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The evolution of stable barotropic vortices in a rotating free-surface fluid

Published online by Cambridge University Press:  26 April 2006

R. C. Kloosterziel  and
G. J. F. Van Heijst
R. C. Kloosterziel
Affiliation:
Institute for Nonlinear Science, University California San Diego, La Jolla, CA 92093, USA
G. J. F. Van Heijst
Affiliation:
Department of Technical Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

Laboratory experiments reveal that, for increasing time, barotropic cyclones typically show an increasing steepness in their flow profiles. This implies that such vortices become barotropically more unstable. This has been confirmed by observations which are further discussed in a companion paper (Kloosterziel & van Heijst 1991). In the present paper the evolutionary process is discussed. It is shown that the observed steepening of the flow profiles is mainly a nonlinear effect due to the advection of relative vorticity by the interior Ekman circulation. The linear Ekman pumping law is found to be a good approximation in the core of the vortices for O(1) Rossby numbers but at larger radii the Ekman pumping is stronger in reality. Free-surface effects are shown to have a broadening effect, which can balance the nonlinear steepening if the Rossby number becomes sufficiently small or the Froude number sufficiently large. In addition it is shown that for the classical spindown problem with a free surface no expansion in the Froude number needs to be introduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 607 - 629
Copyright
© 1992 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A., 1965 Handbook of Mathematical Functions. Dover.
Carnevale, G. F., Kloosterziel, R. C. & Van Heijst, G. J. F.: 1991 Propagation of barotropic vortices over topography in a rotating tank. J. Fluid Mech. 233, 119–139.Google Scholar
Carton, X. J. & Mcwilliams, J. C., 1989 Barotropic and baroclinic instabilities of axisymmetric vortices in a quasi-geostrophic model. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 225–244. Elsevier.
Cederlöf, U.: 1988 Free-surface effects on spin-up. J. Fluid Mech. 187, 395–407.Google Scholar
Flierl, G. R.: 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349–388.Google Scholar
Gent, P. R. & Mcwilliams, J. C., 1986 The instability of circular vortices. Geophys. Astrophys. Fluid Dyn. 35, 209–233.Google Scholar
Greenspan, H. P.: 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. & Howard, L. N., 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.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. & Van Heijst, G. J. F.: 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1–24.Google Scholar
Pedlosky, J.: 1979 Geophysical Fluid Dynamics. Springer.
Rogers, M. H. & Lance, G. N., 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk. J. Fluid Mech. 7, 617–631.Google Scholar
Saunders, P. M.: 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 61–65.Google Scholar
Venezian, G.: 1970 Non-linear spin-up. Topics in Ocean Engineering, vol. 2, pp. 87–96. Gulf.
Wedemeyer, E. H.: 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar
Weidman, P. D.: 1976 On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model. J. Fluid Mech. 77, 685–708.Google Scholar