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Instability of Abyssal Currents in a Continuously Stratified Ocean with Bottom Topography

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  • 1 Applied Mathematics Institute, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
  • | 2 Applied Mathematics Institute, Departments of Mathematical and Statistical Sciences and Earth and Atmospheric Sciences, University of Alberta, Edmonton, Alberta, Canada
  • | 3 Applied Mathematics Institute, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
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Abstract

A theory is developed for the baroclinic destabilization of density-driven abyssal flows over topography in a rotating environment. The dominant instability mechanism being studied is the release of available potential energy caused by gradual downhill slumping of the abyssal current. The present model assumes a two-layer configuration and allows for intersections of the interface with the bottom (i.e., true fronts), as well as continuous stratification in the ambient fluid. The linear instability problem in a channel for a current with parabolic cross section is solved, and the perturbation growth rate and most unstable wavenumber are both shown to increase with current thickness. A similar trend is evident as the stratification number is increased or the current width is decreased. The instability manifests itself in the overlying ocean as an amplifying topographic Rossby wave. Alternating positive/negative pressure anomalies in the upper layer are accompanied by a wavelike deformation of the abyssal current that is most pronounced on the downslope side. Upper-layer vortical features have a distinct vertically tapered shape and are to be interpreted as bottom-intensified eddies. Long-term evolution of the flow is elucidated in a series of simulations employing the fully nonlinear governing equations. It is found that, even though the linear instability calculation relates to a periodic current, the instability characteristics are still valid to a good approximation for the case of a source flow. The abyssal current breaks up into a series of plumes that penetrate downslope into the deeper ocean, producing strong current fluctuations not unlike those observed in Denmark Strait overflow water. Furthermore, introduction of more realistic topography into the numerical simulation leads to the development of coherent baroclinic vortex pairs whose upper-layer component is strongly cyclonic.

Corresponding author address: Dr. Gordon E. Swaters, Department of Mathematical Sciences, University of Alberta, Edmonton, AB T6G 2E1, Canada. Email: gordon.swaters@ualberta.ca

Abstract

A theory is developed for the baroclinic destabilization of density-driven abyssal flows over topography in a rotating environment. The dominant instability mechanism being studied is the release of available potential energy caused by gradual downhill slumping of the abyssal current. The present model assumes a two-layer configuration and allows for intersections of the interface with the bottom (i.e., true fronts), as well as continuous stratification in the ambient fluid. The linear instability problem in a channel for a current with parabolic cross section is solved, and the perturbation growth rate and most unstable wavenumber are both shown to increase with current thickness. A similar trend is evident as the stratification number is increased or the current width is decreased. The instability manifests itself in the overlying ocean as an amplifying topographic Rossby wave. Alternating positive/negative pressure anomalies in the upper layer are accompanied by a wavelike deformation of the abyssal current that is most pronounced on the downslope side. Upper-layer vortical features have a distinct vertically tapered shape and are to be interpreted as bottom-intensified eddies. Long-term evolution of the flow is elucidated in a series of simulations employing the fully nonlinear governing equations. It is found that, even though the linear instability calculation relates to a periodic current, the instability characteristics are still valid to a good approximation for the case of a source flow. The abyssal current breaks up into a series of plumes that penetrate downslope into the deeper ocean, producing strong current fluctuations not unlike those observed in Denmark Strait overflow water. Furthermore, introduction of more realistic topography into the numerical simulation leads to the development of coherent baroclinic vortex pairs whose upper-layer component is strongly cyclonic.

Corresponding author address: Dr. Gordon E. Swaters, Department of Mathematical Sciences, University of Alberta, Edmonton, AB T6G 2E1, Canada. Email: gordon.swaters@ualberta.ca

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