Turbulent Rayleigh–Bénard convection in spherical shells

Gastine, T.; Wicht, Johannes; Aurnou, J. M.

doi:10.1017/jfm.2015.401

Cited by 66 publications

(116 citation statements)

References 85 publications

Supporting

Mentioning

108

Contrasting

Order By: Relevance

“…This scaling appears as a common feature of high-Ra convection in the laboratory setup (see e.g., Ahlers et al 2009 and references therein). Moreover, Boussinesq studies carried out using spherical geometry and symmetric, fixed-temperature boundary conditions (in lieu of internal heating) have demonstrated a similar scaling relationship (Gastine et al 2015).…”

Section: Interpretation Of the Kinetic-energy Scalingmentioning

confidence: 77%

The Spectral Amplitude of Stellar Convection and Its Scaling in the High-Rayleigh-Number Regime

Featherstone

Hindman

2016

ApJ

102

View full text Add to dashboard Cite

Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owingto this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star's interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimatedand high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

show abstract

Section: Interpretation Of the Kinetic-energy Scalingmentioning

confidence: 77%

The Spectral Amplitude of Stellar Convection and Its Scaling in the High-Rayleigh-Number Regime

Featherstone

Hindman

2016

ApJ

102

View full text Add to dashboard Cite

show abstract

“…It can be argued that these two systems, disparate in terms of geometry and Rm o values, cannot be meaningfully related (cf. [29]). However, this intercomparison is ubiquitously made in the dynamo literature when considerations of magnetostrophic balance are put forth.…”

Section: Introductionmentioning

confidence: 99%

The cross-over to magnetostrophic convection in planetary dynamo systems

Aurnou

King²

2017

Proc. R. Soc. A.

View full text Add to dashboard Cite

A contribution to the special feature 'Perspectives in astrophysical and geophysical fluids' . is the system scale magnetic Reynolds number and D is the length scale of the system. On scales well above L X , magnetostrophic convection dynamics should not be possible. Only on scales smaller than L X should it be possible for the convective behaviours to follow the predictions for the magnetostrophic branch of convection. Because L X is significantly smaller than the system scale in most dynamo models, their large-scale flows should be quasi-geostrophic, as is confirmed in many dynamo simulations. Estimating Λ o 1 and Rm o 10 3 in Earth's core, the cross-over scale is approximately 1/1000 that of the system scale, suggesting that magnetostrophic convection dynamics exists in the core only on small scales below those that can be characterized by geomagnetic observations.

show abstract

“…with a scaling exponent that is approximately 2/7 (∼ 0.286). Other studies have found that the Nusselt number scales with the Rayleigh number to the 2/9 power (∼ 0.222) (e.g., Gastine et al 2015), when a flux based Rayleigh number is used. Our results have a steeper exponent because we include the viscous flux and the kinetic energy flux, which act to increase 1/ (1 − f conv ) at any given Rayleigh number.…”

Section: Energy Transportmentioning

confidence: 99%

Prandtl-number Effects in High-Rayleigh-number Spherical Convection

Orvedahl

Calkins

Featherstone

et al. 2018

ApJ

View full text Add to dashboard Cite

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number Pr = ν/κ, where ν is the kinematic viscosity and κ is the thermal diffusion; in stars, Pr is extremely low, Pr ≈ 10 −7 . The influence of Pr on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using Pr ≈ 1. We systematically vary Pr and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower Pr generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in Pr. Importantly, we find that Pr plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

show abstract

Turbulent Rayleigh–Bénard convection in spherical shells

Cited by 66 publications

References 85 publications

The Spectral Amplitude of Stellar Convection and Its Scaling in the High-Rayleigh-Number Regime

The Spectral Amplitude of Stellar Convection and Its Scaling in the High-Rayleigh-Number Regime

The cross-over to magnetostrophic convection in planetary dynamo systems

Prandtl-number Effects in High-Rayleigh-number Spherical Convection

Contact Info

Product

Resources

About