Equilibrium statistical predictions for baroclinic vortices: The role of angular momentum

Mark T. Dibattista, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

We develop a point-vortex equilibrium statistical model for baroclinic quasigeostrophic vortices within the context of a two-layer quasigeostrophic fluid that evolves in all of space. Angular momentum, which follows from the rotational symmetry of the unbounded domain, is the key conserved quantity, introducing a length scale that confines the most probable states of the statistical theory. We apply the theory as a model of localized convection in a preconditioned gyre. To illustrate this application, the preconditioned cyclonic, largely barotropic gyres are modeled as "zero inverse temperature" states, which are explicit solutions to the mean-field equations with a Gaussian probability distribution of vortices. Convection is modeled by a cloud of point-vortex hetons - purely baroclinic arrangements of point vortices, cyclonic above and anticyclonic below - which capture the short-term, geostrophically balanced response to strong surface cooling. Numerical heton studies (Legg and Marshall, 1993, 1998) have shown that a preexisting barotropic rim current can suppress baroclinic instability and confine anomalies of potential vorticity and temperature introduced by the cold-air outbreak. Here, we demonstrate that the lateral extent of the most probable states of the statistical theory are constrained by the angular momentum. Without resolution of the detailed dynamics, the equilibrium statistical theory predicts that baroclinic instability is suppressed for preconditioned flows with potential vorticity of the same sign in each layer provided that the strength of convective overturning does not change the sign of potential vorticity in one of the layers. This result agrees with detailed simulations (Legg and Marshall, 1998) and supports the potential use of these statistical theories as parametrizations for crude closure.

Original languageEnglish (US)
Pages (from-to)293-322
Number of pages30
JournalTheoretical and Computational Fluid Dynamics
Volume14
Issue number5
DOIs
StatePublished - 2001

Fingerprint

Angular momentum
Vortex flow
angular momentum
vortices
Vorticity
baroclinic instability
vorticity
predictions
convection
gyres
surface cooling
rims
Probability distributions
closures
anomalies
Cooling
Temperature
Fluids
temperature
fluids

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Equilibrium statistical predictions for baroclinic vortices : The role of angular momentum. / Dibattista, Mark T.; Majda, Andrew J.

In: Theoretical and Computational Fluid Dynamics, Vol. 14, No. 5, 2001, p. 293-322.

Research output: Contribution to journalArticle

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