==== Table 1. Definitions of benchmark cases ==== -------------------------------------------------------------------------------- Case Ra_0.5 Viscosity l and m variation for initial perturbation Resolution -------------------------------------------------------------------------------- BM1A 7e3 1e0 (3,2) 32x(12x32x32) BM1B 7e3 1e1 (3,2) 32x(12x32x32) BM1C 7e3 2e1 (3,2) 32x(12x32x32) BM1D 7e3 1e2 (3,2) 32x(12x32x32) BM1E 7e3 1e3 (3,2) 32x(12x32x32) BM1F 7e3 1e4 (3,2) 32x(12x32x32) BM1G 7e3 1e5 (3,2) 32x(12x32x32) BM1H 7e3 1e6 (3,2) 32x(12x32x32) BM2A 7e3 1e0 (4,0)+(4,4) 32x(12x32x32) BM2B 7e3 2e1 (4,0)+(4,4) 32x(12x32x32) BM2C 7e3 3e1 (4,0)+(4,4) 32x(12x32x32) BM2D 7e3 1e2 (4,0)+(4,4) 32x(12x32x32) BM2E 7e3 1e3 (4,0)+(4,4) 32x(12x32x32) BM2F 7e3 1e4 (4,0)+(4,4) 32x(12x32x32) BM2G 7e3 1e5 (4,0)+(4,4) 32x(12x32x32) BM2H 7e3 1e6 (4,0)+(4,4) 32x(12x32x32) BM3A 1e5 1e0 (4,0)+(4,4) 48x(12x48x48) BM3B 1e5 1e1 from BM3A 48x(12x48x48) BM3C 1e5 3e1 from BM3A 48x(12x48x48) BM3D 1e5 1e2 from BM3C 48x(12x48x48) -------------------------------------------------------------------------------- Note: 1) Resolution in radial direction (the number outside of the parentheses) for our calculations is refined near the top and bottom boundaries. 2) Resolution for comparison cases is 48x(6x48x48) for Stemmer et al. {2006}, 102x(102x204) for Yoshida and Kageyama {2004}, where the number outside parentheses represents the resolution in radial direction. 3) Ratcliff et al {1996} used different resolution for cubic and tetrahedral symmetry cases, as they considered the symmetry of these cases and did not compute them in a full sphere. For cubic symmetry cases, the equivalent resolution is 32, 64, and 128 cells in radial, co-latitude and longitude directions, respectively, and these numbers are 32, 32, and 64 for the tetrahedral cases.