Theoretical Regime Diagrams for Thermally Driven Flows in a Beta-Plane Channel

J. E. Geisler Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149

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W. W. Fowlis Space Sciences Laboratory, Marshall Space Flight Center, AL 35512

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Abstract

Thermally driven flows in rotating laboratory containers with cylindrical geometry can he axially symmetric or they can be wavelike, depending on experimental parameters. In the traditional regime diagram of thermal Rossby number versus Taylor number the region of axially symmetric motion is separated from the regime of wavelike motion by a knee-shaped boundary. The simplest theoretical model that predicts the shape of this curve is due to Barcilon (1964) and consists of the Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom. Anticipating that rotating fluid experiments might soon be done in spherical shell geometry, we have extended Barcilon's model to a beta-plane channel. The purpose of our study is to predict with a simple model the changes which the beta-effect should produce in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion.

Abstract

Thermally driven flows in rotating laboratory containers with cylindrical geometry can he axially symmetric or they can be wavelike, depending on experimental parameters. In the traditional regime diagram of thermal Rossby number versus Taylor number the region of axially symmetric motion is separated from the regime of wavelike motion by a knee-shaped boundary. The simplest theoretical model that predicts the shape of this curve is due to Barcilon (1964) and consists of the Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom. Anticipating that rotating fluid experiments might soon be done in spherical shell geometry, we have extended Barcilon's model to a beta-plane channel. The purpose of our study is to predict with a simple model the changes which the beta-effect should produce in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion.

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