Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability

Abstract

We consider a horizontal fluid layer between two rigid boundaries, maintained in a stationary thermal nonequilibrium state below the convective Rayleigh-Bénard 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 [formula presented] 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 [formula presented] dependence for larger q to a [formula presented] 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 [formula presented]. © 2002 The American Physical Society.