We briefly describe the morning glory, using this as background and motivation for the presentation that follows. The analysis starts from the general equations for a viscous, compressible fluid written in rotating, spherical coordinates. These are non-dimensionalised and the thin-shell parameter (ε) is introduced. The resulting equations constitute a general description of the atmosphere in motion, with the important elements of the spherical geometry retained, thereby laying the foundations for a careful asymptotic development.
As a specific example of the use of these equations, the wave perturbation of the background state of the atmosphere is considered, the wave propagating in an arbitrary (horizontal) direction, described by variables suitably scaled with respect to ε. It is shown that, at O(ε^2), we obtain the leading-order equation that controls the velocity field associated with the wave; this is nonlinear, dispersive and diffusive. Some properties of this equation are described – we cannot solve it in any general sense – and related to the observed structure of the morning glory. An example (in graphical form) of a relevant solution is presented.