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

2002 ◽  
Vol 570 (2) ◽  
pp. 865-885 ◽  
Author(s):  
Allan Sacha Brun ◽  
Juri Toomre
Keyword(s):  
Differential Rotation ◽  
Turbulent Convection

scholarly journals The Boussinesq approximation in rapidly rotating flows

2013 ◽  
Vol 737 ◽  
pp. 56-77 ◽  
Author(s):  
Jose M. Lopez ◽  
Francisco Marques ◽  
Marc Avila
Keyword(s):  
Differential Rotation ◽  
Fluid Flows ◽  
Boussinesq Approximation ◽  
Accretion Disc ◽  
Rotating Flows ◽  
Turbulent Convection ◽  
Rotating Cylinders ◽  
New Approach ◽  
Type Approximation ◽  
Straightforward Approach

AbstractIn commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. Here we provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. Its application to the accretion-disc problem is discussed. We numerically compare the new approach to the typical one in fluid flows confined between two differentially heated and rotating cylinders. The results justify the need of using the proposed approximation in rapidly rotating flows.

scholarly journals Solar Differential Rotation Revealed by Helioseismology and Simulations of Deep Shells of Turbulent Convection

2004 ◽  
Vol 215 ◽  
pp. 326-331
Author(s):  
Juri Toomre ◽  
Allan Sacha Brun
Keyword(s):  
Differential Rotation ◽  
Magnetic Activity ◽  
Solar Interior ◽  
Turbulent Convection ◽  
Theoretical Modelling ◽  
Dynamo Action ◽  
Diverse Range ◽  
Dynamical Coupling ◽  
Weak Winds ◽  
Distinguishing Features

The sun is supposedly a very simple star, halfway along its long and possibly boring life on the main sequence. Yet it has some distinguishing features. Since we live close to it, our existence is probably blessed by this star having only modest cycles of magnetic activity and weak winds. By being so close, we can observe many aspects of the diverse range of motions and magnetic fields linked to turbulent convection in its convection zone. And this turns out to be anything but simple as we consider the dynamical coupling of convection, rotation and magnetism within this modest star. The lessons that have emerged from recent helioseismic probing of the solar interior and from 3–D numerical simulations of turbulent convection have bearing on differential rotation and magnetic dynamo action also occurring within more complex stars. We consider recent findings from both helioseismology and theoretical modelling on the operation of the deep shell of vigorous convection within our nearest star.

scholarly journals On Theories of Solar Rotation

1976 ◽  
Vol 71 ◽  
pp. 243-295 ◽  
Author(s):  
B. R. Durney
Keyword(s):  
Angular Velocity ◽  
Differential Rotation ◽  
Large Scale ◽  
Convection Zone ◽  
Solar Rotation ◽  
Turbulent Convection ◽  
Viscosity Approximation ◽  
Coriolis Forces ◽  
Solar Differential Rotation ◽  
Stabilizing Effect

The main theories of solar rotation are critically reviewed.The interaction of large-scale convection with rotation gives rise to a transport of angular momentum towards the equator and therefore to differential rotation with equatorial acceleration. (Large-scale convection is defined as follows: in a highly turbulent fluid, the small-scale turbulence acts as a viscosity and organizes fluid motions on a much larger scale.) This transport of angular momentum towards the equator arises because of the highly non-axisymmetric character of the large-scale convective motions in the presence of rotation. These motions tend to be concentrated near the equator. It is not surprising, therefore, that for magnitudes of large-scale convection which are needed to generate the observed solar differential rotation, largeand unobservedpole-equator differences in flux appear in the Boussinesq approximation.It is important, therefore, to take the variations in density into account. Studies of large-scale convection in a compressible rotating medium are still in a very early stage; these studies suggest, however, that the surface layers must indeed rotate differentially.The interaction of rotation with convection appears to be especially efficient in generating a pole-equator difference in flux,Such adrives meridional motions, and the action of Coriolis forces on these motions gives rise to differential rotation. In the ‘large-viscosity’ approximation the problem separates; the meridional motions can be determined first (from the radial and latitudinal equations of motions, and the energy equation) and the angular velocity can be determined next from the azimuthal equation of motion. Since very little is known about compressible large-scale convection, it has been assumed in the development of this theory that the stabilizing effect of rotation onturbulent convectiondepends on the polar angle θ and on depth. The solution for the angular velocity in the large viscosity approximation gives a differential rotation that varies slowly with depth. As a consequence, the large viscosity approximation is not valid over most of the convection zone, the Coriolis term being larger than the viscous term; a thin layer at the top excepted. (It appears, however, that if the angular velocity, ω, is a slowly varying function of depth and the azimuthal stresses vanish at both ends of the convection zone, then the general behavior of ω will be very much like that predicted by the large viscosity approximation.)The stabilizing effect of rotation on turbulent convection is neglected; if differential rotation is significant over the entire convection zone, and if the meridional and large-scale convective velocities are not too large, then in the radial and latitudinal equations of motion, the main balance of forces is between pressure gradients, buoyancy and Coriolis forces. If rotation is not constant along cylinders, then the differential rotation gives rise to latitudinal variations in the convective flux which are proportional to(whereTis the temperature andgis gravity). In the lower part of the convection zone,is of the order of the superadiabatic gradient itself. Therefore large pole-equator differences in flux,will be present unless the angular velocity is constant along cylinders. The meridional velocities associated with this rotation law are not small, however, and could generate a significantIt could well be that larges can be avoided only if rotation is uniform in the lower part of the convection zone. (To be certain of these results, however, it is important to estimate the magnitude of the stabilizing effect of rotation on turbulent convection.)Turbulent convection is driven by the buoyancy force which thus introduces a preferred direction: gravity. In consequence, the turbulence in the sun should be anisotropic and if this is the case the convection zone cannot rotate uniformly. The degree of anisotropy is not known and must be determined from the observed solar differential rotation. The anisotropy is such that the horizontal exchange of momentum is larger than the vertical.The normal mode of vibrations and the inner rotation of the Sun are briefly discussed.

scholarly journals Turbulent Convection and Subtleties of Differential Rotation Within the Sun

2001 ◽  
Vol 203 ◽  
pp. 131-143 ◽  
Author(s):  
J. Toomre ◽  
A. S. Brun ◽  
M. DeRosa ◽  
J. R. Elliott ◽  
M. S. Miesch
Keyword(s):  
Differential Rotation ◽  
Convection Zone ◽  
Numerical Models ◽  
Dynamical Behavior ◽  
Zonal Flow ◽  
Temporal Variations ◽  
Turbulent Convection ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Strong Shear

The solar convection zone exhibits a differential rotation with radius and latitude that poses major theoretical challenges. Helioseismology has revealed that a smoothly varying pattern of decreasing angular velocity Ω with latitude long evident at the surface largely prints through much of the convection zone, encountering a region of strong shear called the tachocline at its base, below which the radiative interior is nearly in uniform solid body rotation. Helioseismic observations with MDI on SOHO and with GONG have also led to the detection of significant variations in Ω with 1.3 yr period in the vicinity of the tachocline. There is another shearing layer just below the solar surface, and that region exhibits propagating bands of zonal flow. Such rich dynamical behavior requires theoretical explanations, some of which are beginning to emerge from detailed 3-D simulations of turbulent convection in rotating spherical shells. We discuss some of the properties exhibited by such numerical models. Although these simulations are highly simplified representations of much of the complex physics occurring within the convection zone, they are providing a very promising path for understanding the solar differential rotation and its temporal variations.

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