Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results

Umurhan, O. M.; Regev, Oded

doi:10.1051/0004-6361:20040573

Cited by 123 publications

(202 citation statements)

References 46 publications

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“…In 2D, the evolution of large-amplitude random vorticity perturbations follows the results reported by others (Godon & Livio 1999, 2000Umurhan & Regev 2004;JG05b). In particular, coherent, large-scale ( horizontal extent larger than the scale height), anticyclonic vortices survive and decay slowly.…”

Section: Discussionsupporting

confidence: 82%

“…We suggest that the reason previous studies (Umurhan & Regev 2004;JG05b) did not find destruction of shearing vortical waves is that they used only small initial perturbation amplitudes and intermediate amplification factors (small j k x;0 /k y j), which did not satisfy the KH instability condition equation (15).…”

Section: Kelvin-helmholtz Instability Of Incompressible Wavesmentioning

confidence: 75%

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Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

Shen

Stone

Gardiner

2006

ApJ

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We carry out three-dimensional, high-resolution (up to 1024 2 ; 256) hydrodynamic simulations of the evolution of vortices in vertically unstratified Keplerian disks using the shearing sheet approximation. The transient amplification of incompressible, linear amplitude leading waves (which has been proposed as a possible route to nonlinear hydrodynamic turbulence in disks) is used as one test of our algorithms; our methods accurately capture the predicted amplification, converge at second order, and are free from aliasing. Waves that are expected to reach nonlinear amplitude at peak amplification become unstable to Kelvin-Helmholtz modes when j W max jk (where W max is the local maximum of vorticity and the angular velocity). We study the evolution of a power-law distribution of vorticity consistent with Kolmogorov turbulence; in two dimensions long-lived vortices emerge and decay slowly, similar to previous studies. In three dimensions, however, vortices are unstable to bending modes, leading to rapid decay. Only vortices with a length-to-width ratio smaller than 1 survive; in three dimensions the residual kinetic energy and shear stress is at least 1 order of magnitude smaller than in two dimensions. No evidence for sustained hydrodynamic turbulence and transport is observed in three dimensions. Instead, at late times the residual transport is determined by the amplitude of slowly decaying, large-scale vortices (with horizontal extent comparable to the scale height of the disk), with additional contributions from nearly incompressible inertial waves possible. Evaluating the role that large-scale vortices play in astrophysical accretion disks will require understanding the mechanisms that generate and destroy them.

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Section: Discussionsupporting

confidence: 82%

Section: Kelvin-helmholtz Instability Of Incompressible Wavesmentioning

confidence: 75%

Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

Shen

Stone

Gardiner

2006

ApJ

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“…To circumvent this problem, we use a remap method similar to the one described by Umurhan & Regev (2004). This routine redefines the sheared frame every T remap = L x /(L y S ), and none of the results presented here seems to be related to this time scale.…”

Section: Shearing Box Model and Equationsmentioning

confidence: 99%

MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites

Longaretti

Lesur

2010

A&A

102

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Context. In the recent years, MRI-driven turbulent transport has been found to depend in a significant way on fluid viscosity ν and resistivity η through the magnetic Prandtl number Pm = ν/η. In particular, the transport decreases with decreasing Pm; if persistent at very large Reynolds numbers, this trend may lead to question the role of MRI-turbulence in YSO disks, whose Prandtl number is usually very small. Aims. In this context, the principal objective of the present investigation is to characterize in a refined way the role of dissipation. Another objective is to characterize the effect of linear (channel modes) and quasi-linear (parasitic modes) physics in the behavior of the transport. Methods. These objectives are addressed with the help of a number of incompressible numerical simulations. The horizontal extent of the box size has been increased in order to capture all relevant (fastest growing) linear and secondary parasitic unstable modes. Results. The major results are the following: i-the increased accuracy in the computation of transport averages shows that the dependence of transport on physical dissipation exhibits two different regimes: for Pm < ∼ 1, the transport has a power-law dependence on the magnetic Reynolds number rather than on the Prandtl number; for Pm > 1, the data are consistent with a primary dependence on Pm for large enough (∼10 3 ) Reynolds numbers. ii-The transport-dissipation correlation is not clearly or simply related to variations of the linear modes growth rates. iii-The existence of the transport-dissipation correlation depends neither on the number of linear modes captured in the simulations, nor on the effect of the parasitic modes on the saturation of the linear modes growth. iv-The transport is usually not dominated by axisymmetric (channel) modes.

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“…The transition has been assumed to be subcritical due to similarities with pipe flow transition, though Schultz-Grunow (1959) stated that the transition appeared to be similar to a Kelvin-Helmholtz instability. No first-principles theory exists for subcritical transition in a rotating shear flow, though recent efforts to identify such a transition mechanism can be found in Chagelishvili et al (2003); Tevzadze et al (2003); Yecko (2004); Umurhan & Regev (2004); Mukhopadhyay et al (2005); Afshordi et al (2005); Lithwick (2007); Rincon et al (2007); Lithwick (2009) ;; Mukhopadhyay & Saha (2011). Phenomenological models have been developed based on the assumption that the observed transition is subcritical in nature (Zeldovich 1981;Richard & Zahn 1999;Longaretti 2002;Dubrulle et al 2005).…”

Section: Introductionmentioning

confidence: 99%

Stability of quasi-Keplerian shear flow in a laboratory experiment

Schartman

Burin

et al. 2012

A&A

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Context. Subcritical transition to turbulence has been proposed as a source of turbulent viscosity required for the associated angular momentum transport for fast accretion in Keplerian disks. Previously cited laboratory experiments in supporting this hypothesis were performed either in a different type of flow than Keplerian or without quantitative measurements of angular momentum transport and mean flow profile, and all of them appear to suffer from Ekman effects, secondary flows induced by nonoptimal axial boundary conditions. Such Ekman effects are expected to be absent from astronomical disks, which probably have stress-free vertical boundaries unless strongly magnetized. Aims. To quantify angular momentum transport due to subcritical hydrodynamic turbulence, if exists, in a quasi-Keplerian flow with minimized Ekman effects. Methods. We perform a local measurement of the azimuthal-radial component of the Reynolds stress tensor in a novel laboratory apparatus where Ekman effects are minimized by flexible control of axial boundary conditions. Results. We find significant Ekman effects on angular momentum transport due to nonoptimal axial boundary conditions in quasiKeplerian flows. With the optimal control of Ekman effects, no statistically meaningful angular momentum transport is detected in such flows at Reynolds number up to two millions. Conclusions. Either a subcritical transition does not occur, or, if a subcritical transition does occur, the associated radial transport of angular momentum in optimized quasi-Keplerian laboratory flows is too small to directly support the hypothesis that subcritical hydrodynamic turbulence is responsible for accretion in astrophysical disks. Possible limitations in applying laboratory results to astrophysical disks due to experimental geometry are discussed.

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Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results

Cited by 123 publications

References 46 publications

Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites

Stability of quasi-Keplerian shear flow in a laboratory experiment

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