Abstract. Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence with vastly improved resolution. The derivative moments for orders 0 ≤ n ≤ 8 are represented well as powers of the Reynolds number, Re, in the range 380 ≤ Re ≤ 5725, where Re is based on the periodic box length L x . These low-Reynolds-number flows give no hint of scaling in the inertial range even when extended self-similarity is applied. Yet, the DNS scaling exponents of velocity gradients agree well with those deduced, using a recent theory of anomalous scaling, from the scaling exponents of the longitudinal structure functions at infinitely high Reynolds numbers. This suggests that the asymptotic state of turbulence is attained for the velocity gradients at far lower Reynolds numbers than those required for the inertial range to appear. We discuss these findings in the light of multifractal formalism. Our numerical studies also resolve the crossover of the velocity gradient statistics from the Gaussian to non-Gaussian behaviour that occurs as the Reynolds number is increased.

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Γ of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is P r = 0.7 throughout the study. The aspect ratio Γ is varied between 0.5 and 12 for a Rayleigh number range between 10 7 and 10 9 . The Nusselt number N u is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law N u = A × Ra β shows a power law dependence of both fit coefficients A and β on the aspect ratio. A minimum of N u(Γ) is found at Γ ≈ 2.5 and Γ ≈ 2.25 for Ra = 10 7 and Ra = 10 8 , respectively. This is the point where the LSC undergoes a transition from a single-roll to a doubleroll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Γ > ∼ 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Γ is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen-Loève or Proper Orthogonal Decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Γ ≥ 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale -the Kolmogorov scale ηK -and the largest scale -the cell height H -are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Γ > ∼ 8).

Summary Currently, it remains controversial how vascular endothelial progenitor cells (angioblasts) establish their arterial or venous fates. We show using zebrafish that the arterial progenitors of the major axial vessels originate earlier and closer to the midline than the venous progenitors. Both medial and lateral progenitor populations migrate to distinct arterial and venous positions and not into a common precursor vessel as previously suggested. Overexpression of VEGF or Hedgehog (Hh) homologs results in the partially randomized distribution of arterial and venous progenitors within the axial vessels. We further demonstrate that the function of the Etv2 transcription factor is required at earlier stages for arterial development than for venous. Our results argue that the medial angioblasts undergo arterial differentiation because they receive higher concentration of Vegf and Hh morphogens than the lateral angioblasts. We propose a revised model of arterial-venous differentiation that explains how angioblasts choose between an arterial and venous fate.

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence time scales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.Comment: 17 pages, 10 Postscript figures (figures 3,4,6,7,8 and 10 are in reduced quality), to appear in Theoretical Computational Fluid Dynamic