CHAOS IN THE THERMAL-CONVECTION OF WEAKLY SHEAR-THINNING FLUIDS

The influence of weak shear thinning on the onset of chaos in thermal convection is examined for a Carreau-Bird fluid. A truncated Fourier r epresentation of the flow and temperature fields leads to a three-dime nsional system that generalizes the classical Lorenz system for a Newt onian fluid. It is found that the critical Rayleigh number at the onse t of thermal convection remains the same as for a Newtonian fluid, but the amplitude and nature of the convective cellular structure is dram atically altered by shear thinning, The presence of shear thinning lea ds to a second Hopf bifurcation around the convective branches in addi tion to the one usually present in the Lorenz system. While chaotic be havior sets in, as the Rayleigh number increases, at the first Hopf bi furcation similarly to the case of a Newtonian fluid, there appears a series of periodic behaviors (inverse period doubling) leading to inte rmittency and again to chaos at a Rayleigh number that becomes increas ingly smaller as the effect of shear thinning increases.