On the (Nearly) Symmetric Instability

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  • 1 Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024
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Abstract

It is shown in the limit of small Ekman number that the preferred mode of the symmetric instability exhibits a slight angle of inclination with the direction of the mean flow. The sign of the angle depends an the sign of P − 1, where P is the Prandtl number. It is likely that owing to this effect the range of Richardson numbers for which the instability occurs is increased significantly beyond the limits derived by Kuo (1956) and by McIntyre (1970). Numerical computations are needed to establish this property quantitatively.

Abstract

It is shown in the limit of small Ekman number that the preferred mode of the symmetric instability exhibits a slight angle of inclination with the direction of the mean flow. The sign of the angle depends an the sign of P − 1, where P is the Prandtl number. It is likely that owing to this effect the range of Richardson numbers for which the instability occurs is increased significantly beyond the limits derived by Kuo (1956) and by McIntyre (1970). Numerical computations are needed to establish this property quantitatively.

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