The frontogenetical forcing of secondary circulations. Part I: the duality and generalization of the Q vector

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. -from Author