The Frontogenetical Forcing of Secondary Circulations. Part I: The Duality and Generalization of theQVector

Abstract

Abstract Hoskins, Draghici, and others have shown that the Q vector is an important quantity in quasi-geostrophic (QG) theory for the diagnosis of ageostrophic circulations. In this paper, a vorticity dynamics perspective is used to develop a generalized Q vector, Q*. An equation that relates the material derivative of the thermal-wind imbalance vector to Q* and ageostrophic terms in isentropic flow is obtained from the primitive equations (PE). The generalized Q vector is the vector mean of two terms: a frontogenetical vector that, for horizontal isentropic flow, is equal to the vector frontogenesis function F, and a vortex stretching term proportional to the stretching and reorientation of vorticity by the horizontal wind. Invoking just one QG assumption, the substitution of geostrophic for total velocity gradients, reduces Q* to Q and leads directly to the omega equation of QG theory. The frontogenetical and vortex stretching parts of the generalized Q vector of PE theory become equal in the QG limit. ...