Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

TL;DR

This study uses three-dimensional numerical simulations to explore how magnetic fields influence wave turbulence on a fluid surface, revealing a transition from capillary to anisotropic magneto-capillary turbulence and drawing parallels with plasma Alfvén waves.

Contribution

It presents the first detailed simulation of free-surface wave turbulence in magnetic fluids under magnetic fields, highlighting the transition and anisotropic behavior predicted by phenomenological models.

Findings

Transition from capillary to anisotropic wave turbulence with increasing magnetic field

Wave turbulence becomes highly anisotropic, cascading mainly perpendicular to the magnetic field

Similar spectral scalings and wave velocities observed as in Alfvén waves in plasma

Abstract

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.