Surface waves in ferrofluids under vertical magnetic field

We present here new experimental results about the waves at the horizontal free surface of a magnetic fluid submitted to a normal magnetic field. The waves art, generated by a small modulation at frequency omega of the vertical field H-e. Using a shadowgraph method, we are able to measure the wavevector k of the 2D waves for a given value of omega and H-e. The dispersion relation of the surface waves is established experimentally. On the other hand, we propose a theoretical derivation of the dispersion equation which includes a more complete treatment of the magnetic term than the previous works. Finally, we conclude that a linear and inviscid analysis is sufficient to fit well the experimental data, except in the vicinity of the critical field where a surface instability occurs.