Magnetohydrodynamic instability with bichromatic perturbations in aluminum reduction cells

The linear stability of the electrically conducting liquid–liquid interface is investigated in a finite, rectangular domain inspired by aluminum reduction cells. interfacial instability known to be effect Lorentz force produced interaction perturbed horizontal current with vertical magnetic field. While much literature points analysis monochromatic perturbations, role bichromatic type investigated, for first time. Considering perturbation, independent wavenumbers along directions, dispersion relation derived that includes effects force, friction, tension, and gravity. This work reveals component field can also introduce instability, particularly when friction negligible. predicted mainly responsible lower modes, destabilizes all modes. For fixed value density, inter-electrode gap at neutral increases an increase ratio cell length width. present findings are applicable any general two-fluid interface, presence ambient