Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis
Abstract
:1. Introduction
2. Convective Magnetic Dynamo: Equations and Numerical Methods
2.1. Statement of the Problem
2.2. Numerical Techniques
2.3. Symmetries
3. Results of Simulation
3.1. Regimes in the Elongated Boxes with the Periodicities 1x2/2x1
- All of them are quasiperiodic hydrodynamic travelling waves.
- The energy ranges and mean (over time) energies coincide.
- The basic frequencies are identical.
- The ranges of the magnetic Reynolds number estimates Rm and Rm and their mean (over time) values coincide.
- The ranges of the kinetic helicity and its temporal mean values are the same.
- The growth rates of the dominant magnetic modes are also equal.
- The flows have the symmetry in the 1x2 cell and in the 2x1 cell.
- Independence of (the energy of the discrepancy averaged over the periodicity cell, equal to the mean energy of the harmonics associated with wave vectors with a non-zero second component, is below 0.25 in the saturated regime for ; it shows the tendency to increase towards the ends of the intervals of almost regular helicity behaviour).
- (for , the mean energy of the discrepancy is below 24.0).
- (for , the mean energy of the discrepancy is below 14.4).
- The flow is approximately 1x1-periodic (for , the spatially averaged mean energy of the discrepancy, equal to the mean energy of the harmonics associated with wave vectors, whose first component is odd, is below 6.1).
- We have performed a hydrodynamic run (the magnetic field being set to zero at each step) in a 2x1-periodic fluid box for an initial condition that is the 2x1.1 flow at (close to the local minimum of the magnetic energy), where the -dependence is suppressed by setting to zero all harmonics associated with wave vectors, whose second component is non-zero. This run has converged fast (in roughly 15 time units) to the double-replicated R, the energy of discrepancy decreasing below .
- The energy of the discrepancies between the 2x1.1 flow at and the flows of the MHD steady states R, S and S is 0.2, 0.2 and 16.1, respectively.
3.2. Regimes in the Elongated Cells with the Periodicities 1x3/3x1
3.3. Regimes in the Elongated Cells with the Periodicities 1x4/4x1
3.4. Regimes in the -Periodicity Cells for
3.5. Videos of the Kinetic and Magnetic Energy Evolution
3.6. Analysis of Integral Parameters of the Regimes
4. Concluding Remarks
