J. Abshagen

End wall effects on the transitions between Taylor vortices and spiral vortices

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, nonrotating lids at the cylinder ends. These transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. In the presence of these axial end walls, pure spiral solutions do not occur as for axially periodic boundary conditions but are substituted by primary bifurcating, stable wavy spiral structures. Similarly to the periodic system, we found a transition from Taylor vortices to wavy spirals mediated by so-called wavy Taylor vortices and, on the other hand, a transition from wavy spirals to Taylor vortices triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wavy spirals out of the basic circular Couette flow with Ekman vortices at the cylinder ends.

Direction reversal of a rotating wave in Taylor-Couette flow

In Taylor-Couette systems, waves, e.g. spirals and wavy vortex flow, typically rotate in the same direction as the azimuthal mean flow of the basic flow which is mainly determined by the rotation of the inner cylinder. In a combined experimental and numerical study we analysed a rotating wave of a one-vortex state in small-aspect-ratio Taylor-Couette flow which propagates either progradely or retrogradely in the inertial (laboratory) frame, i.e. in the same or opposite direction as the inner cylinder. The direction reversal from prograde to retrograde can occur at a distinct parameter value where the propagation speed vanishes. Owing to small imperfections of the rotational invariance, the curves of vanishing rotation speed can broaden to ribbons caused by coupling between the end plates and the rotating wave. The bifurcation event underlying the direction reversal is of higher codimension and is unfolded experimentally by three control parameters, i.e. the Reynolds number, the aspect ratio, and the rotation rate of the end plates.

Multiple localized states in centrifugally stable rotating flow

We report experimental and numerical results from investigations into the onset of novel localized cellular states in the centrifugally stable regime of Taylor–Couette flow at sufficiently high rates of counter-rotation of the outer cylinder. Quantitative comparison is made between experimental results and those obtained from numerical bifurcation studies of the steady axisymmetric Navier–Stokes equations. The onset of the vortices is smooth but they appear over a narrow range of Reynolds number. This enables the use of a suitable measure to produce excellent quantitative agreement between calculation and experiment. The numerical methods are also used to uncover evidence for a homoclinic snake which indicates rich multiplicity in the steady solution set.

Bifurcation behavior of standing waves

Two different types of standing waves (SW0 and SWπ) can appear instead of spiral vortices from a supercritical Hopf bifurcation in counter-rotating Taylor-Couette flow for sufficiently small aspect ratios [1,2]. The bifurcation sequence from basic flow to spiral vortices via SW0 can include modulated waves, homoclinic bifurcations, and hysteresis as a consequence of broken translational invariance [3]. Here we show that the same kind of sequence can also occur for the other type of standing wave, i.e., SWπ. Furthermore we show that SWπ can exist also up to much larger inner Reynolds numbers than is has been found for SW0. Far from onset SWπ can undergo bifurcation sequences that differs qualitatively from those close to onset. These sequences involve a supercritical symmetry breaking as well as a supercritical Hopf bifurcation towards a new type of modulated wave.

Spatio-temporal behavior of spiral vortex flow

Experimental realizations of Taylor-Couette flow often include rigid end plates at bottom and top of the system. As a consequence of such end plates the bifurcation behavior of the basic laminar flow as well as the spatio-temporal properties of the emerging pattern, such as e.g. spiral vortex flow, can change. The latter point is in the focus of our present experimental study. The spatio-temporal behavior of spiral vortex flow in a Taylor-Couette system with rigid end plates is analyzed by a measurement technique based on Doppler-shift. This enables us to determine the spatial amplitude profile of up- and downward propagating spiral vortices within oscillatory flow states. Our study confirms experimentally recent numerical results of Hoffmann et al. [1] on the spatio-temporal properties of the spiral vortex state in finite systems with rigid end plates.