Instabilities appearing in the circular Couette flow with a dilute or semidilute solution of high molecular weight polyethyleneoxide in water have been investigated when the outer cylinder is kept at rest. The shear-thinning behavior of solutions was determined through low shear viscosity measurements. We have found that, depending on concentration, different flow structures can appear at the onset of instability. For dilute concentrations, the critical mode is the stationary and axisymmetric Taylor vortex flow, which bifurcates to time periodic wavy vortex flow for a higher shear rate. The oscillation amplitude of wavy vortex flow decreased with the increasing shear rate. For sufficiently semidilute solutions, the critical mode occurs in the form of standing waves, the frequency of which decreases with the shear rate. The critical Taylor number increases for solutions without a shear-thinning effect and decreases for solutions exhibiting shear thinning.

The thermal convection driven by the dielectrophoretic force is investigated in annular geometry under microgravity conditions. A radial temperature gradient and a radial alternating electric field are imposed on a dielectric fluid that fills the gap of two concentric infinite-length cylinders. The resulting dielectric force is regarded as thermal buoyancy with a radial effective gravity. This electric gravity varies in space and may change its sign depending on the temperature gradient and the cylinder radius ratio. The linear stability problem is solved by a spectral-collocation method. The critical mode is stationary and non-axisymmetric. The critical Rayleigh number and wavenumbers depend sensitively on the electric gravity and the radius ratio. The mechanism behind the instability is examined from an energetic viewpoint. The instability in wide gap annuli is an exact analogue to the gravity-driven thermal instability.

Transition to defect-mediated turbulence in the ribbon patterns observed in a viscoelastic Taylor-Couette flow is investigated when the rotation rate of the inner cylinder is increased while the outer cylinder is fixed. In four polymer solutions with different values of the elasticity number, the defects appear just above the onset of the ribbon pattern and trigger the appearance of disordered oscillations when the rotation rate is increased. The flow structure around the defects is determined and the statistical properties of these defects are analyzed in the framework of the complex Ginzburg-Landau equation.

Torque measurements in Taylor-Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque-speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

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The transition to turbulence in a flow of semidilute shear-thinning viscoelastic solution with a moderate elasticity was investigated in the Taylor-Couette system with a fixed outer cylinder. As the cylinder rotation frequency increases, the base flow bifurcates to a pattern of ribbons and then to disordered oscillations (DOs). Within these DOs, we have identified two particular regimes of turbulence: spatiotemporal intermittency (STI) followed by inertioelastic turbulence (IET) with a net transition between them. This transition is evidenced by a sharp peak of a diffusion velocity and a Weissenberg number.

A linear stability analysis of the flow confined in a differentially rotating cylindrical annulus with a radial temperature gradient has been performed. Depending on values of control parameters (the Taylor number, the Grashof number, and the Froude number), it has shown flow destabilization to axisymmetric or non-axisymmetric modes. Analysis of different terms involved in the evolution rate of the perturbation kinetic energy has allowed us to isolate the dominant terms (centrifugal force or buoyancy force) in the destabilization process. We have shown that the centrifugal buoyancy can induce the asymmetry of the temperature gradient on critical states.