Effect of the horizontal length scale on scaling relations in quasi-static magnetoconvection

The morphology of the flow in Rayleigh-Bénard convection stabilized by the effect of a strong external vertical magnetic field is characterized by the columnar structures directed along the field lines. The resulting anisotropy significantly alters the length scale of the flow; the scaling of which remains of vital importance in the scaling relations for the response parameters. Previous studies concerning heat transport scaling in such a system have considered the domain height L as the sole length scale. In the present study, under the quasi-static assumption, we consider the horizontal width of the columnar structures as a relevant length scale and explore the effect of its dependence on the Chandrasekhar number (l/L~ Q^-1/6) on the scaling of the dimensionless heat transport (Nu), flow velocity (Re), and Ohmic dissipation (ε_η). Based on our theoretical analysis, incorporating the effect of the horizontal length scale, the scaling laws derived for the dimensionless heat transfer (Nu ~ Ra/Q) and flow velocity (Re ∝ RaQ^-5/6) and the Ohmic dissipation (ε_ηL⁴/ν³ ∝ Ra² Q^-1) are successfully validated using our high fidelity 2D DNS data spanning an unprecedented range of input parameters.