Interaction between thermal stratification and turbulence in channel flow

Abstract

Transport phenomena in high Reynolds number wall-bounded stratified flows are dominated by the interplay between the turbulence structures generated at the wall and the buoyancy-induced large-scale waves populating the channel core. In this study, we want to investigate the flow physics of wall-bounded stratified turbulence at relatively high shear Reynolds number $Re_\tau$ and for mild to moderate stratification level – quantified here by the shear Richardson number varying in the range $0\leqslant Ri_{\tau } \leqslant 300$ . By increasing stratification, active turbulence is sustained only in the near-wall region, whereas intermittent turbulence, modulated by the presence of non-turbulent wavy structures (internal gravity waves), is observed at the channel core. In such conditions, the wall-normal transport of momentum and heat is considerably reduced compared with the case of non-stratified turbulence. A careful characterization of the flow-field statistics shows that, despite temperature and wall-normal velocity fluctuations being very large at the channel centre, the mean value of their product – the buoyancy flux – vanishes for $Ri_{\tau } \geqslant 200$ . We show that this behaviour is due to the presence of a $\sim {\rm \pi}/2$ phase delay between the temperature and the wall-normal velocity signals: when wall-normal velocity fluctuations are large (in magnitude), temperature fluctuations are almost zero, and vice versa. This constitutes a blockage effect to the wall-normal exchange of energy. In addition, we show that the friction factor scales as $C_f \sim Ri_{\tau }^{-1/3}$ , and we propose a new scaling for the Nusselt number, $Nu \cdot Re_{\tau }^{-2/3} \sim Ri_{\tau }^{-1/3}$ . These scaling laws, which seem to be robust over the explored range of parameters, complement and extend previous experimental and numerical data, and are expected to help the development of improved models and parametrizations of stratified flows at large $Re_{\tau }$ .