The Couette-Taylor Problem

Chossat, Pascal; Iooss, Gérard

doi:10.1007/978-1-4612-4300-7

Cited by 300 publications

(286 citation statements)

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“…We investigated the impact of changing Ma and Pr on the stability of axisymmetric (steady) modes and of non-axisymmetric (oscillatory) modes with m = 1, which are known to be important in the case of counter-rotating cylinders, for incompressible flows (see, e.g., Davey et al 1968;Chossat & Iooss 1994). Critical values of the Reynolds numbers are referred to as Re 0 1c and Re 1 1c , for modes m = 0 and m = 1 respectively.…”

Section: Counter-rotating Cylindersmentioning

confidence: 99%

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Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Welsh¹,

Kersalé²,

Jones³

2014

J. Fluid Mech.

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Taylor-Couette flow in a compressible perfect gas is studied. The onset of instability is examined as a function of the Reynolds numbers of the inner and outer cylinder, the Mach number of the flow and the Prandtl number of the gas. We focus on the case of a wide gap, with radius ratio 0.5. We find new modes of instability at high Prandtl number, which can allow oscillatory axisymmetric modes to onset first. We also find that onset can occur even when the angular momentum increases outwards, so that the classical Rayleigh criterion can be violated in the compressible case. We have also considered the case of counter-rotating cylinders, where the m = 0 and m = 1 modes can onset simultaneously to give a codimension 2 bifurcation, leading to the formation of complex flow patterns. In compressible flow we also find codimension 3 points. The Mach number and the critical inner and outer Reynolds numbers can be adjusted so that the two neutral curves for the m = 0 and m = 1 modes touch rather than cross. Complex codimension 3 points occur more readily in the compressible case than in the Boussinesq case, and they are expected to lead to a rich nonlinear behaviour.

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Section: Counter-rotating Cylindersmentioning

confidence: 99%

“…This leads to interesting and rich nonlinear behaviour; see e.g. Chossat & Iooss (1994). They are called codimension 2 points because two parameters, often the Reynolds numbers of the outer cylinder and inner cylinder, must have particular values for the simultaneous onset.…”

Section: Introductionmentioning

confidence: 99%

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Welsh¹,

Kersalé²,

Jones³

2014

J. Fluid Mech.

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“…The presence of these symmetries has many consequences on the dynamics and the bifurcations this system can experience. Chossat and Iooss [3] give details specific to the classical Taylor-Couette problem. In our case, due to the symmetries, we need only consider the n ≥ 0, k ≥ 0 cases.…”

Section: Symmetriesmentioning

confidence: 99%

Spatial and temporal resonances in a periodically forced hydrodynamic system

Marqués

Lopez

2000

Physica D: Nonlinear Phenomena

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“…When the symmetries are purely spatial in nature (e.g. reflections, translations, rotations), these consequences have been extensively studied (see, for example, Golubitsky & Schaeffer 1985;Golubitsky, Stewart & Schaeffer 1988;Crawford & Knobloch 1991;Cross & Hohenberg 1993;Chossat & Iooss 1994;Iooss & Adelmeyer 1998;Chossat & Lauterbach 2000;Golubitsky & Stewart 2002). The system may also be invariant to the action of spatio-temporal symmetries.…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking of two-dimensional time-periodic wakes

2005

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A number of two-dimensional time-periodic flows, for example the Kármán street wake of a symmetrical bluff body such as a circular cylinder, possess a spatio-temporal symmetry: a combination of evolution by half a period in time and a spatial reflection leaves the solution invariant. Floquet analyses for the stability of these flows to three-dimensional perturbations have in the past been based on the Poincaré map, without attempting to exploit the spatio-temporal symmetry. Here, Floquet analysis based on the half-periodflip map provides a comprehensive interpretation of the symmetry breaking bifurcations.

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The Couette-Taylor Problem

Cited by 300 publications

References 0 publications

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

Spatial and temporal resonances in a periodically forced hydrodynamic system

Symmetry breaking of two-dimensional time-periodic wakes

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