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Table B.1

Numerical simulations carried out at Pr = 1 and n = 2 and displayed in Figs. 3 and 7.

E χ Nϱ Ra∕Rac Roℓ (ro) Nu ℓmax
1.0 × 10−4 0.35 4.0 1.2 1.8 × 10−2 1.02 1.00 1.06 1.06 1.00 2.3 × 101 65 192
1.0 × 10−4 0.70 0.5 1.5 7.4 × 10−3 1.03 1.00 1.06 1.06 1.00 1.2 × 100 129 256
1.0 × 10−4 0.70 0.5 4.0 2.4 × 10−2 1.25 1.00 1.56 1.56 1.00 3.6 × 101 65 213
1.0 × 10−4 0.70 0.5 8.0 6.0 × 10−2 1.80 1.00 2.51 2.49 1.00 4.7 × 101 65 213
1.0 × 10−4 0.70 0.5 16.0 1.5 × 10−1 3.31 2.61 4.50 3.45 3.17 1.2 × 102 129 288
1.0 × 10−4 0.70 0.5 32.0 3.8 × 10−1 7.51 3.82 14.59 4.63 6.95 1.5 × 102 129 341
1.0 × 10−4 0.70 1.0 1.5 1.0 × 10−2 1.04 1.00 1.08 1.08 1.00 7.7 × 100 65 192
1.0 × 10−4 0.70 1.0 2.0 1.6 × 10−2 1.10 1.00 1.20 1.20 1.00 1.1 × 101 65 192
1.0 × 10−4 0.70 1.0 4.0 4.3 × 10−2 1.43 1.00 1.87 1.86 1.00 1.0 × 102 161 256
1.0 × 10−4 0.70 1.0 8.0 1.1 × 10−1 2.34 1.87 2.71 2.58 1.88 1.4 × 102 65 256
1.0 × 10−4 0.70 1.0 16.0 3.2 × 10−1 5.27 2.89 9.69 3.47 5.60 3.7 × 102 129 256
1.0 × 10−4 0.70 2.0 1.5 2.8 × 10−2 1.07 1.00 1.18 1.18 1.00 1.3 × 101 65 192
1.0 × 10−4 0.70 2.0 2.0 3.9 × 10−2 1.17 1.00 1.35 1.34 1.00 2.7 × 101 65 192
1.0 × 10−4 0.70 2.0 4.0 9.8 × 10−2 1.69 1.19 1.95 1.94 1.20 9.1 × 101 65 192
1.0 × 10−4 0.70 2.0 8.0 3.4 × 10−1 3.78 2.32 6.45 2.67 6.06 5.4 × 101 129 256
1.0 × 10−4 0.70 2.0 16.0 6.5 × 10−1 7.54 3.64 13.16 3.80 9.25 5.7 × 101 129 341
1.0 × 10−4 0.70 4.0 1.5 8.4 × 10−2 1.04 1.00 1.21 1.20 1.00 3.0 × 101 65 341
1.0 × 10−4 0.70 4.0 2.0 1.0 × 10−1 1.08 1.00 1.33 1.32 1.00 4.4 × 101 121 341
3.0 × 10−4 0.35 1.0 1.5 8.7 × 10−3 1.07 1.01 1.08 1.08 1.01 1.8 × 101 65 192
3.0 × 10−4 0.35 1.0 2.0 1.2 × 10−2 1.10 1.02 1.11 1.11 1.02 3.3 × 101 65 192
3.0 × 10−4 0.35 1.0 4.0 2.6 × 10−2 1.36 1.22 1.53 1.28 1.23 2.3 × 101 65 192
3.0 × 10−4 0.35 1.0 8.0 6.7 × 10−2 2.23 1.88 3.25 1.88 2.95 2.8 × 101 65 192
3.0 × 10−4 0.35 1.0 16.0 1.7 × 10−1 4.64 3.14 12.98 3.32 12.62 9.0 × 101 65 192
3.0 × 10−4 0.35 1.0 32.0 3.3 × 10−1 8.90 4.80 27.52 5.37 25.69 4.3 × 101 65 192
3.0 × 10−4 0.35 2.0 2.0 1.9 × 10−2 1.13 1.05 1.21 1.09 1.06 2.1 × 101 65 192
3.0 × 10−4 0.35 2.0 4.0 6.0 × 10−2 1.69 1.34 2.11 1.34 1.96 4.0 × 101 65 192
3.0 × 10−4 0.35 2.0 8.0 1.8 × 10−1 3.64 2.42 12.27 2.48 10.61 4.4 × 101 65 192
3.0 × 10−4 0.35 2.0 16.0 3.5 × 10−1 7.22 4.52 20.32 4.67 18.74 1.3 × 102 65 192
