Angular Momentum Transport in Convectively Unstable Shear Flows

Käpylä, Petri J.; Brandenburg, Axel; Korpi, M. J.; Snellman, Jan; Narayan, Ramesh

doi:10.1088/0004-637x/719/1/67

Cited by 12 publications

(17 citation statements)

References 34 publications

(57 reference statements)

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“…We see that Λ V is negative in most of the convection zone, which is in agreement with the findings from the first-order smoothing approximation (Kitchatinov & Rüdiger 1995, 2005, and with earlier numerical studies (e.g., Pulkkinen et al 1993;Käpylä et al 2004Käpylä et al , 2014Rüdiger et al 2005;Käpylä & Brandenburg 2008). However, for Run E with SL rotation, Λ V is positive at low latitudes and does not change much from maximum to minimum, which is why we show in Another important property is that Λ V is of the same order as ν t , which is consistent with earlier findings (Käpylä et al 2010a). We find that Λ H is positive for both Runs A and E, which is again in agreement with the analytical results.…”

Section: Turbulent Angular Momentum Transportsupporting

confidence: 92%

Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles

Karak

Käpylä

et al. 2015

A&A

149

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Context. Late-type stars rotate differentially owing to anisotropic turbulence in their outer convection zones. The rotation is called solar-like (SL) when the equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations show a transition from SL to AS rotation as the influence of rotation on convection is reduced, but the opposite transition occurs at a different point in the parameter space. The system is bistable, i.e., SL and AS rotation profiles can both be stable. Aims. We study the effect of a dynamo-generated magnetic field on the large-scale flows, particularly on the possibility of bistable behaviour of differential rotation. Methods. We solve the hydromagnetic equations numerically in a rotating spherical shell that typically covers ±75• latitude (wedge geometry) for a set of different radiative conductivities controlling the relative importance of convection. We analyse the resulting differential rotation, meridional circulation, and magnetic field and compare the corresponding modifications of the Reynolds and Maxwell stresses. Results. In agreement with earlier findings, our models display SL rotation profiles when the rotational influence on convection is strong and a transition to AS when the rotational influence decreases. We find that dynamo-generated magnetic fields help to produce SL differential rotation compared to the hydrodynamic simulations. We do not observe any bistable states of differential rotation. In the AS cases we find coherent single-cell meridional circulation, whereas in SL cases we find multi-cellular patterns. In both cases, we obtain poleward circulation near the surface with a magnitude close to that observed in the Sun. In the slowly rotating cases, we find activity cycles, but no clear polarity reversals, whereas in the more rapidly rotating cases irregular variations are obtained. Moreover, both differential rotation and meridional circulation have significant temporal variations that are similar in strength to those of the Sun. Conclusions. Purely hydrodynamic simulations of differential rotation and meridional circulation are shown to be of limited relevance as magnetic fields, self-consistently generated by dynamo action, significantly affect the flows.

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Section: Turbulent Angular Momentum Transportsupporting

confidence: 92%

Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles

Karak

Käpylä

et al. 2015

A&A

149

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“…A reasonable fit within the convection zone is obtained if the Strouhal number is around 1.6 which is consistent with previous results from convection (e.g. Käpylä et al 2010b). Note that the ratio χ t /χ t0 gives a measure of the Strouhal number because in the general case χ t0 = 1 3 τ c u 2 rms = Stu rms /(3k f ), whereas in the main panel of Fig.…”

Section: Turbulent Heat Transportsupporting

confidence: 90%

“…Rüdiger (1989). However, disentangling the two contributions is not possible, see e.g., Snellman et al (2009) and Käpylä et al (2010b). We postpone a detailed study of the turbulent transport coefficients to a future study and concentrate on comparing the total stress with simulations in Cartesian geometry.…”

Section: Reynolds Stressmentioning

confidence: 99%

“…We find that the value of χ t is almost ten times the reference value. The apparently large value is most likely due to the normalization factor which is based on a volume average of the rms velocity and a more or less arbitrary length scale k −1 f (see also Käpylä et al 2010b). The sharp peaks and negative values of χ t towards the bottom and top of the convectively unstable region reflect the sign change of the entropy gradient which is not captured by Eq.…”

Section: Turbulent Heat Transportmentioning

confidence: 99%

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Reynolds stress and heat flux in spherical shell convection

Käpylä

Mantere

Gómez

et al. 2011

A&A

122

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Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims. Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

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“…In addition, the relative contribution between large and small scale fields is also unclear (Blackman 2012) and not yet comprehensively captured in existing simulations. In fact, even the question of when magnetic fields are needed at all in non-self-gravitating disks still lingers (Balbus 2011;Käpylä et al 2010).…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations of Z-Pinch Experiments to Create Supersonic Differentially Rotating Plasma Flows

Bocchi

Ummels

Chittenden

et al. 2013

ApJ

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The physics of accretion disks is of fundamental importance for understanding of a wide variety of astrophysical sources that includes protostars, X-ray binaries, and active galactic nuclei. The interplay between hydrodynamic flows and magnetic fields and the potential for turbulence-producing instabilities is a topic of active research that would benefit from the support of dedicated experimental studies. Such efforts are in their infancy, but in an effort to push the enterprise forward we propose an experimental configuration which employs a modified cylindrical wire array Z-pinch to produce a rotating plasma flow relevant to accretion disks. We present three-dimensional resistive magnetohydrodynamic simulations which show how this approach can be implemented. In the simulations, a rotating plasma cylinder or ring is formed, with typical rotation velocity ∼30 km s −1 , Mach number ∼4, and Reynolds number in excess of 10 7 . The plasma is also differentially rotating. Implementation of different external magnetic field configurations is discussed. It is found that a modest uniform vertical field of 1 T can affect the dynamics of the system and could be used to study magnetic field entrainment and amplification through differential rotation. A dipolar field potentially relevant to the study of accretion columns is also considered.

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Angular Momentum Transport in Convectively Unstable Shear Flows

Cited by 12 publications

References 34 publications

Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles

Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles

Reynolds stress and heat flux in spherical shell convection

Numerical Simulations of Z-Pinch Experiments to Create Supersonic Differentially Rotating Plasma Flows

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