Nonlinear stability of multilayer quasi-geostrophic flow

Mu, M., Qingcun, Z., Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 and Yongming, L. (1994) Nonlinear stability of multilayer quasi-geostrophic flow. Journal Of Fluid Mechanics, 264. pp. 165-184. ISSN 0022-1120 doi: 10.1017/S0022112094000625

Abstract/Summary

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/32901
Identification Number/DOI	10.1017/S0022112094000625
Refereed	Yes
Divisions	No Reading authors. Back catalogue items Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Cambridge University Press
Download/View statistics	View download statistics for this item