Accessibility navigation


Nonlinear saturation of baroclinic instability: part I: the two-layer model

Downloads

Downloads per month over past year

Shepherd, T. G. (1988) Nonlinear saturation of baroclinic instability: part I: the two-layer model. Journal of the Atmospheric Sciences, 45 (14). pp. 2014-2025. ISSN 1520-0469

[img]
Preview
Text - Published Version
· Please see our End User Agreement before downloading.

917Kb

To link to this article DOI: 10.1175/1520-0469(1988)045<2014:NSOBIP>2.0.CO;2

Abstract/Summary

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
ID Code:32906
Publisher:American Meteorological Society

Download Statistics for this item.

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation