Interscale energy transfer in turbulent channels

TL;DR

This paper analyzes the mechanisms of energy transfer across scales in wall-bounded turbulence, identifying key triadic interactions and demonstrating reduced-order models that retain essential dynamics at moderate Reynolds numbers.

Contribution

It introduces a detailed framework for mapping interscale energy transfer in turbulent channels and validates reduced-order simulations based on these identified interactions.

Findings

Key triadic interactions sustain turbulence.

Retaining 30% of interactions reproduces turbulence dynamics.

Near-wall turbulence deviates with fewer interactions.

Abstract

We investigate the energy cascade in wall-bounded turbulence by analysing the interscale transfer between streamwise and spanwise length scales in periodic channels. This transfer originates from the nonlinear interactions in the advective term of the Navier-Stokes equations, which satisfy the classical triadic compatibility relations. Each triadic interaction is examined individually, and its corresponding nonlinear momentum and energy transfer are mapped to assess its relative importance in sustaining turbulence. Motivated by the anisotropy of the flow, we interpret each contribution $\partial_i(u_i u_j)$ to the advection term as carrying distinct physical information, and therefore analyse them separately. Time-averaged maps of the energy transfer across all length scales and wall-normal positions for a channel flow at $Re_\tau \approx 180$ are used to explore the mechanisms underlying the cascade process. As a proof of concept, reduced-order simulations are performed by retaining only the interactions identified as responsible for significant energy transfer based on our framework. Turbulent dynamics are successfully reproduced when 30% or more of the total interactions are included, while noticeable deviations emerge in the near-wall region when this proportion is further reduced.