Surface waves propagation on a turbulent flow forced electromagnetically

TL;DR

This study investigates how electromagnetic forcing-induced turbulence in liquid metal affects surface wave propagation, revealing wavelength shifts and a linear increase in damping with Froude number, contrasting previous quadratic models.

Contribution

It provides the first experimental evidence of linear damping increase with Froude number and analyzes wave deflection caused by turbulence, advancing understanding of wave-turbulence interactions.

Findings

Wavelength increases significantly for small wavelengths due to turbulence.

Damping of waves increases linearly with Froude number, not quadratically.

Wave deflection fluctuations can be estimated from wavelength shifts.

Abstract

We study the propagation of monochromatic surface waves on a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. This forcing creates a quasi two-dimensional (2D) turbulence with strong vertical vorticity. The turbulent flow contains much more energy than the surface waves. In order to focus on the surface wave, the deformations induced by the turbulent flow are removed. This is done by performing a coherent phase averaging. For wavelengths smaller than the forcing lengthscale, we observe a significant increase of the wavelength of the propagating wave that has not been reported before. We suggest that it can be explained by the random deflection of the wave induced by the velocity gradient of the turbulent flow. Under this assumption, the wavelength shift is an estimate of the fluctuations of deflection angle. The local measurements of the wave frequency far from the wavemaker do not reveal such systematic behavior, although a small shift is measured. Finally we quantify the damping enhancement induced by the turbulent flow. We review various theoretical scaling laws proposed previously. Most of them propose a damping that increases as the square of Froude number. In contrast, our experimental results show a turbulent damping increasing linearly with the Froude number. We interpret this linear behaviour as a balance between the time spent by a wave to cross a turbulent structure with the turbulent mixing time. The larger is the ratio of these 2 times, the more energy is extracted from the progressive wave. Finally, mechanisms of energy exchange and open issues are discussed and further studies are proposed.