# Sources and fluxes of scale-energy in the overlap layer of wall turbulence

## TL;DR

This study uses direct numerical simulations to analyze scale-energy sources in turbulent channel flows, revealing two distinct peaks associated with near-wall and outer regions, and their dependence on Reynolds number and wall distance.

## Contribution

It identifies and characterizes two separate scale-energy sources in wall turbulence, linking them to the near-wall cycle and outer layer dynamics, with implications for understanding turbulence structure.

## Key findings

- Two distinct scale-energy source peaks identified.
- Outer source dynamics strongly depend on Reynolds number.
- Inner-outer interactions influence turbulence modulation.

## Abstract

Direct Numerical Simulations of turbulent channel flows at friction Reynolds number 550, 1000, 1500, are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall-distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scale-energy source are identified. The first stronger one belongs to the near-wall cycle. Its location in the space of scales and physical space is found to scale in viscous units while its intensity grows slowly with $Re$, indicating a near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall-distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner-outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.