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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1 | 2 | 3 | 4 | |
1 | 15.8,9.6,21.8 | 21.4,8.0,24.6 | 7.8/11.7,4.3/7.2,12.7/17.6 | |
15.2,12.2,21.7 | 9.9/13.4,6.3/10.5,15.9/18.8 | 7.2/11.6,4.3/6.3,12.0/16.8 | ||
17.1,9.6,23.4 | 11.1/13.6,6.0/13.0,16.0/19.6 | 9.5/11.0,4.2/6.8,13.6/16.2 | ||
2 | 16.2,11.4,21.8 | 36.0,14.1,38.0 | 25.3,9.0,27.3 | 18.8/12.2,6.5/7.7,20.8/17.1 |
15.0,8.5,20.5 | 37.8,15.0,38.1 | 24.6,7.9,26.3 | 18.3/11.2,6.5/7.6,20.0/15.7 | |
25.0,9.0,27.2 | 36.9,14.6,38.0 | 24.9,8.5,26.5 | 18.6/10.9,5.9/7.2,20.2/15.7 | |
3 | 9.8/14.9,5.7/12.1,14.7/20.9 | 25.1,8.2,26.6 | 24.7,8.8,27.1 | 18.4/11.8,6.4/7.2,20.9/17.17 |
9.4/14.1,5.6/11.4,14.7/20.1 | 25.0,8.7,26.9 | 19.7,8.4,25.3 | 18.2/10.2,6.1/7.6,20.3/15.6 | |
10.0/13.9,5.8/11.0,15.1/19.2 | 25.2,8.8,27.2 | 18.9,8.3,24.6 | 18.1/10.4,6.1/7.3,20.6/15.2 | |
4 | 7.4/11.6,4.0/6.9,13.1/16.7 | 18.4/12.6,5.9/7.3,20.7/17.5 | 18.0/23.8,6.3/7.5,20.4/26.2 | 14.1/24.4,6.1/7.9,19.5/26.5 |
7.3/10.8,4.2/7.3,13.2/16.3 | 18.8/11.4,6.0/7.5,20.5/16.6 | 18.6/11.0,6.0/6.9,20.3/14.6 | 18.1/10.8,5.6/6.8,20.5/15.5 | |
7.2/11.3,4.1/7.2,12.9/15.7 | 18.5/10.6,6.3/7.5,20.6/16.1 | 18.6/10.8,6.2/7.6,20.9/15.7 | 10.7/10.2,5.7/7.2,16.1/15.4 |
Run | A/MS | Time | Type | Symmetries | ||||
1x2.1 | A | 135.92 | 109.88 | 133.34 | 156.64 | [75:1016.90] | MHD | |
4 | 4.22 | 8.64 | 20.11 | |||||
0.0476 | 0.0392 | 0.0452 | 0.05 | |||||
MS | 138.66 | 143.55 | 148.48 | [85:152], | HD | |||
1.54 | 0.012 | 0.13 | [655:663], | Q | ||||
0.0441 | 0.0451 | 0.0464 | [805:812] | TW | ||||
MS | 130.80 | 130.87 | 130.93 | [48:50.5] | HD | |||
2.09 | 1.63 | 5.57 | S | |||||
0.0446 | 0.0446 | 0.0460 | ||||||
1x2.2 | A | 100 | 112.36 | 134.09 | 154.22 | [20:300.08] | MHD | |
25 | 0.0350 | 7.76 | 19.27 | |||||
0.01 | 0.0413 | 0.0451 | 0.0493 | |||||
MS | 138.04 | 143.32 | 148.73 | [24:38], | HD | |||
0.0602 | 0.21 | 0.55 | [120:128], | Q | ||||
0.0441 | 0.0451 | 0.0477 | [170:190] | TW | ||||
1x2.3 | A | 100 | 34.38 | 133.34 | 158.94 | [40:1691.82] | MHD | |
400 | 4.42 | 0.66 | 19.65 | |||||
0.01 | 0.0115 | 0.0426 | 0.0506 | |||||
MS | 138.84 | 143.56 | 148.48 | [325:1560] | HD | |||
4.60 | 5.44 | 1.23 | Q | |||||
0.0441 | 0.0451 | 0.0464 | TW | |||||
MS | 34.38 | 82.10 | 143.21 | [40:293] | HD | |||
5.97 | 4.06 | 8.07 | C | |||||
0.0115 | 0.0291 | 0.0478 | ||||||
2x1.1 | A | 135.92 | 97.18 | 137.37 | 150.22 | [40:341.81] | MHD | |
