Tricritical Phenomena in Rotating Couette-Taylor Flow

Aitta, A.; Ahlers, Guenter; Cannell, David S.

doi:10.1103/physrevlett.54.673

Cited by 43 publications

(23 citation statements)

References 9 publications

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“…At onset, the point of direction reversal is accompanied with a change of the Hopf bifurcation from super-to subcritical. Such changes have been referred to as a generalized Hopf bifurcation (Guckenheimer & Holmes 1983) or a tricritical phenomena (Aitta, Ahlers & Cannell 1985).…”

Section: Discussionmentioning

confidence: 99%

Direction reversal of a rotating wave in Taylor–Couette flow

et al. 2008

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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.

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Section: Discussionmentioning

confidence: 99%

Direction reversal of a rotating wave in Taylor–Couette flow

et al. 2008

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“…The presence of hysteresis suggests a transition from a supercritical to a subcritical pitchfork bifurcation with the increase in the occlusion height, which is often associated with tricritical phenomena. 17,18 In order to confirm that the observed behavior is not an artifact of the local measure ␦, we also present results in terms of a global measure of the system, the so-called wet fraction, m =1−⌽ / ͑AU͒, the ratio of the liquid volume that remains once the finger has exited the tube to the total volume of the tube. Above, ⌽ is the flow rate of the liquid and A is the cross-sectional area of the tube.…”

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confidence: 95%

Tube geometry can force switchlike transitions in the behavior of propagating bubbles

et al. 2009

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Microscale process engineering requires precise control of bubbles and droplets. We investigate geometry-induced control and find that a centered constriction in the cross section of rectangular tubes can lead to new families of steadily propagating bubbles, which localize in the least-constricted regions of the cross section. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the flow rate: a mechanism for flow-rate-driven bubble control. The accompanying large change in bubble volume could be significant for liquid recovery applications.

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“…It is known that real fluid is very complex, and various dynamical behaviors can be found in real fluid, including asymmetry, vortices, turbulence [22,23], bifurcation [24], and spatiotemporal chaos [25,26]. These phenomena are also components of glottal airflow [27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Chaotic component obscured by strong periodicity in voice production system

Tao

Jiang

2008

Phys. Rev. E

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The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The twomass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a smallamplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity.

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Tricritical Phenomena in Rotating Couette-Taylor Flow

Cited by 43 publications

References 9 publications

Direction reversal of a rotating wave in Taylor–Couette flow

Direction reversal of a rotating wave in Taylor–Couette flow

Tube geometry can force switchlike transitions in the behavior of propagating bubbles

Chaotic component obscured by strong periodicity in voice production system

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