Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells

Simitev, Radostin D.; Busse, Friedrich H.

doi:10.1017/s0022112005004398

Cited by 99 publications

(110 citation statements)

References 39 publications

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“…One of the main goals of the present paper is therefore to systematically study the effects of varying Prandtl numbers on the differential rotation and dynamo modes excited in the simulations. We note that similar parameter studies have been performed with Boussinesq simulations (e.g., Simitev & Busse 2005;Busse & Simitev 2006). Here we explore the stratified, fully compressible simulations and reach parameter regimes that are significantly more supercritical in terms of both the convection and the dynamo.…”

Section: Introductionmentioning

confidence: 63%

Convection-driven spherical shell dynamos at varying Prandtl numbers

Käpylä

Olspert

et al. 2017

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Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims. We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods. We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results. We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions. Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here.

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Section: Introductionmentioning

confidence: 63%

Convection-driven spherical shell dynamos at varying Prandtl numbers

Käpylä

Olspert

et al. 2017

A&A

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“…In a later paper [13] a particular case of bistability has been mentioned, but no further discussion was given. Transitions between states similar to MD and FD dynamos as a function of P or P/P m caused by the changing strength of the inertial forces have been reported in [11,23]. In the simulations of [13,22] and [23] no-slip boundary conditions for the velocity field have been employed and it is of interest to investigate whether, as we expect, the hysteresis phenomenon persist as the velocity boundary conditions and the heating model are changed.…”

mentioning

confidence: 87%

“…Many numerical studies following [5,6] have attempted a direct comparison with geomagnetic observations and have been remarkably successful in reproducing some of the main properties of the geomagnetic field [7,8] while others have focused on more systematic explorations of the computationally accessible parameter space e.g. [9][10][11][12][13]. Dynamos obtained through numerical simulations are usually turbulent and it is assumed that their time averaged properties are independent of the initial conditions once the computations have run for a sufficiently long time.…”

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confidence: 99%

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

2009

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PACS 91.25.Cw -Origins and models of the magnetic field; dynamo theories PACS 92.60.hk -Convection, turbulence, and diffusion PACS 47.20.Ky -Nonlinearity, bifurcation, and symmetry breaking Abstract. -Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity.

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“…Because the characteristic length scales, velocities, and thermal diffusivity vary throughout the radius of a star, the Rayleigh number and Reynolds number are not specified in a general sense for these simulations. We note that such nondimensional parameters can potentially affect convective heat transport (Ahlers & Xu 2001;Kerr & Herring 2000) and convection dynamo action (Simitev & Busse 2005). In MUSIC, numerical truncation errors contribute to both the viscosity and thermal diffusivity.…”

Section: Resolutionmentioning

confidence: 99%

Spherical-shell boundaries for two-dimensional compressible convection in a star

Pratt

Baraffe

Goffrey

et al. 2016

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Context. Studies of stellar convection typically use a spherical shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, such as our sun at 10 6 years of age. Aims. We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple smaller-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods. We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results. To measure the impact of the spherical shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so-called 321D link. We find that the inclusion in the spherical shell of the boundary between the radiative and convection zones decreases the amplitude of convective velocities in the convection zone. The inclusion of near-surface layers in the spherical shell can increase the amplitude of convective velocities, although the radial structure of the velocity profile established by deep convection is unchanged. The impact from including the near-surface layers depends on the speed and structure of small-scale convection in the near-surface layers. Larger convective velocities in the convection zone result in a commensurate increase in the overshooting layer width and decrease in the convective turnover time. These results provide support for non-local aspects of convection.

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Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells

Cited by 99 publications

References 39 publications

Convection-driven spherical shell dynamos at varying Prandtl numbers

Convection-driven spherical shell dynamos at varying Prandtl numbers

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

Spherical-shell boundaries for two-dimensional compressible convection in a star

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