The vertical-velocity skewness in the inertial sublayer of turbulent wall flows

TL;DR

This paper demonstrates that the skewness of vertical velocity in the inertial sublayer of turbulent wall flows is universally constrained within a specific range, challenging existing predictive models and offering a new theoretical framework.

Contribution

It provides empirical evidence of universal vertical velocity skewness and introduces a theoretical model explaining this behavior, which improves understanding of turbulence in wall flows.

Findings

Sk_w is approximately 0.1-0.16 across different flows.

Theoretical model explains the universal skewness range.

Down-gradient closure models cannot predict Sk_w accurately.

Abstract

We provide empirical evidence that within the inertial sub layer of adiabatic turbulent flows over smooth walls, the skewness of the vertical velocity component $Sk_w$ displays universal behaviour, being constant and constrained within the range $Sk_w \approx 0.1-0.16$, regardless of flow configuration and Reynolds number. A theoretical model is proposed to explain the observed behaviour, including the observed range of variations of $Sk_w$. The model clarifies why $Sk_w$ cannot be predicted from down-gradient closure approximations routinely employed in meteorological and climate models whereby $Sk_w$ impacts cloud formation and dispersion processes. The model also offers an alternative and implementable approach.