Finite-amplitude Rayleigh- Bénard convection for weakly shear thinning fluids

The thermo-gravitational instability in a fluid layer of a weakly shear thinning medium heated from below is investigated. A linear and a weakly nonlinear analysis are successively presented. The shear thinning fluid is modelled by means of Carreau-Bird model. The critical values for the temperature gradient and wave number corresponding to the onset of convection are determined from a linear approach. After motion has set in, particular patterns are predicted taking the form of either rolls, or hexagons. By means of a nonlinear technique, restricted to steady situations, it is determined under which specific conditions one pattern is preferred. The influence of the constitutive equation parameters is examined and discussed in detail.