We report on three-dimensional direct numerical simulation of wave turbulence
on the free surface of a magnetic fluid subjected to an external horizontal
magnetic field. A transition from capillarywave turbulence to anisotropic
magneto-capillary wave turbulence is observed for an increasing field. At high
enough field, wave turbulence becomes highly anisotropic, cascading mainly
perpendicularly to the field direction, in good agreement with the prediction
of a phenomenological model, and with anisotropic Alfv{\'e}n wave turbulence.
Although surface waves on a magnetic fluid are different from Alfv{\'e}n waves
in plasma, a strong analogy is found with similar wave spectrum scalings and
similar magnetic-field dependent dispersionless wave velocities.Comment: in press in Phys. Rev E (Letter). For Supplemental Material, see
http://www.msc.univ-paris-diderot.fr/~falcon/PRE\_Letter22/PRE2022andSuppMat.pd