Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra = 10 9 and Prandtl number σ = 6.4. In this Letter we discuss two topics: the breakdown under rotation of the domain-filling large-scale circulation (LSC) typical for confined convection, and the convective heat transfer through the fluid layer, expressed by the Nusselt number. The presence of the LSC is addressed for several rotation rates. For Rossby numbers Ro 1.2 no LSC is found (the Rossby number indicates relative importance of buoyancy over rotation, hence small Ro indicates strong rotation). For larger Rossby numbers a precession of the LSC in anticyclonic direction (counter to the background rotation) is observed. It is shown that the heat transfer has a maximal value close to Ro = 0.18 being about 15% larger than in the non-rotating case Ro = ∞. Since the LSC is no longer present at this Rossby value we conclude that the peak heat transfer is independent of the LSC.

The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Bénard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena.A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties) σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≤ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≲ Ro ≲ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro−0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found.

Direct numerical simulation and stereoscopic particle image velocimetry of turbulent convection are used to gather spatial data for the calculation of structure functions. We wish to add to the ongoing discussion in the literature whether temperature acts as an active or passive scalar in turbulent convection, with consequences for structure-function scaling. The simulation results show direct confirmation of the scalings derived by Bolgiano and Obukhov for turbulence with an active scalar for both velocity and temperature statistics. The active-scalar range shifts to larger scales when the forcing parameter ͑Rayleigh number͒ is increased. Furthermore, a close inspection of local turbulent length scales ͑Kolmogorov and Bolgiano lengths͒ confirms conjectures from earlier studies that the oft-used global averages are not suited for the interpretation of structure functions. In the experiment, a characterization of the domain-filling large-scale circulation of confined convection is carried out for comparison with other studies. The measured velocity fields are also used to calculate velocity structure functions, further confirming the Bolgiano-Obukhov scalings when interpreted with the local turbulent length scales found in the simulations. An extended self-similarity analysis shows that the relative scalings are different for the Kolmogorov and Bolgiano-Obukhov regimes.

a b s t r a c tDirect numerical simulation is used to assess the importance of compressibility in turbulent channel flow of a mixture of air and water vapor with dispersed water droplets. The dispersed phase is allowed to undergo phase transition, which leads to heat and mass transfer between the phases. We compare simulation results obtained with an incompressible formulation with those obtained for compressible flow at various low values of Mach number. We discuss differences in fluid flow, heat-and mass transfer and dispersed droplet properties. Results for flow properties such as mean velocity obtained with the compressible model converge quickly to the incompressible results in case the Mach number is reduced. In contrast, thermal properties such as the heat transfer, characterized by the Nusselt number, display a systematic difference between the two formulations on the order of 15%, even in the low-Mach limit. This shows the necessity of the use of a compressible formulation for accurate prediction of heat transfer, even in case of an initial relative humidity of 100%. Mass transfer properties display a difference between the models on the order of 5%, for example in the prediction of the droplet mean diameter near the walls.

The effect of rotation on turbulent convective flow between parallel plates has been assessed with direct numerical simulations. With increasing rotation-rate an interesting transition is observed in the vertical-velocity skewness. This transition indicates a localization of motion directed away from the wall and correlates well with changes observed in the heat flux, as well as in the thermal and viscous boundary layer thicknesses. The formation of localized intense vortical structures provides for intensified vertical heat transport through Ekman pumping. At higher rotation-rates this is counteracted by the inhibition of vertical motion by rotation as expressed in the geostrophic thermal-wind balance.

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Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier-Stokes equations in a porous medium. The Euler-Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle-particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle-fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle-particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.

The vortices emerging in rotating turbulent Rayleigh-Bénard convection in water at Rayleigh number Ra = 6.0ϫ 10 8 are investigated using stereoscopic particle image velocimetry and by direct numerical simulation. The so-called Q criterion is used to detect the vortices from velocity fields. This criterion allows distinguishing vorticity-and strain-dominated regions in the flow by decomposing the velocity gradient tensor into symmetric and antisymmetric parts. Vortex densities, mean vortex radii and mean vortex circulations are calculated at two horizontal cross-sections of the cylindrical flow domain and at several rotation rates, described by the Taylor number which takes values between 3.0ϫ 10 8 and 7.7ϫ 10 10. Separate statistics are calculated for cyclonic and anticyclonic vortices. Vortex densities and mean vortex radii are mostly independent of the Taylor number except very close to the bottom and top plates where more vortices are detected when the Taylor number is raised ͑rotation increases͒. The vortex population close to the plate consists mostly of cyclones while further into the bulk of the domain a similar amount of cyclones and anticyclones is found. The cyclonic vortices contain more circulation than the anticyclones. The same vortex analysis of the simulation results at additional vertical positions revealed that the vortices are formed in a boundary layer on the plate with a thickness of approximately two Ekman lengths.