3.76 | 0.91 | 6.98 | 23.93 | C | ||||
0.0476 | 0.0381 | 0.0475 | 0.0501 | |||||
MS | 150.14 | 150.19 | 150.22 | [62.8:63.25] | HD | |||
0.96 | 1.19 | 1.45 | [182.4:182.7] | S2 | ||||
0.0498 | 0.0499 | 0.0500 | [298.8:299.1] | R1 | ||||
2x1.2 | A | 100 | 34.03 | 133.89 | 159.26 | [40:2218.50] | MHD | |
25 | 1.61 | 2.01 | 19.70 | |||||
0.01 | 0.0109 | 0.0432 | 0.0505 | |||||
MS | 138.85 | 143.56 | 148.48 | [300:1500], | HD | |||
3.99 | 5.83 | 1.32 | [1661:1678], | Q | ||||
0.0441 | 0.0451 | 0.464 | [1723:1740] | TW | ||||
MS | 34.03 | 83.34 | 133.71 | [40:270], | HD | |||
3.14 | 5.28 | 1.12 | [2000:2218] | C | ||||
0.0109 | 0.0294 | 0.0445 | ||||||
2x1.3 | A | 1 | 33.85 | 133.05 | 158.90 | [40:3505.05] | MHD | |
400 | 1.71 | 0.15 | 18.76 | |||||
0.01 | 0.0110 | 0.0424 | 0.0505 | |||||
MS | 138.85 | 143.56 | 148.48 | [670:3400] | HD | |||
1.66 | 3.04 | 1.18 | Q | |||||
0.0441 | 0.0451 | 0.0464 | TW | |||||
MS | 33.85 | 82.71 | 153.46 | [40:633.2] | HD | |||
1.83 | 7.26 | 5.66 | C | |||||
0.0110 | 0.0292 | 0.0504 | ||||||
1x3.1 | A | 135.92 | 132.64 | 142.87 | 156.49 | [25:483.79] | HD | |
4 | 1.34 | 6.34 | 5.03 | Q | ||||
0.0476 | 0.0435 | 0.0453 | 0.0476 | TW | ||||
1x3.2 | A | 100 | 132.58 | 142.87 | 156.50 | [100:558.16] | HD | |
25 | 7.25 | 5.26 | 0.0512 | Q | ||||
0.01 | 0.0435 | 0.0453 | 0.0477 | TW | ||||
1x3.3 | A | 1 | 132.64 | 142.87 | 156.46 | [85:1992.79] | HD | |
400 | 3.78 | 1.86 | 6.68 | Q | ||||
0.01 | 0.0435 | 0.0453 | 0.0476 | TW | ||||
3x1.1 | A | 135.92 | 132.59 | 142.85 | 156.49 | [1275:1348.48] | HD | |
3.76 | 3.06 | 2.71 | 0.0432 | Q | ||||
0.0476 | 0.0435 | 0.0453 | 0.0477 | TW | ||||
3x1.2 | A | 100 | 132.64 | 142.80 | 156.46 | [560:597.69] | HD | |
25 | 5.42 | 2.25 | 1.76 | Q | ||||
0.01 | 0.0435 | 0.0453 | 0.0476 | TW | ||||
MS | 139.71 | 139.73 | 139.85 | [8:16] | HD | |||
3.60 | 1.38 | 5.35 | S2 | |||||
0.0468 | 0.0468 | 0.0468 | ||||||
3x1.3 | A | 100 | 132.51 | 142.87 | 156.63 | [160:561.06] | HD | |
400 | 2.54 | 1.79 | 0.0991 | Q | ||||
0.01 | 0.0435 | 0.0453 | 0.0477 | TW | ||||
MS | 139.71 | 139.72 | 139.74 | [10:15.5] | HD | |||
5.84 | 2.84 | 1.27 | S2 | |||||
0.0468 | 0.0468 | 0.0468 | ||||||
1x4.1 | A | 135.92 | 56.81 | 123.87 | 183.43 | [50:202.18] | MHD | |
4 | 1.92 | 1.15 | 14.76 | C | ||||
0.0476 | 0.0180 | 0.0359 | 0.0487 | |||||
MS | 131.67 | 142.41 | 151.88 | [115:121], | HD | |||
1.92 | 8.71 | 3.95 | [9:15.5] | Q | ||||
