Role of the basin boundary conditions in gravity wave turbulence

TL;DR

This study experimentally investigates how basin boundary conditions influence gravity wave turbulence, revealing that boundary types significantly affect wave field properties and spectrum scaling, with results aligning with weak turbulence theory.

Contribution

It demonstrates the impact of boundary conditions on wave turbulence properties and spectrum scaling, providing experimental validation of theoretical predictions.

Findings

Wave spectrum scales as a frequency-power law with an exponent up to -4.

Boundary conditions alter the wave field from quasi-one-dimensional to multidirectional.

The Kolmogorov-Zakharov constant matches recent theoretical estimates.

Abstract

Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with a recent theoretical value.