Coupling between Marangoni and Rosensweig instabilities - Part I: the transverse wave

Two semi-infinite incompressible and immiscible viscous fluids of infinite lateral extent are considered in the gravity field. One of them is ferromag netic and the other is a usual Newtonian liquid. Such a system is submitted to a magnetic field normal to the reference at surface, which separates th e two bulks. Developing the linear stability analysis, we show that the Ros ensweig critical values for transverse waves remain unaffected by a solutal or thermal Marangoni instability.