Stabilitaetsuntersuchungen der Rayleigh-Benard-Konvektion in der Naehe des kritischen Zustands mit Hilfe eines Spektralmodells

Hydrostatic stability of horizontal fluid layer heated from below is lost if the temperature gradient exceeds a critical value. The onset of convection in a fluid near its gas-liquid critical point is investigated theoretically. In a first step hydrostatic density and temperature profiles are computed numerically. Then the orders of magnitude of the terms occuring in the dynamical equations are estimated, showing that due to the divergence of the compressibility in the critical region pressure terms neglected in the Boussinesq approximation have to be retained. A Galerkin method is applied to the two-dimensional problem, and a low order truncation which far from the critical point reduces to the familiar Lorenz equations is analysed. According to this model the critical Rayleigh number decreases to a finite value while the corresponding horizontal wavenumber increases as the system approaches the critical state. (orig.)Available from TIB Hannover: RA 1396(1992,15) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman