On skin friction in wall-bounded turbulence

TL;DR

This paper derives and validates mathematical formulas for accurately estimating the skin friction coefficient in wall-bounded turbulence using mean velocity and Reynolds stress data, applicable at high Reynolds numbers.

Contribution

The paper introduces new integral formulas for skin friction coefficient based on the Reynolds averaged momentum equation, validated with DNS data.

Findings

Formulas estimate skin friction with less than 2% error.

Applicable to turbulent channel and boundary layer flows at high Reynolds numbers.

Provides a practical method when near-wall measurements are difficult.

Abstract

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specially, with the theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region $[h_0, h_1]$. The formulas are validated using the direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than $2\%$. We believe that the present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near wall statistics are very difficult to measure accurately.