Influence of an oblique magnetic field on planar flame front instability

Abstract

We investigate the effect of external magnetic field on the Darrieus-Landau instability (DLI), the linear instability of a planar premixed flame front,in an electrically conducting fluid. This setting has applicability to combustion phenomena of the astrophysical scale. Without magnetic field, the planar flame front is necessarily unstable. Previous investigation treated independently the normal and tangential magnetic fields. Here we focus on the case of their simultaneous application,namely, oblique magnetic field. Rederiving the jump conditions, across the flame front, of the physical variables based on the ideal magnetohydrodyamics equations,we correct the previous treatment of the Markstein effect and extend it to incorporate the disparity of the magnetic permeability. A genuinely oblique magnetic field has an unusual characteristics that discontinuity in tangential velocity across the flame is induced. It is found that the Kelvin-Helmholtz instability takes over the stabilizing effect on the DLI in a limited parameter regime when the normal Alfv´en speed exceeds the normal fluid velocity in both the unburned and burned regions.