Diagnosis of Ageostrophic Circulations in a Two-Dimensional Primitive Equation Model of Frontogenesis

Abstract

Diagnoses are presented of the transverse ageostrophic circulation patterns for two cases from a two-dimensional primitive equation model of frontogenesis forced by a combination of confluence and horizontal shear. The cold advection case (the specified alongfront potential temperature gradient results in differential cold advection by the upper-level jet) realistically simulates upper-level frontogenesis in response to tilting by a cross-front gradient of subsidence. The warm advection case features a frontal system spanning the troposphere, which develops in response to differential horizontal advection. The diagnoses are performed by numerically solving three versions of the two-dimensional Sawyer?Eliassen equation for the streamfunction of the transverse ageostrophic circulation. The quasi-geostrophic (QG) and geostrophic momentum (GM) versions are based on the approximation of cross-front geostrophic balance, while the primitive equation (PE) version includes the possibility of an alongfront component of the ageostrophic flow, which is nondivergent. The PE version reduces to the GM version if the alongtront ageostrophic wind component is neglected. The QG, GM, and PE transverse ageostrophic circulations are compared for the cold and warm advection cases, which are characterized respectively by relatively large and small cross-front geostrophic imbalances. Consequently, the QG and GM circulations underestimate the PE circulation in the cold advection case, and the GM circulation is extremely close to its PE counterpart in the warm advection case. The transverse ageostrophic circulation is then partitioned into components forced by geostrophic confluence and horizontal shear and effects associated with the alongfront ageostrophic flow. In the cold advection case, the latter two forcing mechanisms are shown to be responsible for the frontogenetical midtropospheric configuration of subsidence, which is maximized within and to the warm side of the developing frontal zone. The partitioned ageostrophic circulations also clarify feedback mechanisms in the cold advection case involving the subsidence and upper-level vorticity fields, and involving the transverse ageostrophic circulation and the alongfront ageostrophic flow pattern. Finally, the GM partitioning of the ageostrophic circulation provides a basis for deriving frontogenesis equations for the vorticity and cross-front potential temperature gradient in terms of the net effect of the forcing and response respectively associated with geostrophic confluence and horizontal shear and alongfront ageostrophic flow. The application of these equations to the diagnosis of upper-level frontogenesis in the cold advection case provides an illustrative example.