Properties of the Lagrangian semigeostrophic equations

Abstract

The Lagrangian form of the semigeostrophic equations has been shown to possess discontinuous solutions that have been exploited as a simple model of fronts and other mesoscale flows. In this paper, it is shown that these equations can be integrated forward in time for arbitrarily long periods without breaking down, to give a "slow manifold' of solutions. In the absence of moisture, orography and surface friction, these solutions conserve energy, despite the appearance of discontinuities. This paper shows that there is a unique solution to the equations with general piecewise smooth data, to which the finite parcel approximation converges. -from Authors