On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders

Krueger, E. R.; Groß, Andreas; Prima, R. C. Di

doi:10.1017/s002211206600079x

Cited by 180 publications

(82 citation statements)

References 14 publications

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“…In the absence of the magnetic fields, the dispersion relation determined by the matrix H reduces to that derived already by Krueger et al (1966) for the nonaxisymmetric perturbations of the hydrodynamical TC flow. Choosing, additionally, m = 0, we reproduce the result of Eckhardt & Yao (1995).…”

Section: Short-wavelength Analysis Of Viscous Resistive Mri For Arbimentioning

confidence: 72%

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

Kirillov

Stefani

Fukumoto

2012

ApJ

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The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of small magnetic Prandtl number, the helical and the azimuthal versions of MRI are known to be governed by a quite different scaling behavior than the standard MRI with a vertical applied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid, we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit 2(1 − √ 2) ≈ −0.8284 for the critical Rossby number. From this universal behavior we are also led to the prediction that the instability will be governed by a mode with an azimuthal wavenumber that is proportional to the ratio of axial to azimuthal applied magnetic field, when this ratio becomes large and the Rossby number is close to the Liu limit.

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Section: Short-wavelength Analysis Of Viscous Resistive Mri For Arbimentioning

confidence: 72%

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

Kirillov

Stefani

Fukumoto

2012

ApJ

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“…Although the study of transient growth in Taylor-Couette flow is relatively unexplored, its linear instability has been extensively studied, e.g. [1,5,7,9,21]. the thresholds are so close that the instability was thought to be axisymmetric until 1966, when calculations by Krueger, Gross and DiPrima [5] confirmed experimentally by Coles [2] showed the first instability to be non-axisymmetric for µ sufficiently negative, more precisely µ 0.78 in the narrow-gap limit.…”

Section: A Taylor-couette Flowmentioning

confidence: 99%

“…[1,5,7,9,21]. the thresholds are so close that the instability was thought to be axisymmetric until 1966, when calculations by Krueger, Gross and DiPrima [5] confirmed experimentally by Coles [2] showed the first instability to be non-axisymmetric for µ sufficiently negative, more precisely µ 0.78 in the narrow-gap limit. Note that the correspondence between the streamwise wavenumber α We eliminateû z andp by using (6c) and the condition of incompressibility (6d), obtaining evolution equations in u = (û r ,û θ ).…”

Section: A Taylor-couette Flowmentioning

confidence: 99%

Transient growth in Taylor–Couette flow

et al. 2002

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Transient growth due to non-normality is investigated for the Taylor-Couette problem with counter-rotating cylinders as a function of aspect ratio η and Reynolds number Re. For all Re ≤ 500, transient growth is enhanced by curvature, i.e. is greater for η < 1 than for η = 1, the plane Couette limit. For fixed Re < 130 it is found that the greatest transient growth is achieved for η between the Taylor-Couette linear stability boundary, if it exists, and one, while for Re > 130 the greatest transient growth is achieved for η on the linear stability boundary.Transient growth is shown to be approximately 20% higher near the linear stability boundary at Re = 310, η = 0.986 than at Re = 310, η = 1, near the threshold observed for transition in plane Couette flow. The energy in the optimal inputs is primarily meridional; that in the optimal outputs is primarily azimuthal. Pseudospectra are calculated for two contrasting cases.For large curvature, η = 0.5, the pseudospectra adhere more closely to the spectrum than in a narrow gap case, η = 0.99.

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“…Chossat & Iooss 1994). To simplify this we follow Krueger, Gross & DiPrima (1966) and approximate values of a 1 , a 4 and b 1 by their limiting values as k → 0 (assuming they are regular as δ → 0). The values of b 4 we use are those calculated in Davey et al (1968, p. 39, Table 2).…”

Section: Steady Solutions Of the Amplitude Equationsmentioning

confidence: 99%

A study of particle paths in non-axisymmetric Taylor–Couette flows

Ashwin¹,

King

1997

J. Fluid Mech.

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We study the paths of fluid particles in velocity fields modelling rigidly rotating velocity fields that occur in the concentric Taylor problem. We set up velocity fields using the model of Davey, DiPrima & Stuart (1968) based on small-gap asymptotics. This allows a numerical study of the Lagrangian properties of steady flow patterns in a rotating frame. The spiral and Taylor vortex modes are integrable, implying that in these cases almost all particle paths are confined to two-dimensional surfaces in the fluid. For the case of Taylor vortices the motion on these surfaces is quasi-periodic, whereas for spirals the particles propagate up or down the cylinder on these surfaces.The non-axisymmetric modes we consider are wavy vortices, spirals, ribbons and twisted Taylor vortices. All of these flows have the property that they are steady flows when examined in a rotating frame of reference. For all non-axisymmetric modes with the exception of spirals, we observe the existence of regions of chaotic mixing within the fluid. We discuss mixing of the fluid by these flows with reference to the pattern of stagnation points and some of the periodic trajectories within the fluid and on the boundary.

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On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders

Cited by 180 publications

References 14 publications

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

Transient growth in Taylor–Couette flow

A study of particle paths in non-axisymmetric Taylor–Couette flows

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