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Time-Dependent Fully Nonlinear Geostrophic Adjustment

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  • 1 Program in Applied Mathematics and Department of Applied Physics, Columbia University, New York, New York
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Abstract

Shock-capturing numerical methods are employed to integrate the fully nonlinear, rotating 1D shallow-water equations starting from steplike nongeostrophic initial conditions (a Rossby adjustment problem). Such numerical methods allow one to observe the formation of multiple bores during the transient adjustment process as well as their decay due to rotation. It is demonstrated that increasing the rotation and/or the nonlinearity increases the rate of decay. Additionally, the time required for adjustment to be completed and its dependence on nonlinearity is examined; this time is found to be highly measure dependent. Lastly, the final adjusted state of the system is observed through long time integrations. Although the bores that form provide a mechanism for dissipation, their decay results in a final state in very good agreement with the one computed by well-known (dissipationless) conservation methods.

Corresponding author address: Dr. Lorenzo M. Polvani, Department of Applied Physics, Columbia University, Seeley W. Mudd Bldg., Room 209, 500 West 120th Street, New York, NY 10027.

Email: polvani@columbia.edu

Abstract

Shock-capturing numerical methods are employed to integrate the fully nonlinear, rotating 1D shallow-water equations starting from steplike nongeostrophic initial conditions (a Rossby adjustment problem). Such numerical methods allow one to observe the formation of multiple bores during the transient adjustment process as well as their decay due to rotation. It is demonstrated that increasing the rotation and/or the nonlinearity increases the rate of decay. Additionally, the time required for adjustment to be completed and its dependence on nonlinearity is examined; this time is found to be highly measure dependent. Lastly, the final adjusted state of the system is observed through long time integrations. Although the bores that form provide a mechanism for dissipation, their decay results in a final state in very good agreement with the one computed by well-known (dissipationless) conservation methods.

Corresponding author address: Dr. Lorenzo M. Polvani, Department of Applied Physics, Columbia University, Seeley W. Mudd Bldg., Room 209, 500 West 120th Street, New York, NY 10027.

Email: polvani@columbia.edu

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