. Soc. 98, 247–263.Google Scholar
Flierl, G. R. 1979 A simple model for the structure of warm and cold core rings. J. Geophys. Res. 84, 781–785.Google Scholar
Gill, A. E. 1981 Homogeneous intrusions into a rotating stratified fluid. J. Fluid Mech. 103, 275–295.Google Scholar
Gill, A. E., Green, J. S. A. & Simmons, A. J. 1974 Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. Deep-Sea Res. 21, 499–528.Google Scholar
Gill, A. E., Smith, J. M., Cleaver, R. P., Hide, R. & Jonas, P. R. 1979 The vortex created by mass transfer between layers of a rotating fluid. Geophys. Astrophys. Fluid Dyn. 12, 195–200.Google Scholar
Hart, J. E. 1972 A laboratory study of baroclinic instability. Geophys. Fluid Dyn. 3, 181–209.Google Scholar
Hart, J. E. 1974 On the mixed stability problem for quasi-geostrophic ocean currents. J. Phys. Oceanogr. 4, 349–356.Google Scholar
Hart, J. E. 1980 An experimental study of nonlinear baroclinic instability and mode selection in a large basin. Dyn. Atmos. Oceans 4, 115–136.Google Scholar
Hide, R. 1967 Detached shear layers in a rotating fluid. J. Fluid Mech. 29, 39–60.Google Scholar
Hoskins, B. J. 1976 Baroclinic waves and frontogenesis models. I. Introduction and Eady waves. Quart. J. Roy. Met. Soc. 102, 103–122.Google Scholar
McIntyre, M. E. 1970 Diffusive destabilization of the baroclinic circular vortex. Geophys. Fluid Dyn. 1, 19–57.Google Scholar
Orlanski, I. 1969 The influence of bottom topography on the stability of jets in a baroclinic fluid. J. Atmos. Sci. 26, 1216–1332.Google Scholar
Pedlosky, J. 1976 On the dynamics of finite amplitude baroclinic waves as a function of supercriticality. J. Fluid Mech. 78, 621–637.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Phillips, N. A. 1954 Energy transformations and meridional circulations associated with simple baroclinic waves in a two level quasi-geostrophic model. Tellus 6, 273–86.Google Scholar
Saunders, P. M. 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 61–65.Google Scholar