Kelvin-Helmholtz instability of miscible ferrofluids

Abstract

We study the stability of an interface between two inviscid magnetic fluids of different densities flowing parallel to each other in an oscillatory manner. The system is pervaded by a uniform oblique magnetic field distribution. The analysis allows for mass and heat transfer across the interface. A general eigenvalue relation is derived and discussed analytically. The classical stability criterion is found to be substantially modified due to the effect of the oblique magnetic field with mass and heat transfer. Some previous studies are reported for appropriate data choices. The longitudinal magnetic field has a strong stabilizing influence on all wavelengths, which can be used to suppress the destabilizing influence of the mass and heat transfer. We conclude with a discussion of the stability of unsteady shear layers on the basis of the results. The parametric excitation of the surface waves is analyzed by means of the multiple-time-scales method. The transition curves are obtained analytically.