Three‐dimensional baroclinic instability and summertime frontogenesis in the Australian region

The structure of a mature three‐dimensional baroclinic wave and its attendant cold front is examined using an idealized numerical model with a simple parametrization of dry buoyant convection resulting from diurnal heating. Relative‐flow isentropic analyses of the numerical solution and of an observed Australian summertime frontal system are compared. It is shown that the model well represents the typical synoptic environment accompanying frontogenesis in the Australian region. A diagnosis of the three‐dimensional vertical circulation is obtained using a technique involving a vector streamfunction. The circulation in a cross‐sectional plane parallel with the low‐level temperature gradient is found to be highly two‐dimensional, with geostrophic confluence constituting the principal frontogenetical forcing at low levels, while at upper levels the frontogentical forcing is dominated by geostrophic horizontal shear. In a second cross‐section, taken zonally, the frontogenetic forcing is found to consist almost solely of geostrophic horizontal shear throughout the entire troposphere. However, in this case the circulation in the plane of cross‐section is found to be only qualitatively two‐dimensional, as a significant proportion of the low‐level postfrontal subsidence is associated with circulation normal to the cross‐section. It is shown that the frontal structure analysed is sensitive to the location of the chosen cross‐sectional plane, and that this in turn provides an explanation for the observed relative shallowness of Australian summertime fronts. The effects of diurnal heating are important but confined to the surface‐based mixed layer. With the addition of diurnal heating, the prefrontal updraught amplifies almost threefold and the frontal temperature contrast over the heated region approximately doubles. The diabatic forcing term in the well‐known Sawyer‐Eliassen equation is shown to be negligible. This suggests that the increased low‐level convergence is a reflection of the model's enhanced response to frontogenetic forcing in the presence of low static stability in the surface‐based well‐mixed layer. Finally, the numerical model solution is compared with a simpler two‐dimensional model specifically developed to study Australian summertime fronts.