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Source–sink turbulence in a rotating stratified fluid

Published online by Cambridge University Press:  26 April 2006

P. F. Linden ,
B. M. Boubnov  and
S. B. Dalziel
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
B. M. Boubnov
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Permanent address: Institute of Atmospheric Physics, Moscow.
S. B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

In a recent paper Boubnov, Dalziel & Linden (1994) described the response of a stratified fluid to forcing produced by an array of sources and sinks. The sources and sinks were located in a horizontal plane and the flow from the sources was directed horizontally so that fluid was withdrawn from, and re-injected at, its own density level. As a result vertical vorticity was imparted to the fluid with a minimum of vertical mixing. It was found that when the stratification was strong enough to suppress vertical motions an inverse energy cascade was observed leading to the establishment of a large-scale circulation in the fluid. Those experiments were restricted to eight source-sink pairs. The present paper extends this work in two ways. First, up to forty source-sink pairs are used to force the flow, thereby producing a much wider separation of scales between the forcing and the flow domain. An inverse cascade is again found, but in this case the energy transfer to large scales is more rapid. The basic pattern of the large-scale flow is independent of the number of sources but the detailed structure depends on the energy input scale. Second, the effects of rotation about a vertical axis are investigated. It is found that when the Rossby deformation radius exceeds the size of the flow domain, the inverse energy cascade still occurs. However, for smaller values of the deformation scale, which in these experiments are comparable to or smaller than the forcing scale, the inverse cascade is altered by baroclinic instability. When flow structures develop on a scale larger than the deformation scale, usually by the merging of vortices of like sign, these structures are observed to split into smaller vortices of a scale comparable to the deformation scale. The flow appears to evolve with a balance between an anticascade produced by the two-dimensionality of the flow and a cascade due to baroclinic instability. For Rossby radii much smaller than the domain size the flow evolves into finite clumps of vorticity and an asymmetry between anticyclones and cyclones develops. A predominance of coherent anticyclones is observed, and the cyclonic vorticity is contained in more diffuse structures.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 81 - 112
Copyright
© 1995 Cambridge University Press

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References

Boubnov, B. M., Dalziel, S. B. & Linden, P. F. 1994 Source-sink turbulence in a stratified fluid. J. Fluid Mech. 261 273–303 (referred to herein as BDL).Google Scholar
Colin de Verdierr, A. 1980 Quasi-geostrophic turbulence in a rotating homogeneous fluid. Geophys. Astrophys. Fluid Dyn. 15, 213–251.Google Scholar
Dalziel, S. B. 1992 Decay of rotating turbulence: some particle tracking experiments. J. Appl. Sci. Res. 49, 217–244.Google Scholar
Dalziel, S. B. 1993 Rayleigh-Taylor instability: experiments with image analysis. Dyn. Atmos. Oceans 20, 127–153.Google Scholar
Dritschel, D. G. 1993 Vortex properties of two-dimensional turbulence. Phys. Fluids A 5, 984–997.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. & Linden, P. F. 1981 The stability of vortices in a rotating, stratified flow. J. Fluid Mech. 105, 283–316.Google Scholar
Griffiths, R. W. & Linden, P. F. 1985 Intermittent baroclinic instability and fluctuations in geophysical circulations. Nature 316, 801–803.Google Scholar
Holford, J. M. 1994 The evolution of a front. Ph.D. dissertation, University of Cambridge.
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.Google Scholar
Legras, B., Santangelo, P. & Benzi, R. 1988 High resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 37–42.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Maltrud, M. E. & Vallis, G. K. 1991 Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech. 228, 321–342.Google Scholar
Metais, P., Riley, J. J. & Lesieur, M. 1994 Numerical simulations of stably-stratified rotating turbulence. In Stably-Stratified Flows - Flow and Dispersion over Topography (ed. I. P. Castro & N. J. Rockliff). IMA Conference Series. Oxford University Press.
Yamagata, T. 1982 On nonlinear planetary waves: a class of solutions missed by the traditional quasi-geostrophic approximation. J. Ocean Soc. Japan 38, 236–244.Google Scholar