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Shear Instabilities in the Atmosphere in the Presence of a Jump in the Brunt-Väisälä Frequency

C. PellacaniIstituto di Fisica A. Righi, Università di Bologna, 40126 Bologna, Italy

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C. TebaldiIstituto di Fisica A. Righi, Università di Bologna, 40126 Bologna, Italy

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E. TosiIstituto di Fisica A. Righi, Università di Bologna, 40126 Bologna, Italy

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Abstract

The stability properties of a Helmholtz velocity profile in a stratified, Boussinesq fluid are investigated in the presence of a jump in the Brunt- Väisälä (BV) frequency at a level different from the one where the vortex sheet is located. New unstable modes in the range of low horizontal wavenumbers are found with respect to the case where no BV frequency jump exists. The structure of the associated unstable disturbances is similar to that of neutrally propagating gravity waves. The associated growth rates are rather small but significant because they appear in a range of horizontal wavenumbers which are otherwise stable.

A comparison with the results obtained by Lindzen and Rosenthal and by Lalas et al. shows a strict analogy with the study of the stability properties of a Helmholtz velocity profile in the presence of a lower rigid boundary. The generation of such instabilities is interpreted in terms of multiple overreflexions at the shear interface due to the presence of the reflecting BV frequency jump for neutral propagating waves. Applications for values of the relevant parameters suitable to actual atmospheric cases are discussed.

Abstract

The stability properties of a Helmholtz velocity profile in a stratified, Boussinesq fluid are investigated in the presence of a jump in the Brunt- Väisälä (BV) frequency at a level different from the one where the vortex sheet is located. New unstable modes in the range of low horizontal wavenumbers are found with respect to the case where no BV frequency jump exists. The structure of the associated unstable disturbances is similar to that of neutrally propagating gravity waves. The associated growth rates are rather small but significant because they appear in a range of horizontal wavenumbers which are otherwise stable.

A comparison with the results obtained by Lindzen and Rosenthal and by Lalas et al. shows a strict analogy with the study of the stability properties of a Helmholtz velocity profile in the presence of a lower rigid boundary. The generation of such instabilities is interpreted in terms of multiple overreflexions at the shear interface due to the presence of the reflecting BV frequency jump for neutral propagating waves. Applications for values of the relevant parameters suitable to actual atmospheric cases are discussed.

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