A note on the amplitude modulation phenomenon in non-canonical wall-bounded flows

TL;DR

This paper investigates how non-canonical wall-bounded flows exhibit complex non-linear interactions across turbulence scales, influenced by effects like roughness and pressure gradients, challenging previous assumptions based on canonical flows.

Contribution

It revisits triadic interactions in non-canonical flows, showing they become significant with non-canonical effects, unlike in canonical flows where only large-scale and inner-scale interactions matter.

Findings

Triadic interactions increase with non-canonical effects.

Significant interactions involve all turbulence scales.

Implications for near-wall flow prediction models.

Abstract

The amplitude modulation phenomena, defined originally by Mathis et al. (J. Fluid Mech., 628, 311-337; 2009), corresponds to a unique non-linear interaction between Reynolds number ($Re_{\tau}$) dependent large-scale motions and $Re_{\tau}$-invariant inner-scale motions observed in canonical wall-bounded flows. While similar non-linear interactions have been quantified previously in non-canonical wall-bounded flows, linking them solely to amplitude modulation is questionable due to the fact that each non-canonical effect is associated with distinct variations in the energies of both the large and inner scaled motions. This study revisits analysis of non-linear triadic interactions, with consideration to various non-canonical effects, by analyzing published hot-wire datasets acquired in the large Melbourne wind tunnel. It is found that triadic interactions, across the entire turbulence scale hierarchy, may become statistically significant with increasing intensity of non-canonical effects such as wall roughness, pressure gradients, and spanwise or wall-normal forcing (when compared relative to their respective canonical baseline cases at matched $Re_{\tau}$). This stands in contrast to previous observations made in canonical flows, where only the interaction between inner scales and inertia-dominated large scales was considered dynamically significant for increasing $Re_{\tau}$. The implications of these findings are discussed for near-wall flow prediction models in non-canonical flows, which should take into account \emph{all} non-linear interactions coexisting in wall-bounded flows.