• Armi, L., and E. D'Asaro, 1980: Flow structures of the benthic ocean. J. Geophys. Res, 85 (C1) 469484.

  • Beismann, J-O., R. H. Käse, and J. R. E. Lutjeharms, 1999: On the influence of submarine ridges on translation and stability of Agulhas rings. J. Geophys. Res, 104 (C4) 78977906.

    • Search Google Scholar
    • Export Citation
  • Bell, G. I., 1990: Interaction between vortices and waves in a simple model of geophysical flow. Phys. Fluids, A2 , 575586.

  • Dritschel, D. G., 1988: Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics. J. Comput. Phys, 77 , 240266.

    • Search Google Scholar
    • Export Citation
  • Dunn, D. C., 2002: The evolution of an initially circular vortex near an escarpment. Part II: Numerical results. Eur. J. Mech, 21B , 677699.

    • Search Google Scholar
    • Export Citation
  • Dunn, D. C., N. R. McDonald, and E. R. Johnson, 2001: The motion of a singular vortex near an escarpment. J. Fluid Mech, 448 , 335365.

    • Search Google Scholar
    • Export Citation
  • Dunn, D. C., N. R. McDonald, and E. R. Johnson, 2002: The evolution of an initially circular vortex near an escarpment. Part I: Analytical results. Eur. J. Mech, 21B , 657675.

    • Search Google Scholar
    • Export Citation
  • Gradshteyn, I. S., and I. M. Ryzhik, 1994: Table of Integrals, Series and Products. 5th ed. Academic Press, 1163 pp.

  • Gründlingh, M. L., 1995: Tracking eddies in the southeast Atlantic and southwest Indian oceans with TOPEX/Poseidon. J. Geophys. Res, 100 (C12) 2497724986.

    • Search Google Scholar
    • Export Citation
  • Hamilton, P., 1992: Lower continental slope cyclonic eddies in the central Gulf of Mexico. J. Geophys. Res, 97 (C2) 21852200.

  • Hamilton, P., G. S. Fargion, and D. C. Biggs, 1999: Loop Current Eddy paths in the western Gulf of Mexico. J. Phys. Oceanogr, 29 , 11801207.

    • Search Google Scholar
    • Export Citation
  • Herbette, S., Y. Morel, and M. Arhan, 2003: Erosion of a surface vortex by a seamount. J. Phys. Oceanogr, 33 , 16641679.

  • Hogg, N. G., and H. M. Stommel, 1985: The heton, an elementary interaction between discrete baroclinic geostrophic vortices, and its implications concerning eddy heat flow. Proc. Roy. Soc. London, 397A , 120.

    • Search Google Scholar
    • Export Citation
  • Johnson, E. R., and N. R. McDonald, 2004a: The motion of a vortex near a gap in a wall. Phys. Fluids, 16 , 462469.

  • Johnson, E. R., and N. R. McDonald, 2004b: The motion of a vortex near two circular cylinders. Proc. Roy. Soc. London, 460A , 939954.

  • Kirwan, A. D., W. J. Merrell, K. Lewis, and R. E. Whitaker, 1984: Lagrangian observations of an anticyclonic ring in the Western Gulf of Mexico. J. Geophys. Res, 89 (C3) 34173424.

    • Search Google Scholar
    • Export Citation
  • McDonald, N. R., 1998: The motion of an intense vortex near topography. J. Fluid Mech, 367 , 359377.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed. Springer-Verlag, 710 pp.

  • Stern, M. E., and G. R. Flierl, 1987: On the interaction of a vortex with a shear flow. J. Geophys. Res, 92 (C10) 1073310744.

  • Sutyrin, G. G., I. Ginis, and S. A. Frolov, 2001: Equilibration of baroclinic meanders and deep eddies in a Gulf Stream–type jet over a sloping bottom. J. Phys. Oceanogr, 31 , 20492065.

    • Search Google Scholar
    • Export Citation
  • Sutyrin, G. G., G. D. Rowe, L. M. Rothstein, and I. Ginis, 2003: Baroclinic eddy interactions with continental slopes and shelves. J. Phys. Oceanogr, 33 , 283291.

    • Search Google Scholar
    • Export Citation
  • Thierry, V., and Y. Morel, 1999: Influence of a strong bottom slope on the evolution of a surface-intensified vortex. J. Phys. Oceanogr, 29 , 911924.

    • Search Google Scholar
    • Export Citation
  • Thompson, L., 1993: Two-layer quasigeostrophic flow over finite isolated topography. J. Phys. Oceanogr, 23 , 12971314.

  • Vandermeirsch, F. O., X. J. Carton, and Y. G. Morel, 2003: Interaction between an eddy and a zonal jet. Part I: One-and-a-half-layer model. Dyn. Atmos. Oceans, 36 , 247270.

    • Search Google Scholar
    • Export Citation
  • Wang, X., 1992: Interaction of an eddy with a continental slope. Ph.D. thesis, MIT/WHOI Joint Program in Oceanography, 216 pp.

  • Zavala Sansón, L., 2002: Vortex-ridge interaction in a rotating fluid. Dyn. Atmos. Oceans, 35 , 299325.

  • Zavala Sansón, L., and G. J. F. van Heijst, 2000: Interaction of barotropic vortices with coastal topography: Laboratory experiments and numerical simulations. J. Phys. Oceanogr, 30 , 21412162.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 103 29 2
PDF Downloads 22 3 0

The Motion of a Point Vortex near Large-Amplitude Topography in a Two-Layer Fluid

View More View Less
  • 1 Department of Mathematics, University College London, London, United Kingdom
Restricted access

Abstract

This work examines the dynamics of point vortices in a two-layer fluid near large-amplitude, sharply varying topography like that which occurs in continental shelf regions. Topography takes the form of an infinitely long step change in depth, and the two-layer stratification is chosen such that the height of topography in the upper layer is a small fraction of the overall depth, enabling quasigeostrophic theory to be used in both layers. An analytic expression for the dispersion relation of free topographic waves in this system is found. Weak vortices are studied using linear theory and, if located in the lower layer, propagate mainly because of their image in the topography. Depending on their sign, they are able to produce significant topographic wave radiation in their wakes. Upper-layer vortices propagate much slower and produce relatively small amplitude topographic wave radiation. Contour dynamics results are used to investigate the nonlinear regions of parameter space. For lower-layer vortices, linear theory is a good approximation, but for upper-layer vortices complicated features evolve and linear theory is only valid for weak vortices.

Corresponding author address: Andrew J. White, Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom. Email: awhite@math.ucl.ac.uk

Abstract

This work examines the dynamics of point vortices in a two-layer fluid near large-amplitude, sharply varying topography like that which occurs in continental shelf regions. Topography takes the form of an infinitely long step change in depth, and the two-layer stratification is chosen such that the height of topography in the upper layer is a small fraction of the overall depth, enabling quasigeostrophic theory to be used in both layers. An analytic expression for the dispersion relation of free topographic waves in this system is found. Weak vortices are studied using linear theory and, if located in the lower layer, propagate mainly because of their image in the topography. Depending on their sign, they are able to produce significant topographic wave radiation in their wakes. Upper-layer vortices propagate much slower and produce relatively small amplitude topographic wave radiation. Contour dynamics results are used to investigate the nonlinear regions of parameter space. For lower-layer vortices, linear theory is a good approximation, but for upper-layer vortices complicated features evolve and linear theory is only valid for weak vortices.

Corresponding author address: Andrew J. White, Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom. Email: awhite@math.ucl.ac.uk

Save