• Ball, F. K., 1963: Some general theorems concerning the finite motion of a shallow rotating liquid lying on a paraboloid. J. Fluid Mech., 17 , 240256.

    • Search Google Scholar
    • Export Citation
  • Benilov, E. S., 1996: Beta-induced translation of strong isolated eddies. J. Phys. Oceanogr., 26 , 22232229.

  • Csanady, G. T., 1979: The birth and death of a warm core ring. J. Geophys. Res., 84 , 777780.

  • Cushman-Roisin, B., 1986: Frontal geostrophic dynamics. J. Phys. Oceanogr., 16 , 132143.

  • Cushman-Roisin, B., 1987: Exact analytical solution for elliptical vortices of the shallow-water equations. Tellus, 39A , 235244.

  • Cushman-Roisin, B., E. P. Chassignet, and B. Tang, 1990: Westward motion of mesoscale eddies. J. Phys. Oceanogr., 20 , 758768.

  • Dewar, W. K., 1988: Ventilating beta plane lenses. J. Phys. Oceanogr., 18 , 11931201.

  • Dotsenko, S., and A. Rubino, 2006: Analytical solutions for circular stratified eddies of the reduced-gravity shallow-water equations. J. Phys. Oceanogr., 36 , 16931702.

    • Search Google Scholar
    • Export Citation
  • Firing, E., and R. C. Beardsley, 1976: The behavior of a barotropic eddy on a β-plane. J. Phys. Oceanogr., 6 , 5765.

  • Flierl, G. L., 1977: The application of linear quasigeostrophic dynamics to Gulf Stream rings. J. Phys. Oceanogr., 7 , 365379.

  • Flierl, G. L., M. E. Stern, and J. A. Whitehead Jr., 1983: The physical significance of modons. Dyn. Atmos. Oceans, 7 , 233263.

  • Graef, F., 1998: On the westward translation of isolated eddies. J. Phys. Oceanogr., 28 , 740745.

  • Killworth, P. D., 1983: On motion of isolated lenses on a beta–plane. J. Phys. Oceanogr., 13 , 368376.

  • Larichev, V. D., 1984: Intergral properties of localized eddies on the beta plane. Izv. Atmos. Ocean. Phys., 20 , 654658.

  • McDonald, N. R., 1998: The time-dependent behaviour of a spinning disc on a rotating planet: A model for geostrophical vortex motion. Geophys. Astrophys. Fluid Dyn., 87 , 253272.

    • Search Google Scholar
    • Export Citation
  • Nycander, J., 2001: Drift velocity of radiating quasigeostrophic vortices. J. Phys. Oceanogr., 31 , 21782185.

  • Nof, D., 1981: On the β-induced movement of isolated baroclinic eddies. J. Phys. Oceanogr., 11 , 16621672.

  • Nof, D., 1983: The translation of isolated cold eddies on a sloping bottom. Deep-Sea Res., 30 , 171182.

  • Nof, D., 1984: Oscillatory drift of deep cold eddies. Deep-Sea Res., 31 , 13951414.

  • Reznik, G. M., and W. K. Dewar, 1994: An analytical theory of distributed axisymmetric barotropic vortices on the β plane. J. Fluid Mech., 269 , 301321.

    • Search Google Scholar
    • Export Citation
  • Reznik, G. M., and R. Grimshaw, 2001: Ageostrophic dynamics of an intense localized vortex on a beta plane. J. Fluid Mech., 443 , 351376.

    • Search Google Scholar
    • Export Citation
  • Ripa, P., 1997: “Inertial” oscillations and the β-plane approximation(s). J. Phys. Oceanogr., 27 , 633647.

  • Rubino, A., and P. Brandt, 2003: Warm-core eddies studied by laboratory experiments and numerical modeling. J. Phys. Oceanogr., 33 , 431435.

    • Search Google Scholar
    • Export Citation
  • Rubino, A., and S. Dotsenko, 2006: The stratified pulson. J. Phys. Oceanogr., 36 , 711719.

  • Rubino, A., P. Brandt, and K. Hessner, 1998: Analytical solutions for circular eddies of the reduced-gravity, shallow-water equations. J. Phys. Oceanogr., 28 , 9991002.

    • Search Google Scholar
    • Export Citation
  • Rubino, A., K. Hessner, and P. Brandt, 2002: Decay of stable warm-core eddies in a layered frontal model. J. Phys. Oceanogr., 32 , 188201.

    • Search Google Scholar
    • Export Citation
  • van Leeuwen, P. J., 2007: The propagation mechanism of a vortex on the β plane. J. Phys. Oceanogr., 37 , 23162330.

