The interpretation of the amplitude modulation coefficient and a transport-based alternative

TL;DR

This paper critically examines the amplitude modulation coefficient used in wall-bounded turbulence, revealing its limitations in detecting convective non-linearities, and proposes a new transport-based coefficient, $R_T$, for better analysis.

Contribution

The paper identifies the limitations of the traditional amplitude modulation coefficient and introduces a new coefficient, $R_T$, that better captures convective non-linearities and turbulent energy transport.

Findings

$R$ suppresses convective scale interactions signatures.

$R$ primarily measures linear interactions with the mean flow.

$R_T$ effectively quantifies convective non-linearities and energy transport.

Abstract

The amplitude modulation coefficient, $R$, that is widely used to characterize non-linear interactions between large- and small-scale motions in wall-bounded turbulence is not actually compatible with detecting the convective non-linearity of the Navier-Stokes equations. Through a spectral decomposition of $R$ and a simplified model of triadic convective interactions, we show that $R$ actually suppresses the signature of convective scale interactions, and we suggest that what $R$ likely measures is linear interactions between large-scale motions and the background mean flow. We propose an alternative coefficient which is specifically designed for the detection of convective non-linearities, and we show how this new coefficient, $R_T$, also quantifies the turbulent kinetic energy transport involved in turbulent scale interactions.