Changes in turbulent dissipation in a channel flow with oscillating walls

TL;DR

This study uses direct numerical simulations to analyze how harmonic wall oscillations affect turbulent dissipation and drag reduction in a channel flow, revealing a linear relationship between enstrophy dynamics and drag reduction.

Contribution

It provides a detailed physical mechanism linking wall oscillations, turbulent enstrophy, and drag reduction, with new insights into the role of turbulent dissipation.

Findings

Turbulent dissipation increases with mass flow rate due to wall oscillations.

The dominant oscillation-related enstrophy term causes initial dissipation enhancement.

A linear relation exists between the enstrophy term and drag reduction.

Abstract

Harmonic oscillations of the walls of a turbulent plane channel flow are studied by direct numerical simulations to improve our understanding of the physical mechanism for skin-friction drag reduction. The simulations are carried out at constant pressure gradient in order to define an unambiguous inner scaling: in this case, drag reduction manifests itself as an increase of mass flow rate. Energy and enstrophy balances, carried out to emphasize the role of the oscillating spanwise shear layer, show that the viscous dissipations of the mean flow and of the turbulent fluctuations increase with the mass flow rate, and the relative importance of the latter decreases. We then focus on the turbulent enstrophy: through an analysis of the temporal evolution from the beginning of the wall motion, the dominant, oscillation-related term in the turbulent enstrophy is shown to cause the turbulent dissipation to be enhanced in absolute terms, before the slow drift towards the new quasi-equilibrium condition. This mechanism is found to be responsible for the increase in mass flow rate. We finally show that the time-average volume integral of the dominant term relates linearly to the drag reduction.