Effect of horizontal aspect ratio on convection rolls in the presence of transverse magnetic field

Abstract

We perform three-dimensional direct numerical simulations to investigate the effect of transverse magnetic field on the convection rolls of electrically conducting fluids using the classical Rayleigh–Bénard convection model. The control parameters “Q” (the Chandrasekhar number), “r” (the reduced Rayleigh number), and “Γ” (horizontal aspect ratio) are varied in the ranges 0≤Q≤2000, 1≤r≤25, and 1/2≤Γ≤2, respectively, for two different Prandtl numbers (Pr=0.025 and 0.1). In the absence of the magnetic field, the system allows convection in the form of two dimensional rolls near the onset, and it is suppressed by the Lorentz force appearing in the presence of transverse magnetic field. As a result, primary instability is moved toward higher r for Q>0, and the movement increases with Γ. Interestingly, for weak to moderate magnetic fields, there exists two different kinds of onset depending on Γ and Q. Steady oblique rolls (SOR) and transverse rolls (STR) are preferred at the onset accordingly as Γ<1 and Γ>1, respectively, while for Γ = 1, both STR and SOR are found to occur at the onset depending on Q. On the other hand, stronger transverse magnetic field orients the flow toward itself for Γ≥1. In the considered parameter regime, diverse routes to chaos including period-doubling, quasiperiodic, intermittent, and transient are observed close to the onset along with some interesting scaling laws associated with the oscillatory instability of the rolls.