Accessibility navigation


Nonlinear saturation of baroclinic instability: part III: bounds on the energy

Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1993) Nonlinear saturation of baroclinic instability: part III: bounds on the energy. Journal of the Atmospheric Sciences, 50 (16). pp. 2697-2709. ISSN 0022-4928

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

928kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1175/1520-0469(1993)050<2697:NSOBIP>2.0.CO;2

Abstract/Summary

Rigorous upper bounds are derived on the saturation amplitude of baroclinic instability in the two-layer model. The bounds apply to the eddy energy and are obtained by appealing to a finite amplitude conservation law for the disturbance pseudoenergy. These bounds are to be distinguished from those derived in Part I of this study, which employed a pseudomomentum conservation law and provided bounds on the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. Bounds on the eddy energy are worked out for a general class of unstable westerly jets. In the special case of the Phillips model of baroclinic instability, and in the limit of infinitesimal initial eddy amplitude, the bound states that the eddy energy cannot exceed ϵβ2/6F where ϵ = (U − Ucrit)/Ucrit is the relative supercriticality. This bound captures the essential dynamical scalings (i.e., the dependence on ϵ, β, and F) of the saturation amplitudes predicted by weakly nonlinear theory, as well as exhibiting remarkable quantitative agreement with those predictions, and is also consistent with heuristic baroclinic adjustment estimates.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:32904

Downloads

Downloads per month over past year

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

Page navigation