NCAR TOY - February 2008
22
The leading order conservation laws in the absence of dissipation,
Using the same arguments as Embid and Majda, 1997, there is conservation in time of the slow to fast energy ratio. This means the total energy conservation is composed of both slow and fast dynamics.
But the leading order potential enstrophy is composed only of the slow dynamics.
This is an argument about the slow and fast being orthogonal and the fast operator conserving energy.