Modulation of near-wall turbulence in the transitionally rough regime

TL;DR

This study uses direct numerical simulations and a modified flow decomposition to analyze how different sizes of roughness elements affect turbulence and drag in transitional rough-wall flows, proposing a basis for predictive modeling.

Contribution

It introduces a modified triple decomposition to separate roughness effects from background turbulence and develops a laminar model for roughness-coherent flow contributions.

Findings

Background turbulence is minimally affected by small roughness, mainly displaced vertically.

Increasing roughness enhances energy at short wavelengths, indicating shear-flow instability.

A decomposition of the roughness function helps analyze different drag contributions.

Abstract

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model.