Nongeostrophic Corrections to the Eigensolutions of a Moist Baroclinic Instability Problem

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

The analysis of Emanuel et al. is repeated for the linearized primitive equations. The consideration of the Rossby number is shown to reduce growth rates and increase the width of updrafts. The singularity exhibited by the semigeostrophic equations in the limit qe → 0 is moved to N2 → 0. The result of a vanishing width of the updraft persists in the latter limit and it is shown to be a consequence of the hydrostatic approximation. The value qe = 0 in the updraft is still used as representative of slantwise convective adjustment, but the relevant stability parameter for baroclinic waves is now the Brunt–Väisälä frequency and not the potential vorticity. Their difference is o(Ro2), so that the PE contributions become dominant when (qe/qd) ≲ o(Ro2). The eddy fluxes of heat in the limit of a symmetrically neutral environment are compared with the results for dry baro-clinic waves.

Abstract

The analysis of Emanuel et al. is repeated for the linearized primitive equations. The consideration of the Rossby number is shown to reduce growth rates and increase the width of updrafts. The singularity exhibited by the semigeostrophic equations in the limit qe → 0 is moved to N2 → 0. The result of a vanishing width of the updraft persists in the latter limit and it is shown to be a consequence of the hydrostatic approximation. The value qe = 0 in the updraft is still used as representative of slantwise convective adjustment, but the relevant stability parameter for baroclinic waves is now the Brunt–Väisälä frequency and not the potential vorticity. Their difference is o(Ro2), so that the PE contributions become dominant when (qe/qd) ≲ o(Ro2). The eddy fluxes of heat in the limit of a symmetrically neutral environment are compared with the results for dry baro-clinic waves.

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