Paper

Towards the Understanding of Turbulence


Authors:
Woon Siong Gan
Abstract
In a previous paper, the author proposed turbulence as a second order phase transition with spontaneous broken symmetry. This has been experimentally confirmed by research groups from the University of Illinois and Weizemann Institute of Science. In this paper we propose turbulence as a classical analog of Bose Einstein condensate and the Gross-Pitaevskii equation is used to derive the condensation free energy. The critical value of the order parameter, the condensation wave function is determined. This is the value where turbulence occurs and spontaneous symmetry breaking in the ground state of the condensation free energy takes place. Being a condensate, there is molecular pairing in turbulence. We determine the numerical value of the condensation free energy with the use of the coupled oscillation model for the pair of molecules. Our expression for the condensation free energy also yields a power series in terms of the order parameter in agreement with the Landau phenomenology of second order phase transition. This confirms that turbulence is a condensate since Gross-Pitaevskii equation is the equation for condensate. We conclude that our understanding of turbulence is a second order phase transition and is a condensate with molecular pairing.
Keywords
Second Order Phase Transition; Spontaneous Symmetry Breaking; Condensate; Gross-Pitaesvkii Equation; Condensation Wave Function; Condensation Free Energy; Order Parameter; Molecular Pairing; Coupled Oscillation
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1
EndPage
9
Doi
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