0.0439 | 0.0460 | 0.0478 | ||||||
1x4.2 | A | 100 | 53.62 | 128.35 | 215.63 | [50:200.89] | MHD | |
25 | 3.88 | 3.21 | 17.27 | C | ||||
0.01 | 0.0183 | 0.0389 | 0.05 | |||||
1x4.3 | A | 1 | 43.52 | 122.10 | 200.92 | [50:211.14] | MHD | |
400 | 3.01 | 0.27 | 2.92 | C | ||||
0.01 | 0.0136 | 0.0330 | 0.0485 | |||||
4x1.1 | A | 135.92 | 49.93 | 128.33 | 203.82 | [15:381.79] | MHD | |
4 | 1.77 | 2.15 | 16.71 | C | ||||
0.0476 | 0.0168 | 0.0391 | 0.0487 | |||||
MS | 131.45 | 142.83 | 152.27 | [223:242] | HD | |||
1.92 | 4.22 | 8.51 | Q | |||||
0.0444 | 0.0462 | 0.0476 | TW | |||||
4x1.2 | A | 100 | 51.86 | 124.30 | 205.75 | [50:310.23] | MHD | |
25 | 3.60 | 1.65 | 16.04 | C | ||||
0.01 | 0.0172 | 0.0358 | 0.0499 | |||||
MS | 146.06 | 147.19 | 147.87 | [246:247.75] | HD | |||
7.85 | 0.0799 | 0.30 | S2 | |||||
0.0484 | 0.0486 | 0.0487 | ||||||
4x1.3 | A | 100 | 51.20 | 126.69 | 187.53 | [25:286.47] | MHD | |
900 | 9.13 | 2.33 | 15.10 | C | ||||
0.01 | 0.0179 | 0.0388 | 0.0487 | |||||
MS | 130.19 | 143.60 | 151.34 | [46:51.5] | HD | |||
8.92 | 1.78 | 3.03 | Q | |||||
0.0441 | 0.0466 | 0.0483 | ||||||
MS | 122.37 | 123.00 | 123.76 | [12.5:15] | HD | |||
0.47 | 0.89 | 1.50 | S2 | |||||
0.0419 | 0.0419 | 0.0419 | ||||||
2x2.1 | A | 135.92 | 47.29 | 79.2 | 131.63 | [40:1001.34] | HD | |
4 | 9.49 | 2.01 | 6.90 | C | ||||
0.0476 | 0.0160 | 0.0267 | 0.0393 | |||||
2x2.2 | A | 100 | 48.34 | 78.59 | 118.35 | [40:331.19] | HD | |
25 | 1.77 | 3.59 | 4.69 | C | ||||
0.01 | 0.0166 | 0.0265 | 0.0373 | |||||
2x2.3 | A | 1 | 46.40 | 78.83 | 135.50 | [40:409.44] | HD | |
1225 | 4.30 | 1.18 | 1.98 | C | ||||
0.01 | 0.0171 | 0.0265 | 0.0399 | |||||
2x3.1 | A | 135.92 | 55.55 | 77.88 | 135.61 | [40:204.50] | HD | |
4 | 1.06 | 3.82 | 1.60 | C | ||||
0.0476 | 0.0176 | 0.0258 | 0.0358 | |||||
2x3.2 | A | 100 | 53.37 | 80.47 | 159.21 | [40:540.45] | HD | |
25 | 8.70 | 1.47 | 7.92 | C | ||||
0.01 | 0.0177 | 0.0263 | 0.0413 | |||||
2x3.3 | A | 1 | 47.40 | 79.94 | 149.96 | [40:417.59] | HD | |
400 | 8.98 | 1.51 | 2.21 | C | ||||
0.01 | 0.0161 | 0.0263 | 0.04 | |||||
3x2.1 | A | 135.92 | 55.47 | 80.48 | 136.12 | [40:318.22] | HD | |
4 | 1.56 | 4.52 | 1.16 | C | ||||
0.0476 | 0.0174 | 0.0264 | 0.0395 | |||||
3x2.2 | A | 100 | 53.78 | 80.50 | 149.84 | [40:364.87] | HD | |
25 | 1.79 | 1.12 | 2.41 | C | ||||
0.01 | 0.0188 | 0.0263 | 0.0394 | |||||
3x2.3 | A | 100 | 54.77 | 78.96 | 146.56 | [40:363.77] | HD | |
