Decay of capillary wave turbulence

TL;DR

This paper investigates the decay process of freely decaying capillary wave turbulence, revealing self-similar spectral decay, exponential amplitude damping, and the role of long waves as energy sources, aligning with weak turbulence theory.

Contribution

It provides experimental evidence of self-similar decay and identifies the damping mechanisms and energy transfer processes in decaying capillary wave turbulence.

Findings

Spectral decay follows the same power law as in stationary turbulence.

All Fourier modes decay exponentially at the same rate.

Long wavelengths are damped by viscous boundary layers and sustain turbulence during decay.

Abstract

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent than the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.