Anisotropy of free-surface wave turbulence induced by a horizontal magnetic (electric) field

This work investigates the effects of anisotropy of free-surface wave turbulence under the influence of an external horizontal magnetic (electric) field based on direct numerical simulation technique. As the field increases, the surface wave system passes into the magnetohydrodynamic (MHD) turbulence regime with the formation of anisotropic condensate of capillary waves slowly propagating perpendicular to the external field. In the high field regime, the effect of the formation of discrete levels of frequency broadening in the space–time spectrum of capillary waves is reported for the first time. The performed correlation analysis showed that the resonance curve of the three-wave interaction is compressed with increasing field. This process leads to a non-local energy transfer from large-scale MHD waves to the small-scale capillary waves. Thus, discrete frequency levels in the spectrum of capillary waves arise as a result of the resonant decay of a MHD wave into secondary harmonics. Despite the anisotropy, the angle-averaged spectrum of surface elevations agrees well with the analytical estimate obtained under the assumption of isotropic wave propagation. We explain this contradiction by the fact that magnetic energy fluctuations on the liquid surface are distributed quasi-isotropically, and the anisotropic coherent condensate of capillary waves has a weak effect on the turbulence spectrum.