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Table 2.

General properties and dimensionless quantities of the models.

Name θwidth Nr Nθ Rech Prch PrHI PeHI Nu qSGS qnum qdiff
v036_4_150x20 4 150 20 28.4 0.13 0.04 0.82 1.12 1.19 × 10−3 9.20 × 101 4.813 × 103
v036_4_150x30 4 150 30 42.6 0.08 0.02 0.55 1.09 7.66 × 10−4 1.34 × 102 4.799 × 103

v036_6_150x20 6 150 20 19.0 0.19 0.04 0.57 1.07 1.07 × 10−3 1.22 × 102 2.967 × 103
v036_6_150x30 6 150 30 28.4 0.13 0.04 0.86 1.08 8.56 × 10−4 1.28 × 102 5.152 × 103
v036_6_150x40 6 150 40 37.8 0.09 0.01 0.38 1.06 5.21 × 10−4 1.35 × 102 2.205 × 103
v036_6_150x50 6 150 50 47.5 0.08 0.02 0.52 1.07 5.32 × 10−4 1.27 × 102 4.129 × 103
v036_6_201x20 6 201 20 18.4 0.19 0.04 0.63 1.10 3.56 × 10−4 2.35 × 102 6.873 × 102

v036_8_150x20 8 150 20 14.2 0.25 0.04 0.51 1.04 1.09 × 10−3 1.15 × 102 2.155 × 103
v036_8_150x30 8 150 30 21.3 0.17 0.04 0.68 1.06 8.07 × 10−4 1.14 × 102 4.160 × 103
v036_8_150x40 8 150 40 28.5 0.13 0.03 0.57 1.06 6.80 × 10−4 1.18 × 102 2.338 × 103

v036_9_150x30 9 150 30 18.9 0.19 0.03 0.55 1.06 8.26 × 10−4 1.14 × 102 2.585 × 103

v036_10_150x20 10 150 20 11.4 0.32 0.03 1.15 1.04 1.45 × 10−3 1.04 × 102 5.860 × 103
v036_10_150x30 10 150 30 17.1 0.21 0.06 1.02 1.07 1.19 × 10−3 1.09 × 102 4.348 × 103

v036_12_122x60 12 122 60 28.3 0.13 0.02 0.52 1.05 8.06 × 10−4 7.56 × 101 6.559 × 102
v036_12_150x20 12 150 20 9.5 0.38 0.06 0.94 1.03 1.43 × 10−3 1.54 × 102 4.282 × 103
v036_12_150x30 12 150 30 14.2 0.25 0.05 1.02 1.02 1.15 × 10−3 1.29 × 102 6.612 × 103
v036_12_150x40 12 150 40 18.9 0.19 0.03 0.58 1.05 7.44 × 10−4 1.31 × 102 1.390 × 103

v036_15_150x50 15 150 50 18.8 0.19 0.03 0.61 1.03 7.65 × 10−4 1.49 × 102 1.950 × 103

v036_18_150x60 18 150 60 19.0 0.19 0.04 0.73 1.06 7.25 × 10−4 1.01 × 102 2.053 × 103

v036_45_122x40 45 122 40 5.0 0.71 0.03 0.19 1.02 3.25 × 10−3 8.35 × 101 1.823 × 102
v036_45_122x60 45 122 60 7.5 0.47 0.02 0.24 1.03 2.28 × 10−3 8.89 × 101 2.742 × 102
v036_45_150x20 45 150 20 2.4 1.42 0.03 0.13 1.01 5.99 × 10−3 1.69 × 102 1.710 × 102

v046_6_152x20 6 152 20 19.8 0.21 0.06 1.06 1.28 1.03 × 10−3 3.11 × 102 9.639 × 103
v046_6_152x30 6 152 30 29.2 0.14 0.04 0.92 1.11 7.32 × 10−4 1.85 × 102 3.239 × 103
v046_12_152x40 12 152 40 19.6 0.21 0.06 1.17 1.10 9.38 × 10−4 1.42 × 102 2.859 × 103

Notes. The panels are separated according to the angular size and physical parameters of the models. The columns are (from left to right) the model name, angular extent (θwidth), number of radial shells (Nr), number of horizontal cells (Nθ), characteristic Reynolds number (Rech) defined by Eq. (19), characteristic Prandtl number (Prch) defined by Eq. (18), effective Prandtl number in the HI region (PrHI), Péclet number in the HI region (PeHI), maximum Nusselt number (Nu), median ratio of resolved to unresolved (subgrid scale) kinetic energy (qSGS), the median ratio of numerical to SGS viscosity (qnum) and the median ratio of numerical to SGS energy diffusion (qdiff).

(⋆)

This model did not reach τrelax simulation time, due to the large numerical cost; therefore, it is not reliable. It is only included here to show the trends. Statistical evaluation was performed over an interval of 12–18 days.

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