Publication: Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Benard instability
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2002-09
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American Physical Society
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Abstract
We consider a horizontal fluid layer between two rigid boundaries, maintained in a stationary thermal nonequilibrium state below the convective Rayleigh-Benard instability. We derive an explicit expression for the nonequilibrium structure factor in a first-order Galerkin approximation valid for negative and positive Rayleigh numbers R up to the critical Rayleigh number R(c) associated with the appearance of convection. The results obtained for rigid boundaries by the Galerkin-approximation method are compared with exact results previously derived for the case of free boundaries. The nonequilibrium structure factor exhibits a maximum as a function of the wave number q of the fluctuations. This maximum is associated with a crossover from a q(-4) dependence for larger q to a q(2) dependence for small q. This maximum is present at both negative and positive R, becomes pronounced at positive R and diverges as R approaches the critical value R(c).
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©2002 The American Physical Society. The authors are indebted to G. Ahlers and D. S. Cannell for some valuable comments. The research at the University of Maryland was supported by the Chemical Sciences, Geosciences and Biosciences Division of the Office of Basic Energy Sciences of the U.S. Department of Energy under Grant No. DE-FG-02-95ER14509. J.M.O.Z. acknowledges the hospitality of the Institute for Physical Science and Technology, University of Maryland, where part of the manuscript was prepared.
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