The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part I: Model Development and Dynamical Properties

Gordon E. Swaters Applied Mathematics Institute, Department of Mathematical and Statistical Sciences, and Institute for Geophysical Research, University of Alberta, Edmonton, Alberta, Canada

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Abstract

The equatorward flow of source-driven grounded deep western boundary currents within a stratified basin with variable topography is examined. The model is the two-layer quasigeostrophic (QG) equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic (PG) equations, describing the abyssal layer, on a midlatitude β plane. The model retains subapproximations such as classical Stommel–Arons theory, the Nof abyssal dynamical balance, the so-called planetary shock wave balance (describing the finite-amplitude β-induced westward propagation of abyssal anomalies), and baroclinic instability. The abyssal height field can possess groundings. In the reduced gravity limit, a new nonlinear steady-state balance is identified that connects source-driven equatorward abyssal flow (as predicted by Stommel–Arons theory) and the inertial topographically steered deep flow described by Nof dynamics. This model is solved explicitly, and the meridional structure of the predicted grounded abyssal flow is described. In the fully baroclinic limit, a variational principle is established and is exploited to obtain general stability conditions for meridional abyssal flow over variable topography on a β plane. The baroclinic coupling of the PG abyssal layer with the QG overlying ocean eliminates the ultraviolet catastrophe known to occur in inviscid PG reduced gravity models. The baroclinic instability problem for a constant-velocity meridional abyssal current flowing over sloping topography with β present is solved and the stability characteristics are described.

Corresponding author address: Gordon E. Swaters, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada. Email: gordon.swaters@ualberta.ca

Abstract

The equatorward flow of source-driven grounded deep western boundary currents within a stratified basin with variable topography is examined. The model is the two-layer quasigeostrophic (QG) equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic (PG) equations, describing the abyssal layer, on a midlatitude β plane. The model retains subapproximations such as classical Stommel–Arons theory, the Nof abyssal dynamical balance, the so-called planetary shock wave balance (describing the finite-amplitude β-induced westward propagation of abyssal anomalies), and baroclinic instability. The abyssal height field can possess groundings. In the reduced gravity limit, a new nonlinear steady-state balance is identified that connects source-driven equatorward abyssal flow (as predicted by Stommel–Arons theory) and the inertial topographically steered deep flow described by Nof dynamics. This model is solved explicitly, and the meridional structure of the predicted grounded abyssal flow is described. In the fully baroclinic limit, a variational principle is established and is exploited to obtain general stability conditions for meridional abyssal flow over variable topography on a β plane. The baroclinic coupling of the PG abyssal layer with the QG overlying ocean eliminates the ultraviolet catastrophe known to occur in inviscid PG reduced gravity models. The baroclinic instability problem for a constant-velocity meridional abyssal current flowing over sloping topography with β present is solved and the stability characteristics are described.

Corresponding author address: Gordon E. Swaters, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada. Email: gordon.swaters@ualberta.ca

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