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Propagation of barotropic vortices over topography in a rotating tank

Published online by Cambridge University Press:  26 April 2006

G. F. Carnevale ,
R. C. Kloosterziel  and
G. J. F. Van Heijst
G. F. Carnevale
Affiliation:
Scripps Institute of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
R. C. Kloosterziel
Affiliation:
Institute for Nonlinear Science (INLS), University of California, San Diego, La Jolla, CA 92093, USA
G. J. F. Van Heijst
Affiliation:
Department of Technical Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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Abstract

A small-scale cyclonic vortex in a relatively broad valley tends to climb up and out of the valley in a cyclonic spiral about the centre, and when over a relatively broad hill it tends to climb toward the top in an anticyclonic spiral around the peak. This phenomenon is examined here through two-dimensional numerical simulations and rotating-tank experiments. The basic mechanism involved is shown to be the same as that which accounts for the northwest propagation of cyclones on a β-plane. This inviscid nonlinear effect is also shown to be responsible for the observed translationary motion of barotropic vortices in a free-surface rotating tank. The behaviour of isolated vortices is contrasted with that of vortices with non-vanishing circulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 119 - 139
Copyright
© 1991 Cambridge University Press

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References

Adem, J. 1956 A series solution for the barotropic vorticity equation and its application in the study of atmospheric vortices. Tellus VIII, 364–372.Google Scholar
Bjerkness, J. & Holmboe, J. 1944 On the theory of cyclones. J. Mete. 1, 1–22.Google Scholar
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129–154.Google Scholar
Carnevale, G. F. & Frederiksen, J. S. 1987 Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175, 157–181.Google Scholar
Carnevale, G. F., Vallis, G. K., Purini, R. & Briscolini, M. 1988 Propagation of barotropic modons over topography. Geophys. Astrophys. Fluid Dyn. 41, 45–101.Google Scholar
Carr, L. E. & Williams, R. T. 1989 Barotropic vortex stability to perturbations from axisymmetry. J. Atmos. Sci. 46, 3177–3191.Google Scholar
Chan, J. C. L. & Williams, R. T. 1987 Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci. 44, 1257–1265.Google Scholar
Firing, E. & Beardsley, R. C. 1976 The behavior of a barotropic eddy on a β-plane. J. Phys. Oceanogr. 6, 57–65.Google Scholar
Flierl, G. R. 1977 The application of linear quasi-geostrophic dynamics to gulf stream rings. J. Phys. Oceanogr. 7, 365–379.Google Scholar
Flierl, G. R., Stern, M. E. & Whitehead, J. A. 1983 The physical significance of modons: laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233–263.Google Scholar
Gent, P. R. & McWilliams, J. C. 1986 The instability of barotropic circular vortices. Geophys. Astrophys. Fluid Dyn. 35, 209–233.Google Scholar
Griffiths, R. W. & Hopfinger, E. J. 1987 Coalescing of geostrophic vortices. J. Fluid Mech. 178, 73–97.Google Scholar
Heijst, G. J. F. Van & Kloosterziel, R. C. 1989 Tripolar vortices in a rotating fluid. Nature 338, 569–571.Google Scholar
Herring, J. R. 1977 On the statistical theory of two-dimensional topographic turbulence. J. Atmos. Sci. 34, 1731–1750.Google Scholar
Holloway, G., Riser, D. C. & Ramsden, D. 1986 Tracer anomaly evolution in the flow field of an isolated eddy. Dyn. Atmos. Oceans 10, 165–184.Google Scholar
Holton, J. R. 1979 An Introduction to Dynamic Meteorology. Academic.
Huppert, H. E. & Bryan, K. 1976 Topographically generated eddies. Deep-Sea Res. 23, 655–679.Google Scholar
Kloosterziel, R. C. 1990 On the large-time asymptotics of the diffusion equation on infinite domains. J. Engng Maths 24, 213–236.Google Scholar
Kloosterziel, R. C. & Heijst, G. J. F. van 1989 On tripolar vortices. In Mesoscale/Synoptic coherent Structures in Geophysical Turbulence (ed.) J. C. J. Nihoul, pp. 609–625. Elsevier.
Kloosterziel. R. C. & Heijst, G. J. F. van 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1–24.Google Scholar
Masuda, A., Marubayashi, K. & Ishibashi, M. 1990 A laboratory experiment and numerical simulation of an isolated barotropic eddy in a basin with topographic β J. Fluid Mech. 213, 641–659.Google Scholar
Mcwilliams, J. C. & Flierl, G. R. 1979 On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr. 9, 1155–1182.Google Scholar
Mcwilliams, J. C., Gent, P. R. & Norton, N. J. 1986 The evolution of balanced, low-mode vortices on the β-plane. J. Phys. Oceanogr. 16, 838–855.Google Scholar
Mied, R. P. & Lindemann, G. R. 1979 The propagation and evolution of cyclonic Gulf Stream rings. J. Phys. Oceanogr. 9, 1183–1206.Google Scholar
Mory, M., Stern, M. E. & Griffiths, R. W. 1987 Coherent baroclinic eddies on a sloping bottom. J. Fluid Mech. 183, 45–62.Google Scholar
Patterson, G. S. & Orszag, S. A. 1972 Spectral calculations of isotropic turbulence, efficient removal of aliasing interactions. Phys. Fluids 14, 2538–2541.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Rossby, C. G. 1948 On displacements and intensity changes of atmospheric vortices. J. Mar. Res. VII, 175–187.Google Scholar
Salmon, R., Holloway, G. & Hendershott, M. C. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691–703.Google Scholar
Takematsu, M. & Kita, T. 1988 The behavior of an isolated free eddy in a rotating fluid: Laboratory experiment. Fluid Dyn. Res. 3, 400–406.Google Scholar
Tojo, S. 1953 The dynamics of a vortex embedded in a constant zonal current. J. Met. 10, 175–178.Google Scholar
Willoughby, H. E. 1988 Linear motion of a shallow-water, barotropic vortex. J. Atmos. Sci. 45, 1906–1928.Google Scholar