Chjan C. Lim

Laboratory for Turbulence Research

Joseph Nebus

Monte Carlo Simulations, Statistical Mechanics, and Ground States of the Logarithmic Potential, 2002

Department of Computational Science, National University of Singapore

Sponsors

National University of Singapore

Office of Research and Graduate Studies

The Faculty of Science, National University of Singapore

Dean's Office

Department of Computational Science, National University of Singapore

Research Grants

R-151-000-015-112

R-151-000-024-112

Amount for two years, Singapore $62,000.00

Used to support Joseph Nebus as a research assistant at the National University of Singapore.

Statistical Physics and Turbulence

• Exactly-solvable models in 2D turbulence -- a long range spherical model for energy-enstrophy theories.
• First principles derivation of energy spectra for 2D turbulence and random matrices.

Statistical Physics and Turbulence

• Coherent structures in an energy-enstrophy theory for axisymmetric flows
  Physics of Fluids 15, 478 - 487 (2003)
  xdvi format | Postscript format | PDF format
• Monte-Carlo and Polyhedron-based Simulations I: Extremal States of the Logarithmic N-Body Problem on a Sphere
  Accepted for publication, Discrete and Continuous Dynamical Systems
  xdvi format | Postscript format | PDF format
• Monte Carlo simulations of the spherical model for 2D Euler turbulence on the infinite plane
  Submitted for publication
  xdvi format | Postscript format | PDF format
• A Monte Carlo Algorithm for Free and Coaxial Ring Extremal States of the Vortex N-Body Problem on a Sphere
  Submitted for publication
  xdvi format | Postscript format | PDF format
• A Long Range Spherical Model and Exact Solutions for an Energy-Enstrophy Theory for the Euler Equations
  Phys. Fluids July 2001 pages 1961-1973
  xdvi format | Postscript format | PDF format
• A statistical mechanics barotropic energy-enstrophy theory for super-rotation in planetary atmospheres
  Submitted for publication
  xdvi format | Postscript format
• Point Vortex Dynamics for a Coupled Surface / Interior QG and Propagating heton Clusters in Models for Ocean Convection (with A.J. Majda)
  Appearing Geophysical and Astrophys. Fluid Dynamics, August 2001
  xdvi format | Postscript format
• Exact Solutions of the Energy-Enstrophy Theory for the Barotropic Vorticity Equation
  Physica A, February 2001, pages 131-158
  xdvi format | Postscript format | PDF format
• Equilibrium Energy Density Spectrum for Two-Dimensional Flows in the Zero Viscosity Limit and Random Matrices
  xdvi format | Postscript format
  Referenced figures: Figure 1 | Figure 2a | Figure 2b | Figure 3

Symmetric Dynamics

• Relative equilibria of Point Vortices on a Sphere (with M. Roberts and J. Montaldi)
  Physica D 148 (2001) pages 97 - 135
  xdvi format | PDF format

Spherical Models

Three modes seen in the energy-enstrophy model at different temperatures can be easily simulated. Data sheets for those modes are available. The modes represent:

• Negative temperatures, in which the system organizes itself into hills of positive and negative vorticity
• Checkerboard patterns, in which an antiferromagnetic pattern arises, as sites try to align their vorticity opposite their neighbors
• Banded regions, in which a row of positive vorticity lies next to a row of negative vorticity.

Monte Carlo Results for energy-enstrophy theory on the Sphere

• An animated movie of superrotation from a random initial state at negative temperatures is available. The movie shows the evolution of absolute vorticity into a solid body rotation pattern with red colors representing positive vorticities and blue colors representing negative vorticities.
• Superrotation of the vorticity can be observed in downloadable plots.
• Compared this to theoretical calculations for the superrotation in the atmosphere of Venus as submitted for publication. (The paper can also be downloaded in Postscript format.)
• The alternate mode of wavy banded activity can also be found by experiments. An animated movie of wavy band formation, seen when temperature is small but positive, can be downloaded.

Ising Model

Monte Carlo Simulations of 3D Turbulence

(Under construction.)

International Conference on Dynamical Systems

Beijing, China, June 18 - 22, 2001

Title: Logarithmic Interations, 2-D Turbulence, and Random Matrices

Books

Paul K. Newton's The N-Vortex Problem: Analytical Techniques, Springer, NY.

Web page designed by Joseph Nebus ( nebusj@rpi.edu ).

Last updated 14 February 2003.

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