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Table 2

Summary of numerical parameters.

Parameter Definition Value

Grid size Nx × Ny × Nz 256 × 256 × 256
Aspect ratio lx:ly:lz 6:6:1
CFL number Δx/(ν + cs)/Δt 0.3
Depth of conductive zone in PSHs 1.87
Depth of transition zone in PSHs 1.26
Depth of convective zone in PSHs 3.61
SGS Prandtl number δ = μ/κ 1/3
Deardorff number cμ in Eq. (14) 0.2
Ratio of specific heat γ 5/3
polytropic index m 1 2.728
polytropic index m 2 1.485
Depth parameter Z 1 2
Depth parameter Z 2 3
Initial convective top z 1 0.9

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