  • Warren, B. A., 1967: Notes on translatory movement of rings of current with application to Gulf Stream eddies. Deep-Sea Res., 14 , 505524.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 33 17 0
PDF Downloads 15 12 0

Nonstationary Westward Translation of Nonlinear Frontal Warm-Core Eddies

View More View Less
  • 1 Dipartimento di Scienze Ambientali, Università Ca’Foscari, Venice, Italy
  • | 2 Marine Hydrophysical Institute, Sevastopol, Ukraine
  • | 3 IFM-GEOMAR, Leibniz-Institut für Meereswissenschaften, Kiel, Germany
Restricted access

Abstract

For the first time, an analytical theory and a very high-resolution, frontal numerical model, both based on the unsteady, nonlinear, reduced-gravity shallow water equations on a β plane, have been used to investigate aspects of the migration of homogeneous surface, frontal warm-core eddies on a β plane. Under the assumption that, initially, such vortices are surface circular anticyclones of paraboloidal shape and having both radial and azimuthal velocities that are linearly dependent on the radial coordinate (i.e., circular pulsons of the first order), approximate analytical expressions are found that describe the nonstationary trajectories of their centers of mass for an initial stage as well as for a mature stage of their westward migration. In particular, near-inertial oscillations are evident in the initial migration stage, whose amplitude linearly increases with time, as a result of the unbalanced vortex initial state on a β plane. Such an initial amplification of the vortex oscillations is actually found in the first stage of the evolution of warm-core frontal eddies simulated numerically by means of a frontal numerical model initialized using the shape and velocity fields of circular pulsons of the first order. In the numerical simulations, this stage is followed by an adjusted, complex nonstationary state characterized by a noticeable asymmetry in the meridional component of the vortex’s horizontal pressure gradient, which develops to compensate for the variations of the Coriolis parameter with latitude. Accordingly, the location of the simulated vortex’s maximum depth is always found poleward of the location of the simulated vortex’s center of mass. Moreover, during the adjusted stage, near-inertial oscillations emerge that largely deviate from the exactly inertial ones characterizing analytical circular pulsons: a superinertial and a subinertial oscillation in fact appear, and their frequency difference is found to be an increasing function of latitude. A comparison between vortex westward drifts simulated numerically at different latitudes for different vortex radii and pulsation strengths and the corresponding drifts obtained using existing formulas shows that, initially, the simulated vortex drifts correspond to the fastest predicted ones in many realistic cases. As time elapses, however, the development of a β-adjusted vortex structure, together with the effects of numerical dissipation, tend to slow down the simulated vortex drift.

Corresponding author address: Angelo Rubino, Dipartimento di Scienze Ambientali, Università Ca’ Foscari di Venezia, Calle Larga Santa Marta, Dorsoduro 2137, I-30123 Venezia, Italy. Email: rubino@unive.it

Abstract

For the first time, an analytical theory and a very high-resolution, frontal numerical model, both based on the unsteady, nonlinear, reduced-gravity shallow water equations on a β plane, have been used to investigate aspects of the migration of homogeneous surface, frontal warm-core eddies on a β plane. Under the assumption that, initially, such vortices are surface circular anticyclones of paraboloidal shape and having both radial and azimuthal velocities that are linearly dependent on the radial coordinate (i.e., circular pulsons of the first order), approximate analytical expressions are found that describe the nonstationary trajectories of their centers of mass for an initial stage as well as for a mature stage of their westward migration. In particular, near-inertial oscillations are evident in the initial migration stage, whose amplitude linearly increases with time, as a result of the unbalanced vortex initial state on a β plane. Such an initial amplification of the vortex oscillations is actually found in the first stage of the evolution of warm-core frontal eddies simulated numerically by means of a frontal numerical model initialized using the shape and velocity fields of circular pulsons of the first order. In the numerical simulations, this stage is followed by an adjusted, complex nonstationary state characterized by a noticeable asymmetry in the meridional component of the vortex’s horizontal pressure gradient, which develops to compensate for the variations of the Coriolis parameter with latitude. Accordingly, the location of the simulated vortex’s maximum depth is always found poleward of the location of the simulated vortex’s center of mass. Moreover, during the adjusted stage, near-inertial oscillations emerge that largely deviate from the exactly inertial ones characterizing analytical circular pulsons: a superinertial and a subinertial oscillation in fact appear, and their frequency difference is found to be an increasing function of latitude. A comparison between vortex westward drifts simulated numerically at different latitudes for different vortex radii and pulsation strengths and the corresponding drifts obtained using existing formulas shows that, initially, the simulated vortex drifts correspond to the fastest predicted ones in many realistic cases. As time elapses, however, the development of a β-adjusted vortex structure, together with the effects of numerical dissipation, tend to slow down the simulated vortex drift.

Corresponding author address: Angelo Rubino, Dipartimento di Scienze Ambientali, Università Ca’ Foscari di Venezia, Calle Larga Santa Marta, Dorsoduro 2137, I-30123 Venezia, Italy. Email: rubino@unive.it

Save