The Effect of Along-front Temperature Variation in a Two-Dimensional Primitive Equation Model of Surface Frontogenesis

Abstract

The development of frontal zones is examined in a two-dimensional primitive equation model of frontogenesis formulated for dry, nearly adiabatic and inviscid conditions. The model results are interpreted in the context of the general problem of determining the dynamical properties of cold and warm fronts. The central hypothesis (attributable to Eliassen) is that cold and warm fronts may be distinguished by the orientation of the cross-front thermal wind component and the sense of the associated along-front temperature variation. Three simulations comprising confluent forcing (geostrophic contraction in the cross-front direction) and differing initial specifications of the along-front potential temperature gradient are examined in detail. In the first simulation, referred to as the pure confluence case, the along-front potential temperature gradient is set to zero, establishing a control for specifying along-front potential temperature variations respectively characteristic of cold and warm fronts in the latter two simulations. These simulations are referred to as the cold and warm advection cases, reflecting the initial sense of the potential temperature advection in the along-front direction at low levels in the model atmosphere. Whereas the frontal zone in the pure confluence case is relatively shallow, the frontal zone in the cold advection case is better defined and occupies a deeper extent of the lower troposphere. The associated transverse ageostrophic circulations are centered within the frontal zones and are thermodynamically direct in both cases, but the circulation is significantly stronger in the cold advection case. The frontal zone in the warm advection case is quite shallow and the associated cross-front potential temperature gradient is rather weak, although the low-level vorticity and convergence are well defined. In contrast to the previous two cases, the vertical circulation, although thermodynamically direct, is centered sufficiently far into the cold air for the upward branch to be situated in the baroclinic region within and to the cold side of the surface frontal zone. A comparative analysis of the evolution of the three frontal zones performed with the prognostic equations for cross-front potential temperature gradient and relative vorticity and with diagnostic equations for the vertical circulation leads to the identification of frontogenetical feedbacks involving the convergence field and its dynamical forcing. This analysis further reveals frontogenetical and frontolytical roles for along-front potential temperature variations respectively characteristic of the cold and warm advection cases, a consequence of the correspondence of the frontal zones with regions of cyclonic relative vorticity. Evidence is presented to support the contention that the basic frontal structures identified in the three simulations are compatible with recent classifications of frontal features found in idealized three-dimensional simulations of the evolution of baroclinic waves to finite amplitude. This proposed compatibility suggests that the two-dimensional model formulation considered in this study may be capable of abstracting essential dynamical properties of the frontogenetical environment associated with growing baroclinic disturbances in idealized three-dimensional models and perhaps in nature.