Free-surface deformations induced by three-dimensional turbulence

TL;DR

This study experimentally investigates how three-dimensional turbulence affects free-surface deformations, revealing two main mechanisms and developing a predictive linear response model.

Contribution

It provides the first detailed experimental characterization of free-surface deformations caused by turbulence and introduces a linear response model that captures key spectral features.

Findings

Surface deformation standard deviation scales linearly with subsurface velocity fluctuations.

Spectra show coexistence of coherent structures and passive pressure response mechanisms.

The linear response model accurately predicts spectral shapes and exponents.

Abstract

We report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, we perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (-2.5), suggesting the advection of turbulent structures at the free surface. We develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (-7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold.