Instability of Shielded Surface Temperature Vortices

Benjamin J. Harvey Department of Meteorology, University of Reading, Reading, United Kingdom

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Maarten H. P. Ambaum Department of Meteorology, University of Reading, Reading, United Kingdom

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Xavier J. Carton LPO, UBO/UEB, Brest, France

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Abstract

The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

Corresponding author address: Ben Harvey, Department of Meteorology, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. E-mail: b.j.harvey@reading.ac.uk

Abstract

The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

Corresponding author address: Ben Harvey, Department of Meteorology, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. E-mail: b.j.harvey@reading.ac.uk
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  • Blumen, W., 1978: Uniform potential vorticity flow. Part I: Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci., 35, 774783.

    • Search Google Scholar
    • Export Citation
  • Carton, X., 2009: Instability of surface quasigeostrophic vortices. J. Atmos. Sci., 66, 10511062.

  • Carton, X., G. R. Flierl, X. Perrot, T. Meunier, and M. A. Sokolovskiy, 2010: Explosive instability of geostrophic vortices. Part 1: Baroclinic instability. Theor. Comput. Fluid Dyn., 24, 125130.

    • Search Google Scholar
    • Export Citation
  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 3352.

  • Farrell, B. F., and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53, 20252040.

  • Flierl, G. R., 1988: On the instability of geostrophic vortices. J. Fluid Mech., 197, 349388.

  • Gradshteyn, I. S., and I. M. Ryzhik, 2000: Table of Integrals, Series, and Products. 6th ed. Academic Press, 1163 pp.

  • Harvey, B. J., and M. H. P. Ambaum, 2010a: Instability of surface-temperature filaments in strain and shear. Quart. J. Roy. Meteor. Soc., 136, 15061513, doi:10.1002/qj.651.

    • Search Google Scholar
    • Export Citation
  • Harvey, B. J., and M. H. P. Ambaum, 2010b: Perturbed Rankine vortices in surface quasi-geostrophic dynamics. Geophys. Astrophys. Fluid Dyn., in press, doi:10.1080/03091921003694719.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, 1995: Surface quasi-geostrophic dynamics. J. Fluid Mech., 282, 120.

    • Search Google Scholar
    • Export Citation
  • Juckes, M., 1994: Quasigeostrophic dynamics of the tropopause. J. Atmos. Sci., 51, 27562768.

  • Juckes, M., 1995: Instability of surface and upper-tropospheric shear lines. J. Atmos. Sci., 52, 32473262.

  • Lapeyre, G., and P. Klein, 2006: Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory. J. Phys. Oceanogr., 36, 165176.

    • Search Google Scholar
    • Export Citation
  • Morel, Y. G., and X. J. Carton, 1994: Multipolar votices in two-dimensional incompressible flows. J. Fluid Mech., 267, 2351.

  • Muraki, D. J., and C. Snyder, 2007: Vortex dipoles for surface quasigeostrophic models. J. Atmos. Sci., 64, 29612967.

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