Boundary-layer turbulence in experiments on quasi-Keplerian flows

Lopez, José M.; Avila, Marc

doi:10.1017/jfm.2017.109

Cited by 35 publications

(27 citation statements)

References 47 publications

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“…Ji et al (2001) and Rüdiger & Zhang (2001) suggested the study of the MRI in an electrically conducting fluid sheared between two concentric cylinders, exactly as considered originally by Velikhov (1959) and Chandrasekhar (1961). By appropriately choosing the rotation ratio of the cylinders, velocity profiles of the general form w( ) r r q , including = -q 1.5 for Keplerian rotation, can be well approximated experimentally at very large Reynolds numbers (Edlund & Ji 2015;Lopez & Avila 2017). For an imposed axial magnetic field, Gellert et al (2012) found the transport coefficient α to be independent of magnetic Reynolds Rm and magnetic Prandtl Pm numbers, only scaling linearly with the Lundquist number S of the axial magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Transport Properties of the Azimuthal Magnetorotational Instability

Guseva

Willis

Hollerbach

et al. 2017

ApJ

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The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles w µ r q . We perform direct numerical simulations of a steep profile close to the Rayleigh line  -q 2 and a quasi-Keplerian profile » -q 3 2 and cover wide ranges of Reynolds ( Ŕe 4 10 4 ) and magnetic Prandtl numbers (   0 Pm 1). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with » Rm 50 c , and angular momentum transport scales as Pm Re 2 in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by Rm. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as Rm increases. For the profile close to the Rayleigh line, the instability shares these properties as long as 

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Section: Introductionmentioning

confidence: 99%

Transport Properties of the Azimuthal Magnetorotational Instability

Guseva

Willis

Hollerbach

et al. 2017

ApJ

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“…The conducting medium filling the gap between cylinders is usually a liquid metal (sodium, gallium) characterized by an extremely small ratio of viscosity to Ohmic resistivity, or magnetic Prandtl number, Pm 10 10 6 5 n h =~---. By suitably adjusting the rotation rates of outer and inner cylinders, the TC flow profile can be made very close to the Keplerian one [13][14][15][16], offering a unique possibility to study the disk MRI problem in laboratory as well, which has been up to now mostly carried out both via analytical means and numerical simulations. First experimental efforts to study MRI in the laboratory were made at the University of Maryland [17], at Princeton University [18,19], and at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow

et al. 2018

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Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)-a relative of the standard MRI-in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

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“…The Rayleigh criterion is admittedly a purely linear result and, thus, does not exclude the possibility of a nonlinear, finite-amplitude instability. Nevertheless, there are both experimental [7,8] and numerical [9][10][11][12][13] results which suggest that Keplerian rotation profiles are indeed stable even with respect to finite-amplitude perturbations.…”

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Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow

Guseva¹,

Hollerbach²,

Willis³

et al. 2017

Phys. Rev. Lett.

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We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy Ω o =Ω i ¼ ðr o =r i Þ −3=2 . In this quasi-Keplerian regime, a nonmagnetic system would be Rayleigh stable for all Reynolds numbers Re, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers Rm. For Re ¼ 10 4 and Rm ¼ 10 5 , we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses.

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Boundary-layer turbulence in experiments on quasi-Keplerian flows

Cited by 35 publications

References 47 publications

Transport Properties of the Azimuthal Magnetorotational Instability

Transport Properties of the Azimuthal Magnetorotational Instability

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow

Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow

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