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Table 1

Summary of the spherical runs.

Run grid Ra Pr Ma Re Co Emer/Ekin Erot/Ekin ΔΩ/Ωeq

A0 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.023 38 0.00 0.116 7.7 × 10-5 0.045 0.004

A1 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.022 36 0.13 0.114 6.9 × 10-5 0.016 0.022  −0.15
A2 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.022 36 0.25 0.114 7.2 × 10-5 0.015 0.073  −0.31
A3 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.022 37 0.50 0.113 1.2 × 10-4 0.010 0.438  −1.03
A4 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.029 48 0.94 0.112 1.1 × 10-3 0.016 0.927  −1.74
A5 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.022 36 2.56 0.111 9.9 × 10-4 0.002 0.949  −0.37
A6 128 × 256 × 128 3.1 × 106 1.0 1.4 × 10-4 0.018 30 6.09 0.114 2.3 × 10-4 0.000 0.824 +0.20

B0 128 × 512 × 256 8.6 × 106 1.0 1.4 × 10-4 0.020 54 0.00 0.113 5.8 × 10-5 0.036 0.009

B1 128 × 512 × 256 8.6 × 106 1.0 1.4 × 10-4 0.020 57 1.34 0.112 6.5 × 10-4 0.009 0.927  −1.10
B2 128 × 512 × 256 8.6 × 106 1.0 1.4 × 10-4 0.018 50 3.06 0.113 1.2 × 10-4 0.001 0.689 +0.12
B3 128 × 512 × 256 8.6 × 106 1.0 1.4 × 10-4 0.016 44 6.93 0.113 1.8 × 10-4 0.000 0.833 +0.20

C1 128 × 256 × 128 1.7 × 107 6.7 7.5 × 10-5 0.008 12 7.58 0.114 3.8 × 10-5 0.000 0.817 +0.12

D1 256 × 512 × 256 6.0 × 107 1.0 3.1 × 10-5 0.012 90 5.07 0.113 7.9 × 10-5 0.000 0.796 +0.20
D2 256 × 512 × 256 6.0 × 107 1.0 3.1 × 10-5 0.012 89 7.68 0.113 1.5 × 10-4 0.000 0.895 +0.20

Notes. Here , ΔΩ = Ωeq − Ωpole, where and . and are the volume averaged thermal and total kinetic energies, respectively, in units of GMρ0/R. and are the kinetic energies of the meridional circulation and differential rotation.

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