Bifurcations in rotating spherical shell convection under the influence of differential rotation

2021 ◽  
Vol 31 (11) ◽  
pp. 113112
Author(s):  
Fred Feudel ◽  
Ulrike Feudel
Keyword(s):  
Spherical Shell ◽  
Differential Rotation

scholarly journals Differential Rotation and Magnetic Activity of the Lower Main Sequence Stars

1980 ◽  
Vol 51 ◽  
pp. 296-297
Author(s):  
G. Belvedere ◽  
L. Paterno ◽  
M. Stix
Keyword(s):  
Spherical Shell ◽  
Differential Rotation ◽  
Main Sequence ◽  
Magnetic Activity ◽  
The Sun ◽  
Coupling Constant ◽  
Main Sequence Stars ◽  
Dynamo Theory ◽  
Magnetic Cycles ◽  
Surface Convection

AbstractWe extend to the lower main sequence stars the analysis of convection interacting with rotation in a compressible spherical shell, already applied to the solar case (Belvedere and Paterno, 1977; Belvedere et al. 1979a). We assume that the coupling constant ε between convection and rotation, does not depend on the spectral type. Therefore we take ε determined from the observed differential rotation of the Sun, and compute differential rotation and magnetic cycles for stars ranging from F5 to MO, namely for those stars which are supposed to possess surface convection zones (Belvedere et al. 1979b, c, d). The results show that the strength of differential rotation decreases from a maximum at F5 down to a minimum at G5 and then increases towards later spectral types. The computations of the magnetic cycles based on the αω-dynamo theory show that dynamo instability decreases from F5 to G5, and then increases towards the later spectral types reaching a maximum at MO. The period of the magnetic cycles increases from a few years at F5 to about 100 years at MO. Also the extension of the surface magnetic activity increases substantially towards the later spectral types. The results are discussed in the framework of Wilson’s (1978) observations.

scholarly journals Gravito-inertial waves in a differentially rotating spherical shell

2016 ◽  
Vol 800 ◽  
pp. 213-247 ◽  
Author(s):  
G. M. Mirouh ◽  
C. Baruteau ◽  
M. Rieutord ◽  
J. Ballot
Keyword(s):  
Spherical Shell ◽  
Differential Rotation ◽  
Power Laws ◽  
Boussinesq Approximation ◽  
Theoretical Explanation ◽  
Heat Diffusion ◽  
Complex Spectrum ◽  
Rotating Stars ◽  
Inertial Waves ◽  
Short Period

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.

scholarly journals Dynamo coefficients from the Tayler instability

2010 ◽  
Vol 6 (S271) ◽  
pp. 213-217 ◽  
Author(s):  
Rainer Arlt ◽  
Günther Rüdiger
Keyword(s):  
Spherical Shell ◽  
Northern Hemisphere ◽  
Differential Rotation ◽  
Initial Value ◽  
Dynamo Action ◽  
Fundamental Interest ◽  
Stellar Radiation ◽  
Current Helicity

AbstractCurrent-driven instabilities in stellar radiation zones, to which we refer as Tayler instabilities, can lead to complex nonlinear evolutions. It is of fundamental interest whether magnetically driven turbulence can lead to dynamo action in these radiative zones. We investigate initial-value simulations in a 3D spherical shell including differential rotation. The Tayler instability is connected with a very weak kinetic helicity, stronger current helicity, and a positive αφφ in the northern hemisphere. The amplitudes are small compared to the effect of the tangential cylinder producing an eddy with negative kinetic helicity and negative αφφ in the northern hemisphere. The αφφ from the Tayler instability reaches about 1% of the rms velocity.

scholarly journals Convective dynamo action in a spherical shell: symmetries and modulation

2016 ◽  
Vol 799 ◽  
Author(s):  
Raphaël Raynaud ◽  
Steven M. Tobias
Keyword(s):  
Solar Activity ◽  
Magnetic Fields ◽  
Spherical Shell ◽  
Differential Rotation ◽  
Three Dimensional ◽  
Important Process ◽  
Dynamo Action ◽  
Grand Minima

We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude; for other parameters, the modulation is of type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of ‘supermodulation’ in the solutions, where the activity switches chaotically between type 1 and type 2 modulation; this is believed to be an important process in solar activity.

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