### 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 language | English (US) |
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Pages (from-to) | 293-322 |

Number of pages | 30 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 14 |

Issue number | 5 |

DOIs | |

State | Published - 2001 |

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### 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.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 14, no. 5, pp. 293-322. https://doi.org/10.1007/s001620050142

}

TY - JOUR

T1 - Equilibrium statistical predictions for baroclinic vortices

T2 - The role of angular momentum

AU - Dibattista, Mark T.

AU - Majda, Andrew J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

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U2 - 10.1007/s001620050142

DO - 10.1007/s001620050142

M3 - Article

AN - SCOPUS:0035531558

VL - 14

SP - 293

EP - 322

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 5

ER -