Turbulent Convection under the Influence of Rotation: Sustaining a Strong Differential Rotation

By A. Brun, J. Toomre. 2002

262 citations recorded by the source corpus.

The intense turbulence present in the solar convection zone is a major challenge to both theory and simulation as one tries to understand the origins of the striking differential rotation profile with radius and latitude that has been revealed by helioseismology. The differential rotation must be an essential element in the operation of the solar magnetic dynamo and its cycles of activity, yet there are many aspects of the interplay between convection, rotation, and magnetic fields that are still unclear. We have here carried out a series of three-dimensional numerical simulations of turbulent convection within deep spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. These studies of the global dynamics of the solar convection zone concentrate on how the differential rotation and meridional circulation are established. We have addressed two issues raised by previous simulations with ASH. First, can solutions be obtained that possess the apparent solar property that the angular velocity Ω continues to decrease significantly with latitude as the pole is approached? Prior simulations had most of their rotational slowing with latitude confined to the interval from the equator to about 45°. Second, can a strong latitudinal angular velocity contrast ΔΩ be sustained as the convection becomes increasingly more complex and turbulent? There was a tendency for ΔΩ to diminish in some of the turbulent solutions that also required the emerging energy flux to be invariant with latitude. In responding to these questions, five cases of increasingly turbulent convection coupled with rotation have been studied along two paths in parameter space. We have achieved in one case the slow pole behavior comparable to that deduced from helioseismology and have retained in our more turbulent simulations a consistently strong ΔΩ. We have analyzed the transport of angular momentum in establishing such differential rotation and clarified the roles played by Reynolds stresses and the meridional circulation in this process. We have found that the Reynolds stresses are crucial in transporting angular momentum toward the equator. The effects of baroclinicity (thermal wind) have been found to have a modest role in the resulting mean zonal flows. The simulations have produced differential rotation profiles within the bulk of the convection zone that make reasonable contact with ones inferred from helioseismic inversions, namely, possessing a fast equator, an angular velocity difference of about 30% from equator to pole, and some constancy along radial lines at midlatitudes. Future studies must address the implications of the tachocline at the base of the convection zone, and the near-surface shear layer, on that differential rotation.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/a3da72dacca650b621cc22cb6b2b7ac19f6d563e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Molecular Biology

Citations in the corpus

Structure and Evolution of Giant Cells in Global Models of Solar Convection (2007, methodology): “…parameter sensitivities, convective structure and transport, the maintenance of differential rotation and meridional circulation, and hydromagnetic dynamo processes (Miesch et al. 2000; Elliott et al. 2000; Brun & Toomre 2002; Brun et al. 2004; Miesch et al. 2006; Browning et al. 2006).”
Simulations of Core Convection in Rotating A-Type Stars: Differential Rotation and Overshooting (2003, background): “As dis- cussed in Brun & Toomre (2002), such a balance effectively implies that @v̂ @z ¼ 1 2 0̂cP rŜ rp̂ ¼ g 2 0rcP @Ŝ @ ; ð16Þ where z is parallel to the rotation axis.”
The Internal Rotation of the Sun (2003, methodology): “In recent years, high-resolution simulations of rotating convection in full spherical shells have achieved more turbulent parameter regimes, utilizing spherical harmonicYml expansions up to degreel ∼ 680 (Brun & Toomre 2002, Elliott, Miesch & Toomre 2000, Miesch et al. 2000).”
The standard flare model in three dimensions II: upper limit on solar flare energy (2012, background): “Since those motions are always present because of the solar internal structure (Brun & Toomre 2002), it is difficult to imagine that the Sun will ever produce a large sunspot group consisting of a single pair of giant sunspots.”
Solar Differential Rotation and Meridional Flow: The Role of a Subadiabatic Tachocline for the Taylor-Proudman Balance (2005, methodology): “…is sponsored by the National Science Foundation Electronic address: rempel@hao.ucar.edu Even though recent results by Miesch et al. (2000) and Brun & Toomre (2002) show improvement, the simulations still have problems in reproducing the radial gradient of the differential within the…”
Torsional Oscillation, Meridional Flows, and Vorticity Inferred in the Upper Convection Zone of the Sun by Time-Distance Helioseismology (2004, background): “Some numerical simulations (Brun & Toomre 2002; DeRosa, Gilman, & Toomre 2002) of the multiscale turbulent convection inside the solar convection zone aimed to determine how the differential rotation, torsional oscillation, and meridional flows are sustained, and how these global features are…”
Magnetic Field Generation in Fully Convective Rotating Spheres (2004, background): “Recent simulations still predict angular velocity to be roughly constant on cylinders, although some simulations show at least a tendency toward solar-like angular velocity contours (Miesch et al. 2000; Brun & Toomre 2002).”
Dynamo Action in the Solar Convection Zone and Tachocline: Pumping and Organization of Toroidal Fields (2006, background): “Fairly broad, low-amplitude upflows coexist with fast, concentrated downflows, which are characteristic of turbulent compressible convection (e.g., Brun & Toomre 2002; BMT04; Brummell et al. 2002).”
Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope (2004, methodology): “…using the anelastic spherical harmonic (ASH) code on massively-parallel supercomputers (e.g., Miesch et al. 2000; Elliott, Miesch & Toomre 2000; Brun & Toomre 2002) has permitted attaining fairly turbulent states of convection in which the resulting Ω profiles now begin to capture many…”
Solar Differential Rotation Influenced by Latitudinal Entropy Variations in the Tachocline (2006, methodology): “Depending on the parameter regime, this latitudinally dependent convective heat flux can be considerable and can produce a substantial thermal wind differential rotation that is roughly conical in nature much as in the Sun (Elliott et al. 2000; Robinson & Chan 2001; Brun & Toomre 2002).”
Flux-Transport Dynamos with Lorentz Force Feedback on Differential Rotation and Meridional Flow: Saturation Mechanism and Torsional Oscillations (2006, background): “…been addressed in the past mainly through two approaches: 3D full spherical shell simulations (Glatzmaier & Gilman 1982; Gilman & Miller 1986; Miesch et al. 2000; Brun & Toomre 2002) and axisymmetric meanfield models (Kitchatinov & Rüdiger 1993, 1995; Rüdiger et al. 1998; Küker & Stix 2001).”
MAGNETIC CYCLES IN A CONVECTIVE DYNAMO SIMULATION OF A YOUNG SOLAR-TYPE STAR (2011, background): “The differential rotation profiles realized in these rapidly rotating simulations are substantially in thermal wind balance (e.g., Brun & Toomre 2002; Miesch et al. 2006; Brown et al. 2008), though large departures do arise near the inner and outer boundaries where Reynolds stresses and boundary…”
Simulations of Dynamo Action in Fully Convective Stars (2007, methodology): “We are somewhat encouraged by prior simulations of convection in the solar interior in comparable parameter regimes (Brun & Toomre 2002; Brun, Browning & Toomre 2005; Browning et al. 2006), for these have been relatively successful in matching the detailed observational constraints on, e.g., solar…”