NUS

Chjan C. Lim

Laboratory for Turbulence Research

The Energy-Enstrophy Model

System on the Sphere

These results were obtained using a Monte Carlo algorithm on an energy-enstrophy statistical equilibrium model for quasi-two dimensional turbulence on a sphere at negative temperatures. The lower-right figure compares the Monte Carlo simulation vorticity distribution (with respect to latitude) to the exact vorticity distribution for a rigidly rotating layer of fluid on the sphere.

System Parameters:

Beta (inverse temperature): -100,000 Mu (chemical potential for enstrophy): 1 Maximum site change per flip: 0.2 Random number seed: time of day
Enstrophy unconstrained Site values unconstrained Circulation: 0 Initial enstrophy: 100
Initial State of Absolute Vorticity
Red represents positive vorticity;
blue represents negative vorticity. 		Final State of Rigid Body Rotation
Red represents positive vorticity;
blue represents negative vorticity.
Solid Body Rotation Banded Body Rotation
Dirichlet Quotient versus Sweep,
Solid Body and Wavy Banded Rotations
(The Dirichlet quotient is enstrophy over energy.) 		Plot of Rigid Body Rotation Vorticity,
Numerical versus Theoretical Vorticities
Dirichlet Quotients of the solid and wavy banded modes Solid body rotation vorticity, numerical and theoretical results

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Last updated 26 November 2001.

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