Quantitative experimental observation of weak inertial-wave turbulence

TL;DR

This paper experimentally observes the transition from discrete inertial wave interactions to a continuous weak turbulence regime in rotating turbulence, confirming theoretical predictions with detailed spectral and bicoherence analysis.

Contribution

First experimental validation of weak inertial-wave turbulence theory in rotating turbulence, demonstrating the transition from discrete to continuous spectra with increasing forcing.

Findings

Spectral evolution from discrete peaks to continuous spectrum with increased forcing.

Bicoherence maps show transition from localized peaks to smooth functions.

Spatial spectra follow power-law behavior predicted by weak turbulence theory.

Abstract

We report the quantitative experimental observation of the weak inertial-wave turbulence regime of rotating turbulence. We produce a statistically steady homogeneous turbulent flow that consists of nonlinearly interacting inertial waves, using rough top and bottom boundaries to prevent the emergence of a geostrophic flow. As the forcing amplitude increases, the temporal spectrum evolves from a discrete set of peaks to a continuous spectrum. Maps of the bicoherence of the velocity field confirm such a gradual transition between discrete wave interactions at weak forcing amplitude, and the regime described by weak turbulence theory (WTT) for stronger forcing. In the former regime, the bicoherence maps display a near-zero background level, together with sharp localized peaks associated with discrete resonances. By contrast, in the latter regime the bicoherence is a smooth function that takes values of the order of the Rossby number, in line with the infinite-domain and random-phase assumptions of WTT. The spatial spectra then display a power-law behavior, both the spectral exponent and the spectral level being accurately predicted by WTT at high Reynolds number and low Rossby number.