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Baroclinic instability of three-layer flows Part 2. Experiments with eddies

Published online by Cambridge University Press:  21 April 2006

David A. Smeed
David A. Smeed
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The stability of eddies with three-layer stratification is examined experimentally. When the difference in density between the upper two layers is much greater (or less) than that between the lower two layers baroclinic instability on two different lengthscales (the Rossby radii associated with the upper and the lower interfaces) is possible. The vortices are created using modifications of two techniques described by Griffiths & Linden (1981) in their study of two-layer eddies.

‘Constant-flux’ eddies are generated by the release of a constant flux of buoyant fluid from a small source positioned at the surface of a two-layer fluid. In a second variation of this experiment, the source is positioned at the interface between two layers and fluid of intermediate density is injected. As the horizontal lengthscale increases, the vortices evolve from a stable to an unstable state. It is showns that the size at which the vortices become unstable may be significantly altered by the presence of a second interface. The results agree qualitatively with the conclusions of a linear stability analysis of quasi-geostrophic three-layer flow in a channel (Smeed 1988), but it is necessary to examine the effects of horizontal shear and Ekman dissipation to explain the experimental results.

‘Constant-volume’ eddies are produced by the release of a volume of buoyant fluid, initially contained within a cylindrical barrier, at the surface of a two-layer fluid. After the barrier is removed, the buoyant fluid spreads a distance of the order of the Rossby radius. Similarly, vortices are created by releasing a volume of fluid of density intermediate between the initial two layers. Within a few rotation periods the vortices become unstable to disturbances similar to those observed in two-layer experiments. Qualitative agreement is found between the observed wavelength and the fastest growing mode predicted by the linear stability theory (Smeed 1988). When the disturbances reach large amplitude a change in lengthscale is often observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 233 - 259
Copyright
© 1988 Cambridge University Press

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References

Chia, F., Griffiths, R. W. & Linden, P. F. 1982 Laboratory experiments on fronts. Part II. The formation of cyclonic eddies at upwelling fronts. Geophys. Astrophys. Fluid Dyn. 19, 189–206.Google Scholar
Evans, R. H., Baker, K. S., Brown, O. B. & Smith, R. C. 1985 Chronology of warm-core ring 82-B. J. Geophys. Res. 90, 8803–8811.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, 195–220.Google Scholar
Griffiths, R. W. & Hopfinger, E. J. 1984 The structure of mesoscale turbulence and horizontal spreading at ocean fronts. Deep-Sea Res. 31, 245–269.Google Scholar
Griffiths, R. W., Killworth, P. D. & Stern, M. E. 1982 Ageostrophic instability of ocean currents. J. Fluid Mech. 117, 343–377.Google Scholar
Griffiths, R. W. & Linden, P. F. 1981a The stability of vortices in a rotating, stratified fluid. J. Fluid Mech. 105, 283–316.Google Scholar
Griffiths, R. W. & Linden, P. F. 1981b The stability of buoyancy driven coastal currents. Dyn. Atmos. Oceans 5, 281–306.Google Scholar
Griffiths, R. W. & Linden, P. F. 1982 Laboratory experiments on fronts: Part 1. Density driven boundary currents. Geophys. Astrophys. Fluid Dyn. 19, 159–187.Google Scholar
Griffiths, R. W. & Pearce, A. F. 1985 Satellite images of an unstable warm core eddy derived from the Leeuwin Current. Deep-Sea Res. 32, 1371–1380.Google Scholar
Hart, J. E. 1972 A laboratory study of baroclinic instability. Geophys. Fluid Dyn. 3, 181–209.Google Scholar
Joyce, T. M. & Kennelly, M. A. 1985 Upper ocean velocity structure of Gulf Stream warm-core ring 82-B. J. Geophys. Res. 90, 8813–8822.Google Scholar
Killworth, P. D., Paldor, N. & Stern, M. E. 1984 Wave propagation and growth on a surface front in a two-layer geostrophic current. J. Mar. Res. 42, 761–785.Google Scholar
McIntyre, M. E. 1970 Diffusive destabilisation of the baroclinic circular vortex. Geophys. Fluid Dyn. 1, 19–57.Google Scholar
Olson, D. B., Schmitt, R. W., Kennelly, M. A. & Joyce, T. M. 1985 A two-layer diagnostic model of the long-term evolution of warm-core ring 82-B. J. Geophys. Res. 90, 8813–8822.Google Scholar
Phillips, N. A. 1954 Energy transformation and meridional circulation associated with simple baroclinic waves in a two-level, quasi-geostrophic model. Tellus 6, 273–286.Google Scholar
Saunders, P. M. 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 61–65.Google Scholar
Smeed, D. A. 1986 Eddies in stratified, rotating fluids. Ph.D. thesis, University of Cambridge.
Smeed, D. A. 1987 A laboratory model of benthic fronts. Deep-Sea Res. 34, 1431–1459.Google Scholar
Smeed, D. A. 1988 Baroclinic instability of three-layer flows. Part 1. Linear stability. J. Fluid Mech. 194, 217–231.Google Scholar