| This thesis presents a series of studies on Rayleigh-Benard convection and Taylor-Couette flow.; In chapter 2, the influence of inertia and elasticity on the onset and stability of Rayleigh-Benard convection is examined for highly elastic polymeric solutions with constant viscosity. The Galerkin projection method is used to obtain the departure from the conductive state. The solution is capable of displaying complex dynamical behavior for viscoelastic fluids in the elastic and inertio-elastic ranges. It is found that for a given Rayleigh number smaller than the critical value, RaSC (corresponding to the onset of stationary thermal convection), finite-amplitude periodic oscillatory convection emerges as the fluid elasticity exceeds a threshold. Periodicity is lost as elasticity increases, leading to a T 2 quasi-periodic behavior, and the breakup of the torus as elasticity increases further. Although no experimental data are available for direct comparison, this scenario is reminiscent of the flow sequence observed in the Taylor-Couette flow of a Boger fluid. For fluids with small or moderately small elasticity, stationary thermal convection emerges, via a supercritical bifurcation, as Rayleigh number exceeds RaSC . The amplitude of motion is found to be little influenced by fluid elasticity or retardation time. However, the range of stability of the stationary convection narrows considerably for viscoelastic fluids. In this case, oscillatory convection is favoured. An amplitude equation approach is used to study the stabilities of three stationary convection patterns, namely rolls, hexagons, and squares, and to, simultaneously, establish the validity range of two-dimensional roll patterns. In contrast to Newtonian fluids, the hexagonal patterns are found to be stable for a narrow range of the elasticity as Rayleigh number exceeds RaSC .; In chapter 3, the effect of shear thinning on the stability of the axisymmetric Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low order-dynamical system form the conservation of mass and momentum equations. It is found that the critical Taylor number, corresponding to the loss of stability of the Couette flow, becomes lower as the shear-thinning effect increases. (Abstract shortened by UMI.)... |
