Detailed description of deformation‐induced semi‐geostrophic frontogenesis

A variant of the classical deformation‐induced surface frontogenesis problem is studied in the semigeostrophic limit. The particular flow system examined is the response of a baroclinic, semi‐infinite, stratified, uniform potential vorticity atmosphere to an imposed deformation flow field. This flow system permits the derivation of: a class of simple analytical solutions in geostrophic space; an explicit functional solution of the Sawyer‐Eliassen ageostrophic circulation equation; and a self‐contained nonlinear equation in real space for the surface development of the along‐front wind component. The derived relationships are utilized to examine various frontogenetic aspects of this model system. These include the time scale of frontal development, the co‐occurrence of different frontal types, the slope and movement of frontal features, the structure and strength of the ageostrophic circulation, and the degree of validity of the semi‐geostrophic approximation.