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

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 Alfvén wave turbulence. Although surface waves on a magnetic fluid are different from Alfvén waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.Introduction.-Most of nonlinear wave systems reach a wave turbulence regime as a result of wave interactions [1,2]. This phenomenon occurs in various domains at different scales such as ocean surface waves, plasma waves, hydroelastic or elastic waves, internal or inertial waves, and optical waves [2]. The weakly nonlinear theory (called weak turbulence theory) derived analytically the solutions of the corresponding kinetic equations [1][2][3][4][5]. These solutions, known as the Kolmogorov-Zakharov (KZ) spectra, describe the energy transfers towards small scales (direct cascade) or large ones (inverse cascade). Athough these solutions have been tested in different systems, numerical and experimental works are currently a paramount of interest to understand in what extend this theory can describe real physical systems.One of the most important system is Alfvén waves in magnetohydrodynamics (MHD) [6], initially observed in laboratory plasma [7][8][9][10], and recently in astrophysical plasma such as the Sun's outer [11] or inner [12] atmosphere. Three-dimensional (3D) Alfvén waves in a turbulent regime were initially predicted to follow the isotropic Iroshnikov-Kraichnan spectrum [13,14]. However, they become strongly anisotropic in a presence of an intense magnetic field, and transfer energy mainly in the plane transverse to the field, thus becoming nearly two-dimensional [2,15,16]. The spectrum of this anisotropic weak turbulence regime has been derived [17, 18], then observed in the Jupiter's magnetosphere [19], and confirmed recently numerically [20,21]. An analogous anisotropic behavior is predicted for hydrodynamics waves on the surface a magnetic fluid subjected to a horizontal magnetic field [22]. Although wave turbulence regimes have been observed on the surface of a ferrofluid in an external magnetic field both experimentally [23,24] and numerically [25], the anisotropic regime