On Turbulent Heat Transport in Rotating Convective Zones

Rüdiger, G.

doi:10.1002/asna.2103030505

Cited by 12 publications

(4 citation statements)

References 26 publications

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“…In this regime, the anti-correlation between zonal flows and heat flux which usually characterises the strongest pole/equator luminosity contrasts vanishes. Interestingly, we note that the observation of a uniform energy flux density coexisting with the non-uniform rotation of the solar surface was at the heart of the so-called heat-flux problem in theories aimed at explaining the Sun's differential rotation (Rüdiger 1982). Rast et al (2008) indeed report a weak ≈0.1 % enhancement of the solar intensity at polar latitudes.…”

Section: Resultsmentioning

confidence: 84%

Gravity darkening in late-type stars

Raynaud

Rieutord

Petitdemange

et al. 2018

A&A

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Context. Recent interferometric data have been used to constrain the brightness distribution at the surface of nearby stars, in particular the so-called gravity darkening that makes fast rotating stars brighter at their poles than at their equator. However, good models of gravity darkening are missing for stars that posses a convective envelope. Aims. In order to better understand how rotation affects the heat transfer in stellar convective envelopes, we focus on the heat flux distribution in latitude at the outer surface of numerical models. Methods. We carry out a systematic parameter study of three-dimensional, direct numerical simulations of anelastic convection in rotating spherical shells. As a first step, we neglect the centrifugal acceleration and retain only the Coriolis force. The fluid instability is driven by a fixed entropy drop between the inner and outer boundaries where stress-free boundary conditions are applied for the velocity field. Restricting our investigations to hydrodynamical models with a thermal Prandtl number fixed to unity, we consider both thick and thin (solar-like) shells, and vary the stratification over three orders of magnitude. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity. Results. We report diverse Nusselt number profiles in latitude, ranging from brighter (usually at the onset of convection) to darker equator and uniform profiles. We find that the variations of the surface brightness are mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the dynamics, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. In the presence of a strong background density stratification however, as expected in real stars, the increase of the local Rossby number in the outer layers leads to uniformisation of the surface heat flux distribution.

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Section: Resultsmentioning

confidence: 84%

Gravity darkening in late-type stars

Raynaud

Rieutord

Petitdemange

et al. 2018

A&A

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“…In addition to the Reynolds stresses, such models could be used to study anisotropic turbulent heat transport (e.g. Rüdiger 1982;Kitchatinov et al 1994;Kleeorin & Rogachevskii 2006). Furthermore, these models could help in answering how some enigmatic results of local convection simulations, such as the narrow regions of very strong stresses near the equator (Chan 2001;Käpylä et al 2004;Rüdiger et al 2005) in the rapid rotation regime, can be explained.…”

Section: Discussionmentioning

confidence: 99%

Reynolds stresses from hydrodynamic turbulence with shear and rotation

Snellman¹,

Käpylä

Korpi³

et al. 2009

A&A

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Aims. We study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation. Methods. Three-dimensional numerical simulations are used to study turbulent transport under the influences of large-scale shear and rotation in homogeneous, isotropically forced turbulence. We study three cases: one with only shear, and two others where in addition to shear, rotation is present. These cases differ by the angle (0 or 90• ) the rotation vector makes with respect to the z-direction. Two subsets of runs are performed with both values of θ where either rotation or shear is kept constant. When only shear is present, the off-diagonal stress can be described by turbulent viscosity whereas if the system also rotates, nondiffusive contributions (Λ-effect) to the stress can arise. Comparison of the direct simulations are made with analytical results from a simple closure model. Results. We find that the turbulent viscosity is of the order of the first order smoothing result in the parameter regime studied and that for sufficiently large Reynolds numbers the Strouhal number, describing the ratio of correlation to turnover times, is roughly 1.5. This is consistent with the closure model based on the minimal tau-approximation which produces a reasonable fit to the simulation data for similar Strouhal numbers. In the cases where rotation is present, separating the diffusive and nondiffusive components of the stress turns out to be challenging but taking the results at face value, we can obtain nondiffusive contributions of the order of 0.1 times the turbulent viscosity. We also find that the simple closure model is able to reproduce most of the qualitative features of the numerical results provided that the Strouhal number is of the order of unity.

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“…Much effort has been put into computing these correlations using analytical theories (e.g., Rüdiger 1980Rüdiger , 1982Kitchatinov & Rüdiger 1993;Kitchatinov et al 1994). Most of the analytical studies, however, rely on approximations such as first-order smoothing, the applicability of which in the stellar environments can be contested.…”

Section: Introductionmentioning

confidence: 99%

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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On Turbulent Heat Transport in Rotating Convective Zones

Cited by 12 publications

References 26 publications

Gravity darkening in late-type stars

Gravity darkening in late-type stars

Reynolds stresses from hydrodynamic turbulence with shear and rotation

Reynolds stress and heat flux in spherical shell convection

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