Early onset of half-power scaling laws in turbulent thermomagnetic convection

Abstract

Scaling laws for turbulent thermomagnetic convection are derived through a theoretical approach supported by direct numerical simulations in a two-dimensional square cavity filled with a high-$\mathrm{Pr}$ magnetic fluid. A transport regime consistent with half-power scalings, $\mathrm{Nu}\sim {\mathrm{Ra}}_m^{1/2}$ and $\mathrm{Re}\sim {\mathrm{Ra}}_m^{1/2}$, emerges at the early onset of the laminar-to-turbulent transition and persists over the entire range investigated. Energy-budget and thermo-fluid analyses indicate that this behavior originates from the coupling between thermal and magnetic gradients, which enhances magnetic-force-driven plume ejection and vertical advection across the fluid bulk.

arXiv commentMain body: 7 pages (3 figures). Version 2: Title and abstract updated; 2 additional DNS cases at higher magnetic Rayleigh numbers and kinetic-energy spectra included. The theoretical framework has been refined and extended with a bulk-scaling analysis. The main theoretical predictions, numerical results, and conclusions remain unchanged