Reynolds stresses from hydrodynamic turbulence with shear and rotation

Snellman, Jan; Käpylä, Petri J.; Korpi, M. J.; Liljeström, A. J.

doi:10.1051/0004-6361/200912653

Cited by 23 publications

(49 citation statements)

References 48 publications

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“…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%

Reynolds stress and heat flux in spherical shell convection

Käpylä

Mantere

Gómez

et al. 2011

A&A

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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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Section: Reynolds Stressmentioning

confidence: 99%

Reynolds stress and heat flux in spherical shell convection

Käpylä

Mantere

Gómez

et al. 2011

A&A

Self Cite

122

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“…Furthermore, the subgrid-scale models need to be validated by comparing their results with local numerical simulations (e.g. Snellman et al 2009;Garaud et al 2010).…”

Section: Unresolved Effects Of Turbulencementioning

confidence: 99%

On global solar dynamo simulations

Käpylä¹

2011

Astron Nachr

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Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age-old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucual role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large-scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean-field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some of the current issues of the solar simulations are put forward.

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“…Dynamical equations that incorporate magnetic helicity evolution and employ "minimal τ " closure (e.g. , see also Snellman et al 2009 applied to shear flows) capture MFD saturation. In accretion theory however, there are few models that use anything other than the single diffusion coefficient of the SS73 formalism.…”

Section: Standard Accretion Theory Is a Mean Field Theorymentioning

confidence: 99%

Accretion disks and dynamos: toward a unified mean field theory

Blackman

2012

Phys. Scr.

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Conversion of gravitational energy into radiation near stars and compact objects in accretion disks and the origin of large scale magnetic fields in astrophysical rotators have often been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such ongoing pursuits. Twenty-first century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are really artificially separated pieces of what should ultimately be a single coupled theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small scale magnetic fluctuations, without appealing to the traditional kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, it is important to study each disk hemisphere separately to avoid being potentially misled by the cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still play a fundamental role in large scale dynamo action.

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Reynolds stresses from hydrodynamic turbulence with shear and rotation

Cited by 23 publications

References 48 publications

Reynolds stress and heat flux in spherical shell convection

Reynolds stress and heat flux in spherical shell convection

On global solar dynamo simulations

Accretion disks and dynamos: toward a unified mean field theory

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