The Development of Tropopause Folds in Two-Dimensional Models of Frontogenesis

Abstract

The geostrophic momentum approximation will be employed to investigate the mechanism of tropopause folding that occurs within upper-level fronts formed by the action of a stretching deformation field in a nonuniform potential vorticity fluid. The tropopause, in such a fluid, is represented by a shallow layer in which there is a large change in the potential vorticity. A fold is defined as a region in which the mean tropopause height is a multiple-valued function of the cross-front coordinate. Observational studies have demonstrated that tropopause folds form during frontogenesis as a result of the penetration of stratospheric air down into the troposphere. Earlier studies of this phenomena within the context of semigeostrophic theory have been hampered by the fact that the surface fronts collapse before the upper-level fronts have had a chance to develop. In order to get around this difficulty, previous studies have relied upon unrealistic cross-front temperature gradients, nascent folds, or both to generate any appreciable development at upper levels. In this paper, a different approach is used. It will be shown that the introduction of a cross-front gradient in the potential vorticity field allows one to specify an isentropic lower boundary condition. This allows one to study the frontogenetic processes active in the vicinity of the tropopause in isolation from those active near the surface. As frontogenesis proceeds in such a fluid, deep folds are indeed observed to develop. The structure and evolution of the folds will be shown to be similar to that of observed cases.