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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 2, Pages 305-310

Renormalization group analysis for thermal turbulence

Department of Theoretical and Applied Mechanics, 216 Talbot Laboratory, University of Illinois, 104 S. Wright St., Urbana 61801, Illinois, USA

Received 9 May 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Renormalization group theory is applied to thermal turbulence. Turbulent fluxes for the flow are accounted for by repeatedly recasting the governing equations with the smallest scales represented by effective larger scales. Expressions for nonlinear contributions to eddy viscosity and eddy diffusivity are determined, and leading order contributions due to buoyancy on various results and equations are estimated. Proper scalings for various quantities and variables including temperature are proposed. The results near two fixed points, which correspond to inertial and buoyancy dominated ranges, are determined and discussed