Abstract
Mathematical understanding of the rotating stratified flows observed in the atmosphere is aided by analysing the properties of equations which represent asymptotic limits of the Navier-Stokes equations for small Rossby and/or Froude numbers. Progress is described on a model of almost axisymmetric flow introduced by Craig (Quart. J. Roy. Meteor. Soc., 1991). This model can be written as a mass transportation model in the radial direction together with a wave equation in the azimuthal direction. The main difficulty in formulation is to ensure well-posedness of the boundary conditions, so that the vortex can retain its identity. Essentially the same equations can be derived as a model of long waves in the tropics, Gill (1980), Majda (2003). It appears that there is a good chance of proving short-time existence of solutions, but long-time existence looks unlikely.