Fractal dimensions of strange attractors obtained from the Taylor-Couette experiment

doi:10.1016/0378-4371(92)90583-C

Physica A: Statistical Mechanics and its Applications

Volume 191, Issues 1–4, 15 December 1992, Pages 559-563

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Abstract

We present scenarios from the rotational Taylor-Couette flow, which has been implemented as a high precision hydrodynamic experiment. The system shows a rich variety of routes to chaos, e.g. the period doubling cascade, quasiperiodic and intermittent transitions. From a scalar time series, that is the axial velocity component of the flow field measured with Laser-Doppler velocimetry, strange attractors are reconstructed using Takens' delay time coordinates. To obtain an estimate of the fractal dimensions of these structures in phase space we calculate the correlation dimension from the reconstructed attractors. We discuss the fractal dimension as a function of Reynolds number and geometry of the experiment.

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Propagating vortices in ferrofluidic Couette flow under magnetic fields – Part II: Oblique orientated fields
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Citation Excerpt :
Instead they only involve an axial oscillation close to onset, which changes with variation in field strength in a smooth transition into propagating vortex solutions. Such axially oscillatory flow state has been reported earlier in TCS for either classical fluid, numerical and experimental in [38,39] as well as ferrofluid under magnetic field [19]. The overall goal of this study (first and second part) is to expand the parameter range in which the pV states are existing, stable and unstable, and further to investigate the topology of these solutions in ferrofluids in the presence of different magnetic fields.
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Transition from periodic to non-periodic motion of a Bunsen-type premixed flame tip with burner rotation
2002, Proceedings of the Combustion Institute
Unsteady motions of a Bunsen-type premixed flame tip with burner rotation are experimentally investigatedfrom the viewpoint of nonlinear dynamics. The mean velocity from burner tube U is varied from 0.6 to 1.2 m/s, and the rotational speed of the burner tube N is varied from 0 to 2800 rpm. A rich methane/air mixture with the equivalence ratio of =1.43 is used.
With the Lewis number Le larger than unity, an axisymmetric oscillating flame is formed between aconical flame and a plateau flame at U=0.6m/s and swirl number S=1.14, As U and N increase, but with S constant, the oscillating flame tip motion becomes unstable. This variation in the flame tip motion is shown qualitatively by drawing an attractor and evaluated quantitatively by estimating the correlation dimension. For U≤0.8 m/s, the attractor is a limit cycle and the correlation dimension D_c is estimated at about unity, indicating periodic motion. When U reaches 1.0 m/s, the trajectories of the attractor become rolled up slightly and D_c approaches about 2, indicating quasi-periodic flame tip motion. With a further increase in U, the attractor becomes much more complicated and D_c, is estimated as a non-integer value, indicating a deterministic chaos. These results indicate that the flame tip motion with the burner rotation under the condition of Le>1 varies from periodic to non-periodic (i.e., to chaotic). The present results also show that an analysis based on deterministic chaos theory, such as the correlation dimension, is valid for quantifying the motion of unsteady flames.
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Physica A: Statistical Mechanics and its Applications

Fractal dimensions of strange attractors obtained from the Taylor-Couette experiment

Abstract

Physica D

The Fractal Geometry of Nature

Dynamical Systems and Turbulence

Propagating vortices in ferrofluidic Couette flow under magnetic fields – Part II: Oblique orientated fields

Transition from periodic to non-periodic motion of a Bunsen-type premixed flame tip with burner rotation

Routes into chaos in small and wide gap Taylor-Couette flow

Characterising experimental time series using local intrinsic dimension

Mutual information and global strange attractors in Taylor-Couette flow

Noise reduction on chaotic attractors