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A Buoyancy–Vorticity Wave Interaction Approach to Stratified Shear Flow

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  • 1 Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv, Israel
  • | 2 Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv, and Department of Physics, The Technion, Haifa, Israel, and City College of San Francisco, San Francisco, California
  • | 3 Laboratoire de Meteorologie Dynamique, Ecole Normale Superieure, Paris, France
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Abstract

Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integration of the quasigeostrophic equations with two, rather than one, prognostic equations, and a diagnostic equation for streamfunction through a vorticity inversion.

The invertibility of vorticity allows the development of a gravity wave kernel view, which provides a mechanistic rationalization of many aspects of the linear dynamics of stratified shear flow. The resulting kernel formulation is similar to the Rossby-based one obtained for barotropic and baroclinic instability; however, since there are two independent variables—vorticity and buoyancy—there are also two independent kernels at each level. Though having two kernels complicates the picture, the kernels are constructed so that they do not interact with each other at a given level.

Corresponding author address: Nili Harnik, Dept. of Geophysics and Planetary Sciences, Tel Aviv University, P.O. Box 39040, Tel Aviv 69978, Israel. Email: harnik@tau.ac.il

Abstract

Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integration of the quasigeostrophic equations with two, rather than one, prognostic equations, and a diagnostic equation for streamfunction through a vorticity inversion.

The invertibility of vorticity allows the development of a gravity wave kernel view, which provides a mechanistic rationalization of many aspects of the linear dynamics of stratified shear flow. The resulting kernel formulation is similar to the Rossby-based one obtained for barotropic and baroclinic instability; however, since there are two independent variables—vorticity and buoyancy—there are also two independent kernels at each level. Though having two kernels complicates the picture, the kernels are constructed so that they do not interact with each other at a given level.

Corresponding author address: Nili Harnik, Dept. of Geophysics and Planetary Sciences, Tel Aviv University, P.O. Box 39040, Tel Aviv 69978, Israel. Email: harnik@tau.ac.il

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