In two-dimensional turbulent thermomagnetic convection, an ultimate-like scaling regime with both Nu and Re proportional to Ra_m to the power 1/2 emerges right after the laminar-to-turbulent transition and persists over more than an order of magnitude in Ra_m.
Oberbeck, Ueber die wärmeleitung der flüssigkeiten bei berücksichtigung der strömungen infolge von temper- aturdifferenzen, Annalen der Physik243, 271 (1879)
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Early emergence of ultimate-like transport in two-dimensional turbulent thermomagnetic convection
In two-dimensional turbulent thermomagnetic convection, an ultimate-like scaling regime with both Nu and Re proportional to Ra_m to the power 1/2 emerges right after the laminar-to-turbulent transition and persists over more than an order of magnitude in Ra_m.