# Turbulent kinetic energy production and Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

## TL;DR

This paper analyzes turbulent kinetic energy production and flow structures in turbulent channel flows over smooth and rough walls, revealing key scaling laws and the influence of surface roughness on flow physics.

## Contribution

It demonstrates that the shear parameter scales well with Reynolds number and links flow structures to the second invariant, highlighting effects of wall roughness on turbulence.

## Key findings

- Shear parameter scales with Reynolds number in near-wall region.
- Maximum turbulent kinetic energy production occurs where the second invariant is zero.
- Surface roughness modifies flow structures and increases turbulence production.

## Abstract

Data available in literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (2015), Bernardini et al. (2014), Yamamoto and Tsuji (2018) and Orlandi et al. (2015) in a large range of Reynolds number have been used to find that shear parameter the ratio between the eddy turnover time and the time scale of the mean deformation (1/S), scales very well with the Reynolds number in the near-wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall. the shear parameter is linked to the flow structures, as well as the second invariant, and also this quantity presents a good scaling. It has been found that the maximum of turbulent kinetic energy production occurs in the layer with the second invariant approximately zero, that is where the unstable sheet-like structures roll-up to become rods. The decomposition of production in the contribution of elongational and compressive strain demonstrates that the two contribution present a good scaling. The perfect scaling however holds when the near-wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent channels with different type of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the normal to the wall velocity fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production. These simulations at intermediate Reynolds number indicated that in the outer region the Townsend similarity hypothesis holds.