The global quasigeostrophic approximation in shallow water

It is often said that the quasigeostrophic approximation does far better than it should, meaning that it can often be usefully applied in situations where the conditions assumed in its derivation are poorly satisfied. We will consider how far this statement can be pushed by comparing the full and the approximate dynamics in a simple but geophysically relevant flow in which two of the usual conditions underlying the approximation, small Rossby number and limited latitudinal extent, are clearly violated. The comparison was developed while teaching the quasigeostrophic approximation in the Geophysical Fluid Dynamics course at the University of St Andrews.