Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Fruman, M. D. and Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (2008) Symmetric stability of compressible zonal flows on a generalized equatorial β plane. Journal of the Atmospheric Sciences, 65 (6). pp. 1927-1940. ISSN 0022-4928 doi: 10.1175/2007JAS2582.1

Abstract/Summary

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/32038
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	Planetary waves, Atmospheric circulation, Angular momentum, Potential vorticity
Publisher	American Meteorological Society
Download/View statistics	View download statistics for this item