Table 1
Summary of the simulations in this paper.
| Case | Code | Grid | λ | Pr | Pm | Ta | Ra |  |
Ro_c | Re | Rm | Co | Large-scale |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1 | 1 | 2563 | 2 | 1 | 1 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 57 | 57 | 10.0 | Yes |
| A2 | 2 | 1923 | 2 | 1 | 1 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 57 | 57 | 9.9 | Yes |
| A3 | 3 | 2563 | 2 | 1 | 1 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 58 | 58 | 9.8 | Yes |
| B1 | 2 | 1923 | 2 | 1 | 1.33 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 56 | 74 | 10.2 | Yes |
| B2 | 2 | 1923 | 2 | 1 | 1 | 5 × 108 | 3 × 107 | 47.6 | 0.245 | 73 | 73 | 7.7 | Yes |
| B3a | 2 | 2562 × 224 | 2 | 1 | 1 | 5 × 108 | 4 × 107 | 63.5 | 0.283 | 111 | 111 | 5.1 | Intermittent |
| B3b | 1 | 2883 | 2 | 1 | 1 | 5 × 108 | 4 × 107 | 63.5 | 0.283 | 106 | 106 | 5.3 | Intermittent |
| B4 | 1 | 2883 | 2 | 1 | 1 | 5 × 108 | 5 × 107 | 79.4 | 0.316 | 132 | 132 | 4.3 | Intermittent |
| B5 | 1 | 2883 | 2 | 1 | 1 | 5 × 108 | 6 × 107 | 95.2 | 0.346 | 146 | 146 | 3.9 | Intermittent |
| B6 | 2 | 1282 × 192 | 1 | 1 | 1 | 5 × 109 | 8 × 107 | 27.4 | 0.126 | 92 | 92 | 19.5 | No |
| B7 | 2 | 1282 × 192 | 1 | 1 | 1.33 | 5 × 109 | 8 × 107 | 27.4 | 0.126 | 88 | 117 | 20.3 | No |
| B8 | 2 | 1282 × 192 | 1 | 1 | 1 | 5 × 109 | 1 × 108 | 34.2 | 0.141 | 109 | 109 | 16.4 | No |
| C1 | 2 | 1282 × 192 | 2 | 1 | 1 | 5 × 108 | 2.1 × 107 | 33.3 | 0.205 | 49 | 49 | 11.7 | Yes |
| C2 | 2 | 1923 | 2 | 1 | 1 | 4 × 108 | 2.4 × 107 | 44.2 | 0.245 | 65 | 65 | 7.8 | Yes |
| C3 | 2 | 1282 × 192 | 2 | 1 | 1 | 6 × 108 | 2.4 × 107 | 33.7 | 0.2 | 51 | 51 | 12.2 | Yes |
| C4 | 2 | 1282 × 192 | 2 | 1 | 1 | 7 × 108 | 2.4 × 107 | 30.4 | 0.185 | 47 | 47 | 14.3 | Yes |
| C5 | 2 | 1282 × 192 | 2 | 1 | 1 | 7.5 × 108 | 2.4 × 107 | 29.1 | 0.179 | 46 | 46 | 15.0 | ? |
| D1 | 1 | 2883 | 2 | 1 | 1 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 57 | 57 | 10.0 | Yes |
| D2 | 1 | 2883 | 2 | 1 | 1 | 2 × 109 | 9.6 × 107 | 60.5 | 0.219 | 120 | 120 | 9.5 | Yes |
| D3 | 1 | 5763 | 2 | 1 | 1 | 8 × 109 | 3.84 × 108 | 96.0 | 0.219 | 237 | 237 | 9.6 | Yes |
| E1 | 2 | 1923 | 2 | 1 | 1 | 5 × 108 | 2.4 × 107 | 38.1 | 0.219 | 60 | 60 | 9.5 | Yes |
Notes. A1, A2, andA3 correspond to the reference solution (a detailed comparison of these cases is presented in Appendix A). Simulations B1–8 were initialised from a polytropic state, whilst simulations C1–5 were started from case A2, gradually varying parameters along this solution branch. In Sets D and E the convective Rossby number is fixed at Ro_c = 0.219. In E1 the density contrast is 1.2 in comparison to 4 in the othersets. All input parameters are defined in the text. We recall that the Reynolds numbers, Re and Rm, and the Coriolis number, Co, are measured during the saturated phase of the dynamo (and the quoted values are time-averaged over this phase). The final column indicates whether or not there is a large-scale dynamo.
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