Collapse of statistical equilibrium in large-scale hydroelastic turbulent waves

TL;DR

This paper experimentally studies the decay of large-scale hydroelastic turbulent waves initially in statistical equilibrium, deriving and confirming an energy decay law consistent with viscous damping, with potential applications to other turbulence systems.

Contribution

It introduces a theoretical and experimental framework for understanding the decay of out-of-equilibrium turbulence from a statistical equilibrium state.

Findings

Energy decays as a power law over time.

Derived decay law matches experimental data.

Identified viscous damping as the dissipation mechanism.

Abstract

At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among large-scale modes, in line with the Rayleigh-Jeans spectrum. Key open questions now pertain to either the emergence, decay, collapse, or other nonstationary evolutions from this state. Here, we experimentally investigate the free decay of large-scale hydroelastic turbulent waves, initially in a regime of statistical equilibrium. Using space- and time-resolved measurements, we show that the total energy of these large-scale tensional waves decays as a power law in time. We derive an energy decay law from the theoretical initial equilibrium spectrum and the linear viscous damping, as no net energy flux is carried. Our prediction then shows a good agreement with experimental data over nearly two decades in time, for various initial effective temperatures of the statistical equilibrium state. We further identify the dissipation mechanism and confirm it experimentally. Our approach could be applied to other decaying turbulence systems, with the large scales initially in statistical equilibrium.