Dual Variables in Semigeostrophic Theory
Abstract
This paper is a study of the duality structure present in the semigeostrophic equations of meterology. We explore a new viewpoint, represented by Legendre transformations between alternative choices of independent variables, including space coordinates, geostrophic coordinates and isentropic coordinates. Detailed examples are given, for both uniform and nonuniform potential vorticity, of the modelling of an atmospheric front at a given time in stable flow. In each case the front is a halfline of gradient discontinuity on a continuous convex surface, obtained as the selfintersection on a swallowtail surface, after the latter is convexified so that nonphysical multivaluedness is removed.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 July 1989
 DOI:
 10.1098/rspa.1989.0074
 Bibcode:
 1989RSPSA.424..155C