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Variational analysis of energy-enstrophy theories on the sphere

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  • 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 $\beta$. The unboundedness of the augmented energy functional in this model when $\beta$ is located in the certain intervals will be shown and related to energy catastrophe of the energy-enstrophy model.
    Mathematics Subject Classification: Primary: 76B47, 82B20; Secondary: 65C05.


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