Examination of Scaling Relationships Involving Penetration Distance at the Bottom of a Stellar Convective Envelope

Saikia, Eeshankur; Singh, Harinder P.; Chan, Kalok; Roxburgh, I. W.; Srivastava, M. P.

doi:10.1086/308249

Cited by 27 publications

(33 citation statements)

References 18 publications

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“…The calculation of the extent of the penetration into the upper stable layer has been based on time-and horizontally averaged kinetic flux (F k ). Such a choice is obvious as the kinetic flux is directly related with the motions and the profile is also convenient for estimation of the extent of penetration (Hurlburt et al 1986, Hurlburt et al 1994, Singh et al 1994, Saikia et al 2000, Pal et al 2007). We illustrate this point by plotting the distribution of kinetic energy flux for several sets of models in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The general behaviour of convective transport in a stellar-type setting has been studied using Large Eddy Simulation (LES) approach by several groups (Chan & Sofia 1986, Hossain & Mullan 1991, Muthsam et al 1995, Singh & Chan 1993, Singh et al 1994, 1996, 1998a,b, 2001Saikia et al 2000, Chan 2001, Pal et al 2007). LES, being less demanding on speed and memory as it can have a coarser grid, allows large scale flows to be modeled explicitly while the smaller scales are modeled by some sort of sub-grid scale formulation (Smagorinsky 1963).…”

Section: Parameters Of Computed Modelsmentioning

confidence: 99%

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Turbulent compressible convection with rotation—penetration above a convection zone

Pal

Singh

Chan

et al. 2008

Astrophys Space Sci

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We perform Large eddy simulations of turbulent compressible convection in stellar-type convection zones by solving the Naviér-Stokes equations in three dimensions. We estimate the extent of penetration into the stable layer above a stellar-type convection zone by varying the rotation rate (Ω), the inclination of the rotation vector (θ) and the relative stability (S) of the upper stable layer The computational domain is a rectangular box in an f-plane configuration and is divided into two regions of unstable and stable stratification with the stable layer placed above the convectively unstable layer. Several models have been computed and the penetration distance into the stable layer above the convection zone is estimated by determining the position where time averaged kinetic energy flux has the first zero in the upper stable layer. The vertical grid spacing in all the model is non-uniform, and is less in the upper region so that the flows are better resolved in the region of interest. We find that the penetration distance increases as the rotation rate increases for the case when the rotation vector is aligned with the vertical axis. However, with the increase in the stability of the upper stable layer, the upward penetration distance decreases. Since we are not able to afford computations with finer resolution for all the models, we compute a number of models to see the effect of increased resolution on the upward penetration. In addition, we estimate the upper limit on the upward convective penetration from stellar convective cores.

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Section: Resultsmentioning

confidence: 99%

Section: Parameters Of Computed Modelsmentioning

confidence: 99%

Turbulent compressible convection with rotation—penetration above a convection zone

Pal

Singh

Chan

et al. 2008

Astrophys Space Sci

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“…Direct numerical simulations using the anelastic approximation rather than compressible convection have also been performed in a twodimensional cylindrical geometry (Rogers & Glatzmaier 2005;Rogers et al 2006); these works used a realistic stellar stratification rather than a polytropic stratification, but the thermal diffusivity was artificially increased. Several other early studies have produced large eddy simulations, typically using a standard Smagorinsky subgrid scale model, in a local domain with Cartesian geometry (Xie & Toomre 1993;Singh et al 1995Singh et al , 1998Saikia et al 2000;Pal et al 2007). Direct numerical simulation is a sensible choice when the focus is dynamo action, because when a magnetic field is present, small-scale motions feed back on large scale motions in ways that are not completely understood (Miesch et al 2015).…”

Section: Introductionmentioning

confidence: 99%

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

Pratt

Baraffe

Goffrey

et al. 2016

A&A

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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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“…Direct numerical simulations of convective penetration then is the only alternative to estimate penetration depths. Such calculations have been performed in the past by several authors in two space dimensions (Cattaneo et al 1990;Xie & Toomre 1993;Hurlburt et al 1994) and, more recently, in three space dimensions (Singh et al 1996;Nordlund & Stein 1996;Singh et al 1998a,b;Saikia et al 2000).…”

Section: Introductionmentioning

confidence: 99%

Box simulations of rotating magnetoconvection

Ziegler

Rüdiger

2003

A&A

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Abstract. Various effects of penetration in rotating magnetoconvection are studied by means of three-dimensional numerical simulations employing the code NIRVANA. A local, 2-layer model is applied dividing the computational domain (which is a rectangular box placed tangentially on a sphere at latitude 45• ) in an unstable polytropic region on top of a stable polytropic region. Different realizations of convection are examined parameterized by Taylor numbers Ta = {0, 6×10 4 , 6×10 5 } and magnetic field strengths β = {5, 50, 500, 5000, ∞}. We find a rather distinctive behavior of the penetration depth ∆ on the system parameters (Ta, β). In non-rotating convection ∆ is a monotonically decreasing function of β −1 which is due to magnetic quenching effects. Also, penetration is subject to rotational quenching, i.e. ∆ is reduced for increasing rotation rate. In the intermediate regime of (Ta, β), the effects of rotation and magnetic field on ∆ do not simply add (see Fig. 3). We find, nevertheless, a very strong reduction of the penetration depth of overshooting turbulence by both rotation and magnetism. Penetrative convection is closely associated with the mixing of a passive scalar quantity advected with the flow. In the long term, the tracer material penetrates significantly deeper into the stable layer than suggested by ∆ which is due to the cumulative effect of isolated, fast-moving plumes. In case of a weak magnetic field, penetrative convection also serves to ensure a downward transport of magnetic flux by turbulent pumping with an average rate γ z ≈ −7 × 10 −3 measured in units of the sound speed at the top z-boundary. For larger magnetic fields the pumping effect is quenched and even changes sign in the convection zone. This effect is suggested as being due to the effect of "turbulent buoyancy" which in density-stratified media transports a given magnetic field upwards if it is not too strong (Kichatinov & Rüdiger 1992).

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Examination of Scaling Relationships Involving Penetration Distance at the Bottom of a Stellar Convective Envelope

Cited by 27 publications

References 18 publications

Turbulent compressible convection with rotation—penetration above a convection zone

Turbulent compressible convection with rotation—penetration above a convection zone

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

Box simulations of rotating magnetoconvection

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