Rayleigh-Benard Convection in a Near-Critical Fluid in the Neighborhood of the Stability Threshold

Steady-state Rayleigh-Benard convection in a medium with parameters close to the thermodynamic critical point is simulated within the framework of the complete Navier-Stokes equations with a two-scale representation of the pressure and the Van-der-Waals equation of state. A calibration relation is obtained for a realistic Rayleigh number in a compressible stratified medium. The parameters of the numerical simulation are determined from experimental data for near-critical helium on the basis of the calibration relation. The threshold Rayleigh numbers are found without and with allowance for stratification and a comparison with the experimental and theoretical data is carried out. The effect of compressibility of the near-critical fluid on steady-state convection flows is investigated beyond the stability threshold and the effect of adiabatic compression of the medium is analyzed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 48–61.Original Russian Text Copyright © 2005 by Polezhaev and Soboleva.