Diagnosing balance in rotating stratied turbulence

Towards understanding the motion of the Earths atmosphere and oceans many studies have tried to nd simplifying concepts which are central to these ows. One such concept which applies to rotating stably-stratied geophysical ows is that of "balance " (see [4] and [1]). Put simply a balanced ow is one where the dynamics of the ow are controlled solely by the "potential vorticity " (PV), a materially conserved quantity. Balance holds to a high degree for intermediate to large scale uid motions in the Earth's atmosphere and oceans where motions tend to be weak compared to the background planetary rotation (small Rossby number Ro 1) and the stable density stratication (small Froude number Fr 1) greatly inhibits vertical motion. However balance does not hold absolutely, there does exist motions due to inertia-gravity waves (IGWs). These waves can be spontaneously emitted during the ow evolution and represent a departure from the leading order balance, or in other words the "imbalance". For a long time it has been recognised that geophysical ows remain close to balance, but because balance has no precise mathematical denition, there was no rigorous way of sep-arating a general nonlinear uid ow into its balanced and unbalanced parts. Recently, thi