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Two-Layer Models of Abyssal Equator-Crossing Flow

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 2 Applied Mathematics Institute, Department of Mathematical and Statistical Sciences, and Institute for Geophysical Research, University of Alberta, Edmonton, Canada
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Abstract

The role of baroclinicity in the dynamics of abyssal equator-crossing flows is examined by studying two-layer models of the flow valid in the equatorial region. Three new analytical models are derived from two-layer shallow-water theory. One of these models (Equatorial Model I, or EMI) reduces to the Swaters and Flierl coupled model in the midlatitude limit. In the equatorial limit, the lower-layer dynamics of EMI are that of the complete shallow-water equations, and the upper-layer dynamics are built upon quasigeostrophic potential vorticity conservation with a balance equation to relate the streamfunction and pressure. Simple numerical simulations are performed using this model to investigate its behavior in certain idealized situations, including equator-crossing lenses and currents. In the midlatitudes, the dynamics of EMI are characterized by strong baroclinic interactions between the layers, while near the equator all three models exhibit a partial decoupling of the layers. This motivates the use of a one-layer reduced-gravity model to simulate abyssal dynamics in the immediate vicinity of the equator. Such simulations are reported elsewhere. A uniformly valid metamodel is derived that contains all of the necessary terms so that it may reduce, in the appropriate parameter limit, to any of the three models derived here.

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

Abstract

The role of baroclinicity in the dynamics of abyssal equator-crossing flows is examined by studying two-layer models of the flow valid in the equatorial region. Three new analytical models are derived from two-layer shallow-water theory. One of these models (Equatorial Model I, or EMI) reduces to the Swaters and Flierl coupled model in the midlatitude limit. In the equatorial limit, the lower-layer dynamics of EMI are that of the complete shallow-water equations, and the upper-layer dynamics are built upon quasigeostrophic potential vorticity conservation with a balance equation to relate the streamfunction and pressure. Simple numerical simulations are performed using this model to investigate its behavior in certain idealized situations, including equator-crossing lenses and currents. In the midlatitudes, the dynamics of EMI are characterized by strong baroclinic interactions between the layers, while near the equator all three models exhibit a partial decoupling of the layers. This motivates the use of a one-layer reduced-gravity model to simulate abyssal dynamics in the immediate vicinity of the equator. Such simulations are reported elsewhere. A uniformly valid metamodel is derived that contains all of the necessary terms so that it may reduce, in the appropriate parameter limit, to any of the three models derived here.

Corresponding author address: Prof. 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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