Anisotropy of propagation of spatial surface wave in ferrofluid under the influence of a horizontal magnetic field

In the linear formulation, the problem of the propagation of a spatial wave on the free surface of a ferrofluid under the influence of a uniform horizontal magnetic field is analytically solved. The resulting formula describes the dependence of the magnetic susceptibility of the ferrofluid on the magnitude of the magnetic field vector. Gravity, magnetic force, and surface tension are taken into account. It is assumed that the wavelength is much smaller than the thickness of the ferrofluid layer. The study investigates how the angle between the wave vector and the magnetic field vector affects both the phase and group velocities of the wave.