2023/10/12 by Shujaut H. Bader, Bader, Shujaut H., Xiaojue Zhu +1 · 1 citation
Physics and Astronomy · Earth and Planetary Sciences · Engineering · #Solar and Space Plasma Dynamics #Oceanographic and Atmospheric Processes #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.2310.08000
The scaling law for the horizontal length scale ℓ relative to the domain height L, originating from the linear theory of quasi-static magnetoconvection, ℓ/L ∼ Q-1/6, has been verified through two-dimensional (2D) direct numerical simulation (DNS), particularly at high values of the Chandrasekhar number (Q). This relationship remains valid within a specific flow regime characterized by columnar structures aligned with the magnetic field. Expanding upon the Q-dependence of the horizontal length scale, we have derived scaling laws for the Nusselt number Nu and the Reynolds number Re as functions of the driving forces (Rayleigh number Ra and Q) in quasi-static magnetoconvection influenced by a strong magnetic field. These scaling relations, Nu ∼ Ra/Q and Re ∼ Ra Q-5/6, have been successfully validated using 2D DNS data spanning a wide range of five decades in Q, ranging from 105 to 109. The successful validation of the relations at large Q values, combined with our theoretical analysis of dissipation rates and the incorporation of the horizontal length scale's influence on scaling behavior, presents a \textcolorblackvalid approach for deriving scaling laws under various conditions.