Diagnosis of the role of vertical deformation in a two-dimensional primitive equation model of upper-level frontogenesis

In the present equations for the temporal rates of change of the magnitudes of potential temperature and absolute momentum vector gradients that are projected onto vertical planes transverse to straight frontal zones, the terms involving the transverse ageostrophic circulation are of the same mathematical form, and in a kinematic sense are also analogous to, the divergence and deformation terms that involve the horizontal wind field in Pettersen's (1936) classic equation for frontogenesis in the potential temperature field. The proposed frontogenesis equation form for the magnitude of the potential temperature gradient in the transverse plane is illustrated with the results of two simulations from an idealized, two-dimensional primitive equation model in which upper level frontogenesis proceeds by very different mechanisms.