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    Guo, Chuncheng Ilicak, Mehmet Fer, Ilker Darelius, Elin and Bentsen, Mats 2014. Baroclinic Instability of the Faroe Bank Channel Overflow*. Journal of Physical Oceanography, Vol. 44, Issue. 10, p. 2698.

    Kida, Shinichiro Yang, Jiayan and Price, James F. 2009. Marginal Sea Overflows and the Upper Ocean Interaction. Journal of Physical Oceanography, Vol. 39, Issue. 2, p. 387.

    Swaters, Gordon E. 2009. Ekman destabilization of inertially stable baroclinic abyssal flow on a sloping bottom. Physics of Fluids, Vol. 21, Issue. 8, p. 086601.

    Hughes, G.O. and Griffiths, R.W. 2006. A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Modelling, Vol. 12, Issue. 1-2, p. 46.

    Swaters, Gordon E. 2006. The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part I: Model Development and Dynamical Properties. Journal of Physical Oceanography, Vol. 36, Issue. 3, p. 335.

    Swaters, Gordon E 2001. On the collision between deep anticyclones and seamounts. European Journal of Mechanics - B/Fluids, Vol. 20, Issue. 4, p. 471.

  • Journal of Fluid Mechanics, Volume 408
  • April 2000, pp. 149-177

On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

  • DOI:
  • Published online: 01 April 2000

The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections of that layer are not small with respect to its scale height. The upper-layer dynamics are quasi-geostrophic, with the Eulerian velocity field principally driven by baroclinic stretching and a background topographic vorticity gradient.

Necessary conditions for instability, a semicircle-like theorem for unstable modes, bounds on the growth rate and phase velocity, and a sufficient condition for the existence of a high-wavenumber cutoff are presented. The linear stability equations are solved exactly for the case where the gravity current initially corresponds to an annulus flow with parabolic height profile with two incroppings, i.e. a coupled front. The dispersion relation for such a current is solved numerically, and the characteristics of the unstable modes are described. A distinguishing feature of the spatial structure of the perturbations is that the perturbations to the downslope incropping are preferentially amplified compared to the upslope incropping. Predictions of the model are compared with recent laboratory data, and good agreement is seen in the parameter regime for which the model is valid. Direct numerical simulations of the full model are employed to investigate the nonlinear regime. In the initial stage, the numerical simulations agree closely with the linear stability characteristics. As the instability develops into the finite-amplitude regime, the perturbations to the downslope incropping continue to preferentially amplify and eventually evolve into downslope propagating plumes. These finally reach the deepest part of the topography, at which point no more potential energy can be released.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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