Abstract: This paper is concerned with the fundamental role played by contact transformations and their corresponding generating functions in determining the structure and dynamical properties of a very general class of semigeostrophic ...

Abstract: For semigeostrophic (SG) theories derived from the Hamiltonian principles suggested by Salmon it is known that a duality exists between the physical coordinates and geopotential, on the one hand, and isentropic geostrophic ...

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 ...

Abstract: An efficient method is proposed for performing the grid interpolations required at each advective time step of a multilevel, limited-area semi-Lagrangian model. The distinctive feature of the method is that it is composed ...

Abstract: Having recently demonstrated that significant enhancement of forecast accuracy in a semi-Lagrangian model results from the application of high-order time integration methods to the second-derivative form of the equations ...

Abstract: It is shown both in theory and in practice that the accuracy of time-split finite-difference methods may be increased by the very simple device of incrementally adding a portion of the advection term in the adjustment step ...

Abstract: Traditional finite-difference numerical forecast models usually employ relatively low-order approximations on grids staggered in both the horizontal and the vertical. In a previous study, Purser and Leslie (1988) demonstrated ...

Abstract: The Lagrangian conservation law form of the semi-geostrophic equations used by Hoskins and others is studied further in two and three dimensions. A solution of the inviscid equations containing discontinuities corresponding ...