Direction reversal of a rotating wave in Taylor–Couette flow

Abstract

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-aspectratio 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.

Pinning of rotating waves to defects in finite Taylor–Couette flow

“…In this section, we compare our results with different high-precision experiments that have been very carefully conducted for more than 20 years by the experimental group led by Professor G. Pfister in Kiel (Pfister et al 1988(Pfister et al , 1991(Pfister et al , 1992Abshagen et al 2008a). Figure 12 shows a regime diagram from the laboratory experiments of Abshagen et al (2008a).…”

“…see direct comparisons between experimentally and numerically determined bifurcations and nonlinear dynamics in Taylor-Couette flows with Γ ∼ 3, presented in Abshagen et al 2005aAbshagen et al , b, 2008b. However, in specific parameter regimes, the same type of highprecision experiments (Pfister et al 1988;Pfister, Schulz & Lensch 1991;Pfister, Buzug & Enge 1992;Abshagen et al 2008a) reveal some behaviour which is unaccountable in simulations of the Z 2 × SO(2) system (Marques & Lopez 2006).…”

“…Numerical simulations of the Z 2 × SO(2)-symmetric system in this parameter regime were unable to reproduce the dynamics, in particular no infinite-period global bifurcations have been detected numerically. The most recent set of experiments (Abshagen et al 2008a) specifically studied the imposed breaking of the Z 2 × SO(2) by tilting one of the endwalls by a small amount and made convincing arguments for the cause of the infinite-period bifurcations being due to the pinning of the rotating wave to the imperfection (the tilted endwall) in the neighbourhood of parameter space where the precession frequency is small.…”

Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

“…Figure 9a shows a bifurcation diagram from the laboratory experiments of Abshagen et al [16]. These experiments show that, without an imposed tilt, the natural imperfections of the system produce a measurable pinning region, and that the additional tilting of one endwall increases the extent of the pinning region.…”

“…Figure 9. Bifurcation diagrams for the one-cell state from (a) the experimental results of Abshagen et al [16] with natural imperfections, and (b) the numerical results of Pacheco et al [23] with a tilt of 0.1…”