A Technique for Representing Three-Dimensional Vertical Circulations in Baroclinic Disturbances

Abstract

The problem of representing vertical circulations in frontal zones is reexamined with the objective of devising a methodology sufficiently general to apply in situations where these circulations are no longer confined to the cross-front (transverse) vertical plane and therefore must be viewed as fully dimensional. The proposed methodology, which builds upon the earlier work of Hoskins and Draghici and of Eliassen, consists of adopting a vector streamfunction that describes the vertical velocity and the horizontal irrotational flow. This generalized streamfunction, referred to as the psi vector, may be determined uniquely from the vertical velocity field over a limited region provided that suitable lateral boundary conditions on the velocity potential for the irrotational part of the horizontal velocity can be specified. A key property of the psi vector is that its projections onto arbitrary orthogonal vertical planes yield two independent vertical circulations, providing an objective means for separating a three-dimensional vertical circulation into cross- and alongfront components. The psi-vector methodology is applied to surface and upper-level frontal zones simulated in an f plane primitive equation channel model of a finite-amplitude baroclinic wave in which all diabatic and frictional influences are neglected except for horizontal diffusion. Both along and cross-front vertical circulations are diagnosed and interpreted for upper-level frontal zones associated with jet streams and jet streaks situated within curved flowed and for surface fronts possessing attributes of observed warm and cold fronts. In all of these frontal systems, the transverse vertical circulation is dominant in the sense that the cross-front component of the vertical velocity is larger in magnitude than the corresponding alongfront component. The lateral scale of the cross-front circulation is of a frontal dimension, whereas the scale of the alongfront circulation is characteristic of the baroclinic wave. The orientations of the cross-front circulations relative to the respective frontal zones are broadly consistent with those discussed in earlier two-dimensional models. These findings support interpretations 1) that three- dimensional vertical circulations in midiatitude cyclones may be viewed conceptually as a superposition of vertical circulations associated with the baroclinic wave and with the embedded fronts, and 2) that confluence and horizontal shear forcing mechanisms, although strictly applicable to two-dimensional frontogenesis models, may carry over to describe transverse vertical circulations in three-dimensional systems.