The Mathematical Theory of Frontogenesis

Abstract

For over one hundred years it has been known that atmospheric depressions have cold frontal regions in which typically the temperature falls rapidly, the wind changes, and precipitation occurs. Sixty years ago Norwegian meteorologists shaped their polar front model in which depressions were considered to grow on a preexisting sloping thermal discontinuity; as the depressions grew it was considered that they distorted the discontinuity into a cold front and also a warm front. The dynamical view changed thirty years ago with the discovery by Charney (1947) and Eady (1949) that realistic depression structures may be obtained as the normal modes of the baroclinic instability of a smooth rather than discontinuous thermal contrast. Fronts then had to be viewed as being formed in a growing nonlinear baroclinic wave, though this secondary role in no way diminished their importance in practical meteorology. The theoretical interest shifted towards the mechanism for generating fronts, namely frontogenesis. When upper air data became available in the 1950s it was apparent that strong frontal regions occurred in the upper troposphere as well as near the surface. Many studies (e.g. Reed & Danielsen 1959) suggested strongly that these upper air fronts are associated with the descent of a tongue of stratospheric air into the troposphere. The existence of fronts in the ocean has been known for many years and when vertical sections were obtained (e.g. Voorhis & Hersey 1964 and Katz 1969) they suggested many structural similarities with atmospheric fronts. Further, the experimental work of Fultz (1952) and Faller ( 1956) has shown that fronts can be reproduced in laboratory experiments using differentially heated rotating water. Thus we conclude that details of latent·heat release and other diabatic heating, and of the boundary layer