400 | 1.61 | 1.10 | 2.59 | C | ||||
0.01 | 0.0183 | 0.0261 | 0.0382 | |||||
2x4.1 | A | 135.92 | 56.35 | 83.93 | 165.97 | [40:244.38] | HD | |
4 | 1.25 | 1.77 | 2.77 | C | ||||
0.0476 | 0.0171 | 0.0263 | 0.0382 | |||||
2x4.2 | A | 100 | 54.33 | 82.05 | 159.80 | [40:381.79] | HD | |
25 | 1.94 | 9.28 | 1.62 | C | ||||
0.01 | 0.0196 | 0.0262 | 0.0375 | |||||
2x4.3 | A | 100 | 57.54 | 80.22 | 152.08 | [40:326.87] | HD | |
400 | 6.23 | 1.55 | 1.46 | C | ||||
0.01 | 0.0188 | 0.0259 | 0.0348 | |||||
4x2.1 | A | 135.92 | 56.54 | 79.66 | 153.39 | [40:290.67] | HD | |
4 | 6.00 | 1.60 | 8.01 | C | ||||
0.0476 | 0.0194 | 0.0261 | 0.0355 | |||||
4x2.2 | A | 225 | 55.31 | 80.67 | 146.53 | [40:366.17] | HD | |
25 | 1.49 | 7.81 | 1.50 | C | ||||
0.01 | 0.0194 | 0.0260 | 0.0349 | |||||
4x2.3 | A | 1 | 52.71 | 81.42 | 164.80 | [40:391.69] | HD | |
100 | 1.88 | 6.09 | 7.67 | C | ||||
0.01 | 0.0161 | 0.0260 | 0.0379 | |||||
3x3.1 | A | 135.92 | 59.34 | 80.38 | 133.18 | [40:201.10] | HD | |
4 | 4.48 | 6.42 | 5.76 | C | ||||
0.0476 | 0.0195 | 0.0262 | 0.0354 | |||||
3x3.2 | A | 100 | 55.04 | 79.20 | 108.71 | [40:321.50] | HD | |
25 | 9.71 | 4.57 | 4.75 | C | ||||
0.01 | 0.0186 | 0.0259 | 0.0327 | |||||
3x3.3 | A | 100 | 56.12 | 78.41 | 106.72 | [40:312.34] | HD | |
400 | 3.92 | 2.25 | 2.38 | C | ||||
0.01 | 0.0182 | 0.0259 | 0.0334 | |||||
3x4.1 | A | 135.92 | 60.18 | 78.74 | 120.72 | [40:200.17] | HD | |
4 | 6.08 | 3.19 | 3.62 | C | ||||
0.0476 | 0.0197 | 0.0256 | 0.0319 | |||||
3x4.2 | A | 225 | 63.75 | 79.86 | 121.48 | [40:295.39] | HD | |
100 | 1.11 | 1.20 | 8.99 | C | ||||
0.01 | 0.0203 | 0.0259 | 0.0323 | |||||
3x4.3 | A | 1 | 62.18 | 79.26 | 117.60 | [40:285.44] | HD | |
900 | 5.22 | 7.20 | 5.29 | C | ||||
0.01 | 0.0206 | 0.0258 | 0.0327 | |||||
4x3.1 | A | 135.92 | 60.75 | 79.99 | 112.65 | [40:200.01] | HD | |
4 | 6.26 | 1.07 | 5.83 | C | ||||
0.0476 | 0.0190 | 0.0259 | 0.0338 | |||||
4x3.2 | A | 225 | 59.81 | 79.15 | 110.28 | [40:337.28] | HD | |
100 | 2.34 | 7.68 | 5.46 | C | ||||
0.01 | 0.0202 | 0.0258 | 0.0321 | |||||
4x3.3 | A | 100 | 53.78 | 78.80 | 109.92 | [40:296.86] | HD | |
400 | 1.44 | 6.20 | 5.71 | C | ||||
0.01 | 0.0183 | 0.0257 | 0.0324 | |||||
4x4.1 | A | 135.92 | 65.55 | 79.53 | 106.56 | [40:200.51] | HD | |
4 | 5.33 | 1.03 | 7.88 | C | ||||
0.0476 | 0.0212 | 0.0257 | 0.0313 | |||||
4x4.2 | A | 225 | 61.65 | 79.41 | 105.68 | [40:528.55] | HD | |
100 | 8.18 | 3.14 | 5.88 | C | ||||
