Scaling relations in quasi-static magnetoconvection with a strong vertical magnetic field

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 similar to Q(-1/6), has been verified through two-dimensional (2-D) 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 similar to Ra/Q and Re similar to RaQ(-5/6), have been successfully validated using 2-D DNS data spanning a wide range of five decades in Q, ranging from 10(5) to 10(9). 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 behaviour, presents a valid approach for deriving scaling laws under various conditions.

Automated summary

This study verifies the scaling law for the horizontal length scale in quasi-static magnetoconvection and derives scaling laws for the Nusselt number and the Reynolds number. The derived scaling relations are successfully validated using 2-D DNS data spanning a wide range of Q values.