Stability of density-stratified viscous Taylor-Couette flows

Shalybkov, D. A.; Rüdiger, G.

doi:10.1051/0004-6361:20042492

Cited by 47 publications

(86 citation statements)

References 13 publications

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“…This is consistent with the predictions of Shalybkov & Rüdiger (2005) and Rüdiger & Shalybkov (2009), who showed that stratified Taylor-Couette flow between infinite cylinders is generally stable for µ < η. For the HS case, the presence of end-plates does not seem to impact the structure of the mode far from the end-plates (see 5(c)).…”

Section: 'Low-shear Case'supporting

confidence: 92%

“…However, despite the fully stratified solutions being significantly closer to the base flow, the computed axisymmetric solution cannot actually be observed in an experiment as the flow is, again, subject to a linear instability. The structure of the most unstable mode, shown for Re = 1500 in figure 5(c)), is clearly reminiscent of the SRI as described in Shalybkov & Rüdiger (2005) and Rüdiger & Shalybkov (2009): the mode is nonaxisymmetric and almost axially periodic, with an axial wavelength smaller than the gap (for infinite cylinders, Shalybkov & Rüdiger (2005) found the scaling λ ∼ Ri −1/2 l for the critical axial wavelength λ). However, the production of total disturbance energy is localised near the inner cylinder, which suggests that the instability mechanism for our wide-gap configuration η = 0.417 is closer to the radiative mechanism of Le Dizès & .…”

Section: Mitigating End-effects With Stratificationmentioning

confidence: 75%

“…Originally discovered by Molemaker et al (2001) and Yavneh et al (2001), the instability was theoretically predicted to develop for any value of µ < 1 (cyclonic regime) in the inviscid, small-gap limit. Shalybkov & Rüdiger (2005) and Rüdiger & Shalybkov (2009) later extended these results to the wide gap and viscous case with the help of numerical methods. These authors showed that the instability range was narrower than initially thought, as SRI could only be found for a very limited range of rotation ratios µ beyond η, if at all, depending on the radius ratio and stratification.…”

Section: Introductionmentioning

confidence: 94%

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Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

et al. 2016

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Efforts to model accretion disks in the laboratory using Taylor–Couette flow apparatus are plagued with problems due to the substantial impact the end plates have on the flow. We explore the possibility of mitigating the influence of these end plates by imposing stable stratification in their vicinity. Numerical computations and experiments confirm the effectiveness of this strategy for restoring the axially homogeneous quasi-Keplerian solution in the unstratified equatorial part of the flow for sufficiently strong stratification and moderate layer thickness. If the rotation ratio is too large, however (e.g. ${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{3/2}$, where ${\it\Omega}_{o}/{\it\Omega}_{i}$ is the angular velocity at the outer/inner boundary and $r_{i}/r_{o}$ is the inner/outer radius), the presence of stratification can make the quasi-Keplerian flow susceptible to the stratorotational instability. Otherwise (e.g. for ${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{1/2}$), our control strategy is successful in reinstating a linearly stable quasi-Keplerian flow away from the end plates. Experiments probing the nonlinear stability of this flow show only decay of initial finite-amplitude disturbances at a Reynolds number $Re=O(10^{4})$. This observation is consistent with most recent computational (Ostilla-Mónico, et al.J. Fluid Mech., vol. 748, 2014, R3) and experimental results (Edlund & Ji, Phys. Rev. E, vol. 89, 2014, 021004) at high $Re$, and reinforces the growing consensus that turbulence in cold accretion disks must rely on additional physics beyond that of incompressible hydrodynamics.

