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Table 1.

Summary of the runs with smoothly varying profiles of K.

Run ℱn RaRad [107] RaSGS [106] Re ReOZ Nu Δρ dos/Hp K
K-3 4.5 × 10−4 0.12 0.5 0.4 15 1.3 0.5 19 55 1.29 Kramers
K-2 1.8 × 10−4 0.64 0.6 0.5 17 1.2 0.7 36 74 1.05 Kramers
K-1 9.1 × 10−5 1.7 0.8 0.7 18 1.2 0.8 51 91 0.90 Kramers
K0 4.5 × 10−5 4.0 0.9 0.8 19 1.1 0.9 63 108 0.79 Kramers
K1 1.8 × 10−5 9.9 1.0 0.9 20 1.0 0.8 77 128 0.69 Kramers
K2 9.1 × 10−6 18 1.1 0.9 20 0.9 0.8 84 139 0.63 Kramers
K3 4.6 × 10−6 28 1.1 0.9 20 0.9 0.8 88 147 0.60 Kramers
K4 1.8 × 10−6 55 1.1 1.0 19 0.8 0.8 92 154 0.55 Kramers
K5 9.1 × 10−7 94 1.1 1.0 19 0.8 0.8 94 158 0.51 Kramers
K6 4.6 × 10−7 157 1.2 1.0 19 0.8 0.7 96 161 0.49 Kramers
K7 1.8 × 10−7 302 1.2 1.0 19 0.8 0.8 98 164 0.46 Kramers
K-3h 4.6 × 10−4 0.39 2.4 0.2 34 2.8 0.7 24 58 1.28 Kramers
K-2h 1.8 × 10−4 1.7 3.1 0.4 37 2.8 1.1 41 76 1.04 Kramers
K-1h 9.1 × 10−5 4.3 3.6 0.5 39 2.7 1.4 55 93 0.88 Kramers
K0h 4.5 × 10−5 9.6 4.2 0.6 41 2.5 1.6 68 111 0.77 Kramers
K1h 1.8 × 10−5 23 4.7 0.7 42 2.3 1.7 80 130 0.67 Kramers
K2h 9.1 × 10−6 40 4.8 0.8 42 2.1 1.7 87 141 0.61 Kramers
K3h 4.6 × 10−6 65 4.7 0.9 41 2.0 1.8 91 150 0.58 Kramers
K4h 1.8 × 10−6 130 5.0 0.9 41 2.0 1.9 94 157 0.53 Kramers
K5h 9.1 × 10−7 221 5.3 1.0 40 2.0 1.9 97 161 0.50 Kramers
K6h 4.6 × 10−7 367 5.5 1.0 40 1.9 1.8 98 163 0.47 Kramers
K7h 1.8 × 10−7 700 5.6 1.0 40 1.7 1.7 99 166 0.45 Kramers
P-1 8.9 × 10−5 0.27 0.8 0.7 19 1.3 0.9 71 86 0.86 K-profile
P0 4.5 × 10−5 0.47 0.9 0.8 19 1.1 0.9 71 106 0.76 K-profile
P1 1.8 × 10−5 0.92 1.0 0.9 20 1.0 0.9 71 127 0.68 K-profile
P2 9.1 × 10−6 15 1.1 0.9 20 0.9 0.8 71 139 0.63 K-profile
P3 4.5 × 10−6 23 1.1 0.9 19 0.9 0.8 71 146 0.61 K-profile
P4 1.8 × 10−6 42 1.1 1.0 19 0.8 0.8 71 154 0.56 K-profile
P5 9.1 × 10−7 71 1.2 1.0 19 0.8 0.8 71 158 0.52 K-profile
P6 4.6 × 10−7 116 1.2 1.0 19 0.8 0.8 71 161 0.49 K-profile

Notes. The Nusselt number is quoted from z/d = 0.85 and refers to the effective Prandtl number at z/d = 0 here and in all following tables. The grid resolution in all runs is 2883.

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