Kraichnan's energy-enstrophy theory for 2D inviscid flows on the sphere is discussed within
a variational framework. We will give necessary and sufficient conditions for the existence
and uniqueness for the extremals of the energy with zero circulation under different values of
the temperature parameter β. The unboundedness of the augmented energy functional in
this model when β is located in the certain intervals will be shown and related to energy
catastrophe of the energy-enstrophy model. 1. Introduction. The energy-enstrophy theory of …