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

Empirical evidence is provided that within the inertial sublayer (i.e. logarithmic region) of adiabatic turbulent flows over smooth walls, the skewness of the vertical-velocity component $S_w$ displays universal behaviour, being a positive constant and constrained within the range $S_w \approx 0.1\unicode{x2013}0.16$, regardless of flow configuration and Reynolds number. A theoretical model is then proposed to explain this behaviour, including the observed range of variations of $S_w$. The proposed model clarifies why $S_w$ cannot be predicted from down-gradient closure approximations routinely employed in large-scale meteorological and climate models. The proposed model also offers an alternative and implementable approach for such large-scale models.