0.01 | 0.0201 | 0.0258 | 0.0333 | |||||
4x4.3 | A | 100 | 62.51 | 80.20 | 113.30 | [40:342.84] | HD | |
400 | 1.16 | 2.58 | 2.61 | C | ||||
0.01 | 0.0210 | 0.0259 | 0.0319 |
Run | G | Interval | Rm | Rm | Rm | Rm | |||||
4x4.2 | 51–528.55 | 0.223 | 22.413 | 0.223 | 22.416 | 0.206 | 20.722 | 0.206 | 20.720 | 12.58 | |
4x2.1 | 232.40–290.65 | 0.219 | 21.769 | 0.219 | 21.770 | 0.241 | 23.988 | 0.241 | 23.983 | 12.43 | |
3x3.3 | 220.46–312.34 | 0.220 | 21.843 | 0.220 | 21.842 | 0.241 | 24.011 | 0.241 | 24.004 | 12.43 | |
2x2.3 | 310.15–409.44 | 0.219 | 21.879 | 0.220 | 21.885 | 0.242 | 24.115 | 0.242 | 24.103 | 12.46 | |
2x3.1 | 100–204.50 | 0.219 | 21.920 | 0.219 | 21.923 | 0.241 | 24.113 | 0.241 | 24.108 | 12.50 | |
4x3.3 | 223.17–296.86 | 0.221 | 22.050 | 0.221 | 22.047 | 0.242 | 24.176 | 0.242 | 24.167 | 12.48 | |
2x3.2 | 505.52–540.45 | 0.220 | 22.092 | 0.220 | 22.101 | 0.242 | 24.280 | 0.242 | 24.278 | 12.53 | |
3x2.3 | 251.39–363.77 | 0.221 | 22.183 | 0.221 | 22.190 | 0.243 | 24.365 | 0.242 | 24.358 | 12.55 | |
3x4.1 | 42.18–200.17 | 0.222 | 22.273 | 0.222 | 22.277 | 0.243 | 24.377 | 0.243 | 24.369 | 12.55 | |
3x4.3 | 219.42–295.39 | 0.221 | 22.281 | 0.221 | 22.283 | 0.243 | 24.400 | 0.242 | 24.393 | 12.57 | |
4x3.2 | 290.74–337.38 | 0.222 | 22.337 | 0.222 | 22.332 | 0.243 | 24.414 | 0.243 | 24.406 | 12.56 | |
4x4.3 | 201–336 | 0.223 | 22.385 | 0.223 | 22.385 | 0.243 | 24.439 | 0.243 | 24.436 | 12.56 | |
4x3.1 | 42–200.02 | 0.223 | 22.396 | 0.223 | 22.397 | 0.243 | 24.481 | 0.243 | 24.480 | 12.57 | |
3x4.2 | 246.87–285.44 | 0.223 | 22.454 | 0.223 | 22.446 | 0.243 | 24.497 | 0.243 | 24.486 | 12.57 | |
3x3.2 | 278.28–321 | 0.224 | 22.467 | 0.223 | 22.459 | 0.244 | 24.533 | 0.244 | 24.518 | 12.56 | |
2x3.3 | 309.16–417.59 | 0.221 | 22.382 | 0.221 | 22.415 | 0.243 | 24.554 | 0.243 | 24.560 | 12.65 | |
3x3.1 | 42.91–201.10 | 0.222 | 22.468 | 0.222 | 22.473 | 0.243 | 24.574 | 0.243 | 24.568 | 12.62 | |
2x2.2 | 200–331.19 | 0.221 | 22.333 | 0.221 | 22.356 | 0.245 | 24.698 | 0.244 | 24.680 | 12.62 | |
4x4.1 | 100–200.51 | 0.223 | 22.619 | 0.224 | 22.623 | 0.244 | 24.689 | 0.244 | 24.685 | 12.65 | |
2x2.1 | 719.70–800.70 | 0.221 | 22.484 | 0.221 | 22.502 | 0.243 | 24.788 | 0.243 | 24.779 | 12.73 | |
2x4.2 | 317.09–381 | 0.223 | 22.741 | 0.224 | 22.784 | 0.243 | 24.795 | 0.243 | 24.810 | 12.73 | |
2x4.3 | 223.93–326 | 0.224 | 22.806 | 0.224 | 22.816 | 0.244 | 24.850 | 0.244 | 24.846 | 12.72 | |