3.0 × 10−4 0.35 2.0 32.0 6.7 × 10−1 13.00 9.00 26.30 9.06 25.52 6.6 × 101 129 192
3.0 × 10−4 0.35 4.0 2.0 6.3 × 10−2 1.21 1.01 1.31 1.31 1.01 5.0 × 101 65 192
3.0 × 10−4 0.35 4.0 4.0 1.9 × 10−1 2.13 1.63 4.41 1.77 4.31 5.8 × 101 65 192
3.0 × 10−4 0.35 4.0 8.0 3.6 × 10−1 3.76 2.64 7.27 2.69 6.81 6.1 × 101 65 192
3.0 × 10−4 0.35 4.0 16.0 7.5 × 10−1 6.39 5.26 10.55 5.36 10.27 8.5 × 101 65 192
3.0 × 10−4 0.35 6.0 2.0 1.3 × 10−1 1.12 1.00 1.28 1.28 1.00 8.8 × 101 65 192
3.0 × 10−4 0.35 6.0 4.0 3.8 × 10−1 1.68 1.38 2.29 1.58 2.22 9.3 × 101 65 192
3.0 × 10−4 0.35 6.0 8.0 5.3 × 10−1 2.42 1.96 3.30 2.12 3.24 6.7 × 101 65 192
3.0 × 10−4 0.35 6.0 16.0 7.9 × 10−1 3.43 2.95 4.39 2.96 4.30 1.4 × 102 129 192
3.0 × 10−4 0.35 6.0 32.0 2.6 × 100 5.51 5.45 6.29 6.20 6.07 3.6 × 101 129 192
3.0 × 10−4 0.35 8.0 2.0 3.1 × 10−1 1.13 1.00 1.22 1.21 1.00 3.1 × 101 129 192
3.0 × 10−4 0.35 8.0 4.0 7.4 × 10−1 1.44 1.35 1.60 1.38 1.57 2.4 × 101 257 288
3.0 × 10−4 0.35 8.0 8.0 1.1 × 100 1.73 1.63 1.89 1.63 1.83 2.9 × 101 257 288
3.0 × 10−4 0.35 8.0 16.0 1.6 × 100 2.12 2.06 2.27 2.09 2.24 3.3 × 101 257 288
3.0 × 10−4 0.35 8.0 32.0 2.7 × 100 2.76 2.73 2.88 2.75 2.85 3.7 × 101 257 288
3.0 × 10−4 0.35 8.0 48.0 2.8 × 100 2.91 2.65 2.80 2.65 2.72 4.0 × 100 257 512
3.0 × 10−4 0.70 1.0 2.0 2.8 × 10−2 1.10 1.00 1.20 1.20 1.00 3.4 × 101 65 192
3.0 × 10−4 0.70 2.0 2.0 6.8 × 10−2 1.16 1.00 1.34 1.34 1.00 3.8 × 101 65 192
3.0 × 10−4 0.70 4.0 2.0 1.8 × 10−1 1.10 1.00 1.33 1.33 1.00 2.3 × 101 65 192
3.0 × 10−4 0.70 4.0 8.0 9.6 × 10−1 2.74 2.05 3.88 2.23 3.78 2.5 × 101 97 256
3.0 × 10−4 0.70 6.0 2.0 5.0 × 10−1 1.13 1.00 1.25 1.24 1.00 2.1 × 101 65 288
3.0 × 10−4 0.70 6.0 4.0 1.4 × 100 1.53 1.44 1.65 1.44 1.64 1.0 × 101 65 288
3.0 × 10−4 0.70 6.0 8.0 2.0 × 100 1.91 1.77 2.13 1.77 2.10 4.5 × 100 65 426
3.0 × 10−4 0.70 6.0 16.0 3.3 × 100 2.56 2.46 2.82 2.47 2.80 2.1 × 101 129 426
3.0 × 10−4 0.70 6.0 32.0 6.1 × 100 3.45 3.37 3.64 3.56 3.58 4.4 × 100 129 512
3.0 × 10−4 0.70 6.0 48.0 8.0 × 100 4.31 4.18 4.47 4.26 4.41 3.7 × 100 257 512

Notes. Part of the high resolution runs may not be fully resolved nor relaxed. We checked this has no influence on the latitudinal profile of the Nusselt number, but it may be of importance for it absolute value; hence we recommend not using it, for instance when studying Nusselt scalings.

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