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2005, 2005(Special): 611-620. doi: 10.3934/proc.2005.2005.611

Variational analysis of energy-enstrophy theories on the sphere

Chjan C. Lim 1, and  Da Zhu 1,

1. 

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States, United States

Received  September 2004 Revised  April 2005 Published  September 2005

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.
Keywords: unboundedness., energy-enstrophy, variational analysis.
Mathematics Subject Classification: Primary: 76B47, 82B20; Secondary: 65C0.
Citation: Chjan C. Lim, Da Zhu. Variational analysis of energy-enstrophy theories on the sphere. Conference Publications, 2005, 2005 (Special) : 611-620. doi: 10.3934/proc.2005.2005.611
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