3x2.1 | 231.77–318 | 0.223 | 22.723 | 0.223 | 22.728 | 0.244 | 24.863 | 0.244 | 24.857 | 12.72 | |
4x2.3 | 268.69–366.17 | 0.224 | 22.855 | 0.224 | 22.860 | 0.244 | 24.902 | 0.244 | 24.895 | 12.73 | |
2x4.1 | 102–207.69 | 0.225 | 22.959 | 0.226 | 22.973 | 0.245 | 24.954 | 0.245 | 24.961 | 12.73 | |
3x2.2 | 304.32–364 | 0.223 | 22.978 | 0.224 | 23.022 | 0.244 | 25.093 | 0.244 | 25.104 | 12.86 | |
4x2.2 | 334.41–391.69 | 0.225 | 23.106 | 0.226 | 23.135 | 0.245 | 25.106 | 0.245 | 25.113 | 12.81 | |
3x1.1 | 100–249.39 | 0.227 | 27.379 | 0.227 | 27.279 | 0.247 | 29.761 | 0.246 | 29.608 | 15.04 | |
2x1.2 | M | 1946.90–1980.90 | 0.227 | 26.638 | 0.228 | 26.815 | 0.254 | 29.868 | 0.255 | 29.949 | 14.68 |
3x1.2 | 285.85–377.67 | 0.227 | 28.423 | 0.226 | 28.342 | 0.245 | 30.675 | 0.244 | 30.537 | 15.65 | |
1x4.3 | M | 130–211.14 | 0.242 | 29.726 | 0.243 | 29.786 | 0.254 | 31.235 | 0.254 | 31.163 | 15.34 |
4x1.3 | M | 108.81–241.99 | 0.233 | 29.797 | 0.233 | 29.727 | 0.248 | 31.701 | 0.247 | 31.589 | 15.96 |
4x1.2 | M | 200–310.23 | 0.238 | 30.258 | 0.238 | 30.170 | 0.253 | 32.107 | 0.252 | 31.986 | 15.85 |
4x1.1 | M | 168–330 | 0.238 | 29.814 | 0.238 | 29.770 | 0.256 | 32.060 | 0.256 | 32.015 | 15.65 |
1x4.1 | M | 140–192 | 0.242 | 30.969 | 0.241 | 30.894 | 0.252 | 32.300 | 0.251 | 32.165 | 16.00 |
1x4.2 | M | 120–200 | 0.237 | 31.140 | 0.236 | 31.098 | 0.259 | 34.047 | 0.257 | 33.888 | 16.45 |
1x2.1 | M | 185–245 | 0.238 | 30.339 | 0.238 | 30.333 | 0.267 | 34.018 | 0.267 | 34.003 | 15.92 |
1x2.3 | M | 1606–1691 | 0.238 | 30.534 | 0.238 | 30.526 | 0.267 | 34.206 | 0.267 | 34.181 | 16.01 |
2x1.3 | M | 3460–3505.05 | 0.239 | 30.794 | 0.238 | 30.787 | 0.266 | 34.407 | 0.266 | 34.383 | 16.13 |
1x2.2 | M | 50–300 | 0.239 | 31.193 | 0.239 | 31.188 | 0.266 | 34.715 | 0.266 | 34.684 | 16.32 |
2x1.1 | M | 152–277.81 | 0.248 | 33.000 | 0.248 | 32.987 | 0.261 | 34.777 | 0.261 | 34.739 | 16.64 |
1x3.3 | 50–354.35 | 0.234 | 31.566 | 0.234 | 31.568 | 0.263 | 35.499 | 0.263 | 35.483 | 16.87 | |
1x3.1 | 25–487.12 | 0.234 | 31.668 | 0.234 | 31.659 | 0.263 | 35.589 | 0.263 | 35.566 | 16.90 | |
1x3.2 | 83–558.16 | 0.234 | 31.669 | 0.234 | 31.660 | 0.263 | 35.590 | 0.263 | 35.567 | 16.90 | |
3x1.3 | 330.20–365.60 | 0.234 | 31.676 | 0.234 | 31.667 | 0.263 | 35.597 | 0.263 | 35.574 | 16.90 |
Run | Phase | Interval | Rm | Rm | Rm | Rm | |||||
