Stability of Stationary Thermal Convection with Temperature-Dependent Viscosity

Abstract

Multi-valued stationary solutions of two-dimensional Bénard convection of a fluid with temperature-dependent viscosity were obtained in the previous papers for Rayleigh number 3000 and Prandtl number 1000 by numerical computation. In this paper stabilities of the two-valued stationary solutions are treated numerically in the presence of types of disturbances with finite amplitude. By solving the time-dependent governing equation numerically, it is found that the stability characteristics can be expressed conventionally in terms of a distance of non-steady solution from the stationary solutions.