Session F08: Convection: Stratified Flow

Structured input-output analysis of stably stratified plane Couette flow

We extend a recently developed structured input-output analysis (SIOA) to analyze streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds number (Re) low-bulk Richardson number (Ri) intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths of oblique turbulent bands that have been difficult to study due to the need for large channel extents to capture their full spatial extent. SIOA also identifies the quasi-horizontal flow structures resembling turbulent-laminar layers observed in the high-Re number high-Ri intermittent regime. We exploit SIOA to show that the classical Miles-Howard stability criterion (Ri≤1/4) appears to be associated with a change in the most amplified flow structures for Pr∼1. However, for Pr <<1, the most amplified flow structures are determined by the product Pr Ri. For Pr >>1,  SIOA identifies another quasi-horizontal flow structure that we show is associated with density perturbations. The dominance of this density-associated flow structure in the high Pr limit is further demonstrated by the analytical scaling of amplification over Re and Pr under Ri=0 and streamwise constant assumptions.   

Heat and Momentum Transfer in Stably Stratified Channel Flow with Spanwise Heterogeneous Surface Temperature

Recent studies have demonstrated that large secondary flows are excited by spanwise heterogeneous surface roughness with dominant length scales of the order of the boundary layer height. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature on stably stratified closed channel flow (Ri_τ =120 - 960, Re_τ = 180 - 550) with DNS. The configuration consists of high- and low temperature strips at the bottom and top boundaries, while a vertical temperature difference across the channel induces overall stable stratification. Results show similar secondary flow patterns as for heterogeneous roughness, with alternating high- and low-momentum pathways and in-plane vortices. By systematically varying the width of the strips (π/8 < λ/h <4π) we find that the impact of the surface heterogeneity on the outer layer depends strongly on this spanwise length scale. Comparison to homogeneous stable channel flow reveals that in most cases, heterogeneous surface temperatures lead to increased friction coefficients. However for the high-Re cases and λ/h > π/2, we find a reduction of the friction coefficient. In contrast, the Nusselt number was reduced for all heterogeneous cases, though a clear dependence on λ/h is present.   

Spatial distributions of scalar mixing in stratified turbulence

We consider a series of direct numerical simulations of stratified turbulence at fixed buoyancy Reynolds number ($Re_b$), spanning a range of Froude ($Fr$) and Prandtl ($Pr$) numbers. We characterize each dataset by considering the spatial distributions of the dissipation rates of turbulent kinetic energy $\epsilon$ and scalar variance $\chi$, providing independent information about the power available to driving mixing and the rate of resulting scalar diffusion, respectively. Mixing rates are found to be highly variable throughout the domain and unexpected correlations between local properties of the turbulent and scalar fields are highlighted. Implications for the measurement and parameterization of turbulent thermal fluxes within the ocean are discussed.   

Increasing stratification in turbulent channel flow at Reτ=1000

In this work we investigate the behavior of stably-stratified channel turbulence by running a series of  Direct Numerical Simulations (DNS) under the Oberbeck-Boussinesq (OB) approximation, at shear Reynolds number Re_τ=1000 and shear Richardson number in the range  0≤Ri_τ≤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, 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. By performing a cross power spectral density analysis of temperature and the wall-normal velocity fluctuation signals we show the presence of a ∼π/2 phase delay between these two signals.This constitutes a blockage effect to the wall-normal exchange of energy. In addition, we also show the scaling laws for friction factor and Nusselt number. These scaling laws, which seem robust over the explored range of parameters, are consistent with previous experimental and numerical data, and are expected to help the development of improved models and parametrizations of stratified flows at large Re_τ.   

Velocity measurements in rotating Rayleigh-Bénard convection and the Boundary Zonal Flow

We report on velocity measurements in rotating Rayleigh-Bénard convection (RBC). Experiments are conducted in a cylindrical plexiglass transparent cell

with diameter (D) and height (H) of 20 cm, resulting in the aspect ratio Γ=D/H=1. As working fluid, we use mixtures of water and glycerol, resulting in Prandtl numbers between 6.6≤Pr≤75, and Rayleigh numbers in the range 10⁸≤Ra≤3×10⁹. The cell rotates around its cylinder axis with rotation rates that correspond to Ekman numbers 1.5×10^-5≤Ek. We measure horizontal velocity components at a cross-section at half height using Particle Image Velocimetry. With our results we show the first direct measurements of the Boundary Zonal Flow - BZF, which develops near the sidewall and was recently discovered in numerical simulations (see Zhang et al., Phys.Rev.Lett.  2020) and localised temperature measurements (Wedi et al., JFM 2021). We analyse the thickness δ₀ of the near wall region as well as typical velocities therein as function of Pr, Ra, and Ek, and compare these results with numerical simulations.   

Scaling of cloud microphysical properties in a convection-cloud chamber

Scaling of cloud microphysical properties in a convection--cloud chamber is explored using theoretical and computational models. The fidelity of the models is evaluated using observations of cloud liquid water content versus aerosol injection rate, performed in the Pi Chamber. The models and experiments are based on steady injection of aerosol particles that are activated to form cloud droplets, balanced by the removal of cloud droplets through sedimentation. Limits of fast and slow microphysics, compared to the turbulent mixing time scale, are explored. Measured liquid water contents in the Pi convection-cloud chamber agree, to within the measurement uncertainty, with the predicted power-law scaling with cloud droplet concentration. Expressions for the scaling of microphysical properties with chamber depth are obtained. Finally, required conditions for onset of droplet growth by collisions are explored using the models.