Table 1
Summary of runs.
| Run | Resolution | Size |
|
ρ bot / ρ surf | Re | PrM | B eq0 / B 0 |
|
|
|
|
BR | |
|
|
|||||||||||||
| A1 | 5122 × 1024 | (2π)2 × 3π | 0.1 | 1.4 | 38.0 | 0.5 | 40 | –0.021 | 39 | 1.6 | – | NO | |
| A2 | 5122 × 1024 | (2π)2 × 3π | 0.5 | 4.8 | 38.0 | 0.5 | 41 | –0.023 | 52 | 3.8 | 2.1 | WEAK | |
| A3 | 5122 × 1024 | (2π)2 × 3π | 0.7 | 8.9 | 38.1 | 0.5 | 42 | –0.026 | 56 | 5.4 | 1.9 | YES | |
| A4 | 5122 × 1024 | (2π)2 × 3π | 0.85 | 14 | 38.1 | 0.5 | 42 | –0.020 | 56 | 5.5 | 1.6 | YES | |
| A5 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 43 | –0.022 | 67 | 9.2 | 1.1 | YES | |
| A6 | 5122 × 1024 | (2π)2 × 3π | 1.20 | 42 | 38.4 | 0.5 | 44 | –0.023 | 74 | 8.1 | 1.2 | YES | |
| A7 | 5122 × 1024 | (2π)2 × 3π | 1.40 | 79 | 38.6 | 0.5 | 46 | –0.017 | 72 | 8.8 | 1.1 | YES | |
| A8 | 5122 × 1024 | (2π)2 × 3π | 1.50 | 108 | 38.7 | 0.5 | 48 | –0.017 | 58 | 6.6 | 0.7 | YES | |
|
|
|||||||||||||
| R1 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.0625 | 43 | –0.018 | 8.7 | 2.9 | – | NO | |
| R2 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.125 | 43 | –0.015 | 19 | 4.4 | 1.8 | WEAK | |
| R3 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.25 | 43 | –0.020 | 31 | 6.0 | 1.5 | YES | |
| R4 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 43 | –0.022 | 67 | 9.2 | 1.1 | YES | |
| R5 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 35.7 | 1 | 40 | –0.028 | 91 | 4.3 | 2.0 | WEAK | |
|
|
|||||||||||||
| B1 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.5 | 431 | –0.019 | 202 | 13 | 2.6 | WEAK | |
| B2 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.5 | 173 | –0.023 | 138 | 14 | 3.6 | YES | |
| B3 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.3 | 0.5 | 86 | –0.022 | 92 | 6.1 | 2.3 | YES | |
| B4 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 43 | –0.022 | 67 | 9.2 | 1.1 | YES | |
| B5 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.1 | 0.5 | 17 | –0.030 | 30 | 4.8 | 0.9 | YES | |
| B6 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 37.7 | 0.5 | 8.5 | –0.059 | 16 | 3.2 | 0.8 | YES | |
| B7 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 36.1 | 0.5 | 1.6 | –0.125 | 3.3 | 0.2 | – | NO | |
|
|
|||||||||||||
| S1 | 5123 | (2π)2 × 2π | 1.00 | 23 | 38.2 | 0.5 | 42 | –0.030 | 52 | 7.8 | 1.0 | YES | |
| S2 | 5122 × 1024 | (2π)2 × 3π | 1.00 | 512 | 38.9 | 0.5 | 49 | –0.024 | 57 | 4.9 | 1.1 | YES | |
| S3 | 10243 | (4π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 43 | –0.013 | 80 | 17 | 1.8 | YES | |
|
|
|||||||||||||
| THW | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 45 | –0.022 | 56 | 5.3 | 0.6 | YES | |
| V | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.1 | 0.5 | 43 | –0.021 | 107 | 30 | 3.9 | SP | |
| INC | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.2 | 0.5 | 43 | –0.022 | 86 | 21 | 3.9 | YES | |
|
|
|||||||||||||
| F | 5122 × 1024 | (2π)2 × 3π | 1.00 | 23 | 38.7 | 0.5 | 45 | –0.049 | 50 | 10 | 1.7 | YES | |
Notes. Here, is the normalized gravitational acceleration and ρbot and ρsurf are the horizontally averaged densities at the bottom and surface (z = 0) of the domain, respectively. Re is the fluid Reynolds number, PrM is the magnetic Prandtl number, B0 is the imposed field, Beq0 = Beq(z = 0) is the equipartition value at the surface (z = 0), and is the minimum of the averaged effective magnetic pressure 
defined by Eq. (9); see also bottom row of Fig. 4. 
is the maximum value of vertical magnetic field, 
is the maximum value of the Fourier-filtered vertical magnetic field; both are taken at the surface (z = 0). is the time when is taken in terms of turbulent-diffusive time. BR indicates whether or not there are bipolar regions or a single spot (SP). The runs R4 and B4 are the same as A5.
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