Scaling behaviour of small-scale dynamos driven by Rayleigh–Bénard convection

• Published in: Journal of fluid mechanics 2021-03, Vol.915, Article A15
• Main Authors: Yan, M., Tobias, S.M., Calkins, M.A.
• Format: Article
• Language: English
• Subjects: Convection; Energy; Fluid flow; Heat transport; Investigations; JFM Papers; Kinetic energy; Length; Magnetic field; Magnetic fields; Numerical analysis; Ohmic dissipation; Rayleigh-Benard convection; Reynolds number; Rotating generators; Scaling; Simulation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2021.61

A numerical investigation of convection-driven dynamos is carried out in the plane layer geometry. Dynamos with different magnetic Prandtl numbers $Pm$ are simulated over a broad range of the Rayleigh number $Ra$. The heat transport, as characterized by the Nusselt number $Nu$, shows an initial departure from the heat transport scaling of non-magnetic Rayleigh–Bénard convection (RBC) as the magnetic field grows in magnitude; as $Ra$ is increased further, the data suggest that $Nu$ grows approximately as $Ra^{2/7}$, but with a smaller prefactor in comparison with RBC. Viscous ($\epsilon _u$) and ohmic ($\epsilon _B$) dissipation contribute approximately equally to $Nu$ at the highest $Ra$ investigated; both ohmic and viscous dissipation approach a Reynolds-number-dependent scaling of the form $Re^a$, where $a \approx 2.8$. The ratio of magnetic to kinetic energy approaches a $Pm$-dependent constant as $Ra$ is increased, with the constant value increasing with $Pm$. The ohmic dissipation length scale depends on $Ra$ in such a way that it is always smaller, and decreases more rapidly with increasing $Ra$, than the viscous dissipation length scale for all investigated values of $Pm$.