### Abstract

An expression is derived for the quasi-horizontal part of the mass transport across a given potential vorticity contour on an isentropic surface, in terms of the rate of change of absolute circulation around the contour and frictional and diabatic terms on the contour. It is deduced that this mass transport is small if the circulation around the contour of interest is steady and if frictional forces and diabatic effects can be neglected on the contour. In a single-layer model the corresponding result is that the total mass transport is zero. In a three-dimensional model the implication is that the dominant mass transport across a vortex edge that tilts in the vertical occurs through vertical advection. It is argued that these constraints on the mass transport are relevant to the estimation of transport across the edge of the stratospheric polar vortex, and the relationship to other similar results that have appeared recently in the literature is discussed. In addition, a new expression is derived for the total mass flux across a three-dimensional surface whose intersection with each isentropic surface is a potential vorticity contour. This expression generalizes previous results that were confined to steady flows and hydrostatic scaling.

Original language | English (US) |
---|---|

Pages (from-to) | 942-947 |

Number of pages | 6 |

Journal | Journal of the Atmospheric Sciences |

Volume | 56 |

Issue number | 7 |

State | Published - Apr 1 1999 |

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### ASJC Scopus subject areas

- Atmospheric Science

### Cite this

*Journal of the Atmospheric Sciences*,

*56*(7), 942-947.

**Constraints on the mean mass transport across potential vorticity contours.** / Buhler, Oliver; Haynes, Peter H.

Research output: Contribution to journal › Article

*Journal of the Atmospheric Sciences*, vol. 56, no. 7, pp. 942-947.

}

TY - JOUR

T1 - Constraints on the mean mass transport across potential vorticity contours

AU - Buhler, Oliver

AU - Haynes, Peter H.

PY - 1999/4/1

Y1 - 1999/4/1

N2 - An expression is derived for the quasi-horizontal part of the mass transport across a given potential vorticity contour on an isentropic surface, in terms of the rate of change of absolute circulation around the contour and frictional and diabatic terms on the contour. It is deduced that this mass transport is small if the circulation around the contour of interest is steady and if frictional forces and diabatic effects can be neglected on the contour. In a single-layer model the corresponding result is that the total mass transport is zero. In a three-dimensional model the implication is that the dominant mass transport across a vortex edge that tilts in the vertical occurs through vertical advection. It is argued that these constraints on the mass transport are relevant to the estimation of transport across the edge of the stratospheric polar vortex, and the relationship to other similar results that have appeared recently in the literature is discussed. In addition, a new expression is derived for the total mass flux across a three-dimensional surface whose intersection with each isentropic surface is a potential vorticity contour. This expression generalizes previous results that were confined to steady flows and hydrostatic scaling.

AB - An expression is derived for the quasi-horizontal part of the mass transport across a given potential vorticity contour on an isentropic surface, in terms of the rate of change of absolute circulation around the contour and frictional and diabatic terms on the contour. It is deduced that this mass transport is small if the circulation around the contour of interest is steady and if frictional forces and diabatic effects can be neglected on the contour. In a single-layer model the corresponding result is that the total mass transport is zero. In a three-dimensional model the implication is that the dominant mass transport across a vortex edge that tilts in the vertical occurs through vertical advection. It is argued that these constraints on the mass transport are relevant to the estimation of transport across the edge of the stratospheric polar vortex, and the relationship to other similar results that have appeared recently in the literature is discussed. In addition, a new expression is derived for the total mass flux across a three-dimensional surface whose intersection with each isentropic surface is a potential vorticity contour. This expression generalizes previous results that were confined to steady flows and hydrostatic scaling.

UR - http://www.scopus.com/inward/record.url?scp=18844468628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18844468628&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18844468628

VL - 56

SP - 942

EP - 947

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 7

ER -