ON BAROCLINIC INSTABILITY AS A FUNCTION OF THE VERTICAL PROFILE OF THE ZONAL WIND

A. WIIN-NIELSEN Department of Meteorology and Oceanography, University of Michigan, Ann Arbor, Mich.

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Abstract

The quasi-geostrophic, baroclinic stability problem is solved for an arbitrary zonal wind profile U = U(p) and for an adiabatic lapse rate. It is shown that the phase speed of the waves in this case depends on the vertical integrals of U and U2. Due to the assumption of an adiabatic stratification there is no short wave cutoff, but the effect of the variation of the Coriolis parameter will in all cases give stability for sufficiently long waves.

A number of numerical examples show that the region of instability, in a coordinate system with wavelength as abscissa and wind shear as ordinate, is the largest when the wind maximum is situated in the upper part of the atmosphere, and when the curvature of the zonal wind profile at the wind maximum has an intermediate value.

Abstract

The quasi-geostrophic, baroclinic stability problem is solved for an arbitrary zonal wind profile U = U(p) and for an adiabatic lapse rate. It is shown that the phase speed of the waves in this case depends on the vertical integrals of U and U2. Due to the assumption of an adiabatic stratification there is no short wave cutoff, but the effect of the variation of the Coriolis parameter will in all cases give stability for sufficiently long waves.

A number of numerical examples show that the region of instability, in a coordinate system with wavelength as abscissa and wind shear as ordinate, is the largest when the wind maximum is situated in the upper part of the atmosphere, and when the curvature of the zonal wind profile at the wind maximum has an intermediate value.

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