Quasi-static magnetoconvection with a tilted magnetic field

A numerical study of convection with stress-free boundary conditions in the presence of an imposed magnetic field that is tilted with respect to the direction of gravity is carried out in the limit of small magnetic Reynolds number. The dynamics are investigated over a range of Rayleigh number Ra and Chandrasekhar numbers up to Q = 2×10⁶, with the tilt angle between the gravity vector and imposed magnetic field vector fixed at 45^°. Heat and momentum transport, as characterized by the Nusselt and Reynolds numbers, are quantified and compared with the vertical field case. Ohmic dissipation dominates over viscous dissipation in all cases investigated. 

Provided Ra is sufficiently large, all investigated values of Q exhibit an inverse kinetic energy cascade that yields large scale flows. The interaction of these mean flows with the imposed field results in the formation of Hartmann boundary layers.

For fixed Q the mean flow is initially stronger in the direction perpendicular to the imposed magnetic field, but as Ra is increased we observe relaxation oscillations in which both along-field and cross-field mean flows are comparable in magnitude. Our findings suggest that both field direction and magnitude are critical factors in nonlinear magnetoconvection dynamics.