Linear Development of Quasi-Geostrophic Baroclinic Disturbances with Condensational Heating

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  • 1 Department of the Geophysical Sciences, The University of Chicago, Chicago, IL 60637
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Abstract

This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave–CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem.

Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. For sufficiently large values of the heating amplitude, the free modes display unphysical behavior with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave–CISK disturbances exist on the f-plane.

The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favorably to observations of intermediate scale disturbances on the Baiu front.

The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.

Abstract

This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave–CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem.

Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. For sufficiently large values of the heating amplitude, the free modes display unphysical behavior with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave–CISK disturbances exist on the f-plane.

The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favorably to observations of intermediate scale disturbances on the Baiu front.

The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.

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