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Section: 'Low-shear Case'supporting

confidence: 92%

Section: Mitigating End-effects With Stratificationmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 94%

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Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

et al. 2016

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“…It has been shown theoretically Yavneh et al 2001;Dubrulle et al 2005;Shalybkov & Rüdiger 2005;Umurhan 2006) and in the laboratory (Le Bars & Le Gal 2007) that a combination of a centrifugal-stable nonuniform rotation law and a stable axial density stratification leads to the SRI in the Taylor-Couette flow. This instability exists only for nonaxisymmetric disturbances.…”

Section: Introductionmentioning

confidence: 99%

Stratorotational instability in MHD Taylor-Couette flows

Rüdiger¹,

Shalybkov

2008

A&A

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Aims. The stability of the dissipative Taylor-Couette flow with a stable axial density stratification and a prescribed azimuthal magnetic field is considered. Methods. Global nonaxisymmetric solutions of the linearized MHD equations with toroidal magnetic field, density stratification, and differential rotation are found for both insulating and conducting cylinders. Results. Hydrodynamic calculations for various gap widths show that flat rotation laws such as the Kepler rotation are always unstable against SRI. Quasigalactic rotation laws, however, are stable for wide gaps. The influence of a current-free toroidal magnetic field on SRI strongly depends on the magnetic Prandtl number Pm: SRI is supported by Pm > 1 and it is suppressed by Pm < ∼ 1. For rotation laws that are too flat, when the hydrodynamic SRI ceases, a smooth transition exists to the instability that the toroidal magnetic field produces in combination with the differential rotation. For the first time this nonaxisymmetric azimuthal magnetorotational instability (AMRI) has been computed in the presence of an axial density gradient. If the magnetic field between the cylinders is not current-free, then the Tayler instability occurs, too. The transition from the nonmagnetic centrifugal instability to the magnetic Tayler instability in the presence of differential rotation and density stratification proves to be complex. Most spectacular is the "ballooning" of the stability domain by the density stratification: already a small rotation stabilizes magnetic fields against the Tayler instability. An azimuthal component of the electromotive force u × B for the instability only exists for density-stratified flows. The related α-effect for magnetic-influenced SRI with Kepler rotation appears to be positive for negative dρ/dz < 0.

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“…These stratorotational instabilities (Dubrulle 2004), which are distinct from instabilities giving rise to buoyant convection, have been identified from linear stability analysis Yavneh et al 2001;Dubrulle et al 2004;Shalybkov & Rudiger 2005;) and have been proposed to operate in Keplerian disks. Yavneh et al (2001) numerically demonstrated that such effects leads to significant non-linear activity in small-gap limit simulations of Taylor-Couette flows in a uniform gravitational field.…”

Section: Introductionmentioning

confidence: 99%

Global axisymmetric dynamics of thin viscous accretion disks

Umurhan¹,

Nemirovsky²,

Regev³

et al. 2006

A&A

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The purpose of this paper is to explore the steady state and dynamical behavior of thin, axisymmetric, viscous accretion disks. To facilitate an analytical treatment we replace the energy equation with a general polytropic assumption. The asymptotic expansion of Kluźniak & Kita (2000, Three-dimensional structure of an alpha accretion disk [arXiv:astro-ph/0006266]), which extended the method of Regev (1983, A&A, 126, 146) to a full steady polytropic disk (with n = 3/2), is further developed and implemented for both the steady (for any polytropic index) and time-dependent problems. The spatial form and temporal behavior of selected dynamical disturbances are studied in detail. It is shown that the transient dynamics resulting from initial perturbations on the linearly stable steady state gives rise to substantial growth of perturbations. We identify the initial perturbation space which leads to such transient growth and provide analytical solutions which manifest this behavior three terms (physical causes) responsible for the appearance of transient dynamics are identified. Two depend explicitly on the viscosity while the third one is relevant also for inviscid disks. The main conclusion we draw is that transient dynamics and, in particular, significant perturbation energy amplification occurs in disks on a global scale. We speculate on the possible implications of these findings to accretion disk theory.

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Stability of density-stratified viscous Taylor-Couette flows

Cited by 47 publications

References 13 publications

Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

Stratorotational instability in MHD Taylor-Couette flows

Global axisymmetric dynamics of thin viscous accretion disks

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