# Wave turbulence of a liquid surface in an external tangential electric field

## TL;DR

This study uses numerical simulations to explore wave turbulence on a liquid dielectric surface under a tangential electric field, revealing energy cascades, Gaussian boundary inclinations, and power-law spectra similar to magnetohydrodynamic turbulence.

## Contribution

It demonstrates the generation of energy cascades and chaotic boundary behavior in liquid surface waves influenced by an external electric field, linking wave turbulence to MHD turbulence spectra.

## Key findings

- Counter-propagating wave interactions generate a direct energy cascade.
- Boundary inclination angles tend to a Gaussian distribution in steady state.
- Surface perturbation spectrum follows a $k^{-5/2}$ power law.

## Abstract

A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the interaction of counter-propagating nonlinear waves can generate a direct energy cascade. In the quasistationary energy dissipation regime, probability density functions for angles of inclination of the boundary tend to a Gaussian distribution and the shape of the boundary becomes complex and chaotic. The spectrum of the surface perturbations in this regime is described by a power law $k^{-5/2}$. The energy spectrum has the form $k^{-3/2}$, which coincides with the Iroshnikov-Kraichnan energy spectrum and indicates that the observed wave turbulence of the liquid surface and the weak magnetohydrodynamic turbulence of interacting Alfv\'en waves have a related nature.