Eigenvalues of a Baroclinic Stability Problem with Ekman Damping

B. N. Antar The University of Tennessee Space Institute, Tullahoma, TN 37388

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W. W. Fowlis Space Sciences Laboratory, Marshall Space Flight Center, AL 35812

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Abstract

An analytical solution is presented for the baroclinic stability problem of a Boussinesq fluid in a β-plane channel with Ekman suction boundary conditions. All of the modes, stable and unstable, belonging to this problem are identified. It is found that an unstable mode exists for only a certain range of values of the Burger number. The value of the Burger number at the upper limit of this range increases as the Ekman number decreases. Beyond this upper limit only a damped mode exists. It is also found that this transition in parameter space from the unstable to the stable mode occurs in a discontinuous manner.

Abstract

An analytical solution is presented for the baroclinic stability problem of a Boussinesq fluid in a β-plane channel with Ekman suction boundary conditions. All of the modes, stable and unstable, belonging to this problem are identified. It is found that an unstable mode exists for only a certain range of values of the Burger number. The value of the Burger number at the upper limit of this range increases as the Ekman number decreases. Beyond this upper limit only a damped mode exists. It is also found that this transition in parameter space from the unstable to the stable mode occurs in a discontinuous manner.

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