This is a Research Dataset associated with the journal article

@article{Gupta2023,
  doi = {10.3390/fluids8110288},
  url = {https://doi.org/10.3390/fluids8110288},
  year = {2023},
  month = oct,
  publisher = {{MDPI} {AG}},
  volume = {8},
  number = {11},
  pages = {288},
  author = {Parag Gupta and David MacTaggart and Radostin D. Simitev},
  title = {Differential Rotation in Convecting Spherical Shells with Non-Uniform Viscosity and Entropy Diffusivity},
  journal = {Fluids}
}

ABSTRACT

Contemporarythree-dimensionalphysics-basedsimulationsofthesolarconvectionzone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three- dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

KEYWORDS

Solar differential rotation; convection-driven spherical dynamo; magnetohydrodynamic numerical simulations

1) Data formats and software for analysis

The data is either in ascii text format or in the format of FORTRAN
".F" files, Python ".py", or MATLAB ".m" files.

2) Description of datasets

We consider typical solutions from six distinct dynamo regimes 

       (A)      (B)        (C)     (D)         (E)      (F)
Type Uniform Non-uniform Uniform Non-uniform Uniform Non-uniform

eta   0.65      0.65        0.65      0.65      0.65     0.65
R     3 X 10^6  3 X 10^6    3 X 10^6  3 X 10^6  3 X 10^6 3 X 10^6
Tau   2000      2000        2000      2000      2000     2000
P_r   0.3       0.3         0.3       0.3       0.3      0.3
N_rho 3         3           3         3         3        3
n     2         2           2         2         2        2  
P_m   1         1           1         1         1        1


The Pseudospectral code to solve the MHD equations

* ./01_SourceCode/2012-11-09-drs20104-anel-NewNondimAngMom-butfly  - Uniform cases
* ./01_SourceCode/2012-11-16-drs20104-anel-VarVrmmKrmm1            - Non-uniform cases

Datasets for all the cases

* ./02_Datasets_And_Cases/a.mv.e065p03t2r3000000m1p1N3                  - (A)
* ./02_Datasets_And_Cases/a.mv.e065p03t2r3000000m1p1N3m3.vr3.8kr3       - (B)
* ./02_Datasets_And_Cases/a.mv.e065p1t2r3000000m1p4N3                   - (C) 
* ./02_Datasets_And_Cases/a.mv.e065p1t2r3000000m1p4N3m3.vr3.8kr3        - (D)
* ./02_Datasets_And_Cases/a.mv.e065p5t2r3000000m1p10N3                  - (E)
* ./02_Datasets_And_Cases/a.mv.e065p5t2r3000000m1p10N3m3.vr3.8kr3       - (F)

Data and the ploting scripts for all the figures 

* 03_Figures