1x2.1 | T | 10–65 | 0.215 | 22.690 | 0.214 | 22.615 | 0.249 | 26.325 | 0.249 | 26.265 | 13.20 |
G | 75–170 | 0.240 | 32.566 | 0.240 | 32.553 | 0.263 | 35.653 | 0.263 | 35.638 | 16.93 | |
S | 185–250 | 0.238 | 30.425 | 0.238 | 30.418 | 0.267 | 34.099 | 0.267 | 34.083 | 15.96 | |
1x2.2 | T | 0–13.8 | 0.220 | 24.205 | 0.220 | 24.172 | 0.245 | 26.928 | 0.244 | 26.765 | 13.72 |
G | 20–40 | 0.240 | 32.557 | 0.240 | 32.543 | 0.263 | 35.665 | 0.263 | 35.648 | 16.93 | |
S | 50–115 | 0.238 | 30.439 | 0.238 | 30.432 | 0.267 | 34.165 | 0.267 | 34.151 | 15.98 | |
1x2.3 | D | 10–293 | 0.214 | 22.367 | 0.214 | 22.350 | 0.246 | 25.699 | 0.246 | 25.627 | 13.03 |
G | 300–1597 | 0.240 | 32.584 | 0.240 | 32.571 | 0.263 | 35.667 | 0.263 | 35.653 | 16.94 | |
S | 1606–1691.82 | 0.238 | 30.534 | 0.238 | 30.526 | 0.267 | 34.206 | 0.267 | 34.181 | 16.01 | |
2x1.1 | T | 0–8 | 0.244 | 32.150 | 0.244 | 32.151 | 0.260 | 34.363 | 0.260 | 34.362 | 16.50 |
S | 12–277.81 | 0.248 | 33.010 | 0.248 | 32.993 | 0.261 | 34.789 | 0.261 | 34.737 | 16.65 | |
2x1.2 | D | 40–270 | 0.216 | 22.533 | 0.214 | 22.374 | 0.246 | 25.743 | 0.245 | 25.585 | 13.06 |
G | 285–1555 | 0.241 | 32.658 | 0.240 | 32.621 | 0.263 | 35.727 | 0.263 | 35.699 | 16.95 | |
S | 1570–1962 | 0.239 | 31.254 | 0.239 | 31.170 | 0.266 | 34.814 | 0.266 | 34.743 | 16.33 | |
2x1.3 | D | 40–633.2 | 0.215 | 22.265 | 0.214 | 22.161 | 0.246 | 25.559 | 0.245 | 25.448 | 12.97 |
G | 646–3445 | 0.240 | 32.611 | 0.240 | 32.579 | 0.263 | 35.686 | 0.263 | 35.662 | 16.95 | |
S | 3460–3505.05 | 0.239 | 30.794 | 0.238 | 30.787 | 0.266 | 34.407 | 0.266 | 34.383 | 16.13 |
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Jeyabalan, S.R.; Chertovskih, R.; Gama, S.; Zheligovsky, V. Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis. Mathematics 2022, 10, 2957. https://doi.org/10.3390/math10162957
Jeyabalan SR, Chertovskih R, Gama S, Zheligovsky V. Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis. Mathematics. 2022; 10(16):2957. https://doi.org/10.3390/math10162957
Chicago/Turabian StyleJeyabalan, Simon Ranjith, Roman Chertovskih, Sílvio Gama, and Vladislav Zheligovsky. 2022. "Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis" Mathematics 10, no. 16: 2957. https://doi.org/10.3390/math10162957
APA StyleJeyabalan, S. R., Chertovskih, R., Gama, S., & Zheligovsky, V. (2022). Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis. Mathematics, 10(16), 2957. https://doi.org/10.3390/math10162957