Interaction of thermal and solutal stratification with turbulence in wall-bounded flows

Abstract

In this thesis, we investigate numerically the physical mechanisms that govern the dynamics of a stratified fluid flow. Two different cases of practical interest are con- sidered: stable thermal stratification in wall-bounded turbulence, and double diffusive convection (DDC) subject to shear in a confined fluid layer. We first investigated the interaction between stable thermal stratification and wall-bounded turbulence. Current physical mechanisms and scaling laws in stratified channel turbulence have been tested by Direct Numerical Simulations (DNS) up to shear Reynolds number Re=550. In this study, we aim at extending present results to higher Reynolds numbers, by running a series of DNSs of stratified channel turbulence at Re=1000 and shear Richardson number – which measures the relative importance of buoyancy compared to inertia – in the range 0<300. By increasing stratification, active turbulence is sustained only in the near-wall region, where as intermittent turbulence, modulated by the presence of non-turbulent wavy structures (Internal Gravity Waves, IGW), is observed at the channel core. In such conditions, the wall-normal transport of momentum and heat is considerably reduced compared to 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 cen- ter, the mean value of their product – the buoyancy flux – vanishes for Ri>200. We show that this behavior is due to the presence of a approx 90 deg. 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 viceversa. This constitutes a blockage effect to the wall-normal exchange of energy. In addition, we present the scaling law for friction factor Cf , and we propose a new scaling for the Nusselt number, Nu. These scaling laws, which seem robust over the explored range of parameters, complement and extend previous experimental and numerical data up to Re=1000, and are expected to help the development of improved models and parametrizations of stratified flows at large Re. We also investigate the energetics and mixing in wall-bounded stably stratified turbulence, and we propose a new param- eterization for the irreversible flux Richardson number Rf – which is a measures for irreversible mixing – as a function of gradient Richardson number Rig. In the second part of this thesis, we examine the effect of mixed slip/no-slip boundary conditions on DDC subject to shear in a confined fluid layer. DDC results from the competing action of a stably stratified, rapidly-diffusing scalar (temperature) and an unstably stratified, slowly diffusing scalar (salinity), which is characterized by fingering instabilities. This problem has five governing parameters: The salinity Prandtl number, Prs (momentum to salinity diffusivity ratio); the salinity Rayleigh number, Ras (measure of the fluid instability due to salinity differences); the Lewis number, Le (thermal to salinity diffusivity ratio); the density ratio, Λ (measure of the effective flow stratification), and the shear rate, Γ. We investigate fingering dynamics at varying shear rate via highly-resolved numerical simulations. Simulations are performed at fixed Prs , Ras , Le and Λ, while the effect of shear is accounted for by considering different values of Γ. Preliminary results show that shear tends to damp the growth of fingering instability, leading to highly anisotropic DDC dynamics associated with the formation of regular salinity. In turn, these dynamics result in significant modifications of the vertical heat transport and solute concentration.