Travelling waves on a free surface of a magnetic fluid layer

Plane flow of a layer of an incompressible viscous magnetic fluid with constant magnetic permeability under the action of an alternating magnetic field is investigated. The strength of the magnetic field creating a travelling sinusoidal finite-amplitude wave on the surface of the fluid is found and the average volume flow-rate is calculated. The magnetic field strength amplitude is found as a function of the wavelength and other parameters of the problem. The existence of the minimum magnetic field amplitude at a certain length of the surface wave is shown.