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The leading edge bulge is a known defect in stereolithography with free-surface recoating. It is a resin excess that remains after deposition over a deep-to-shallow topographic transition, the leading edge of the cavity. In this paper, we explore an approach based on changing the gap between the recoating blade and the previously cured layer to minimize the local resin surface unevenness by suppressing resin excess. By means of numerical simulations, different blade trajectory configurations have been considered. The results show that the amplitude of the leading edge bulge can be reduced to a minimal value by a blade actuation protocol of lowering then raising the blade as it moves over the leading edge, without increasing the recoating process time.

Rotating Rayleigh--B\'enard convection is an oft-employed model system to evaluate the interplay of buoyant forcing and Coriolis forces due to rotation, an eminently relevant interaction of dynamical effects found in many geophysical and astrophysical flows. These flows display extreme values of the governing parameters: large Rayleigh numbers $Ra$, quantifying the strength of thermal forcing, and small Ekman numbers $E$, a parameter inversely proportional to the rotation rate. This leads to the dominant geostrophic balance of forces in the flow between pressure gradient and Coriolis force. The so-called geostrophic regime of rotating convection is difficult to study with laboratory experiments and numerical simulations given the requirements to attain simultaneously large $Ra$ values and small values of $E$. Here, we use flow measurements using stereoscopic particle image velocimetry in a large-scale rotating convection apparatus in a horizontal plane at mid-height to study the rich flow phenomenology of the geostrophic regime of rotating convection. We quantify the horizontal length scales of the flow using spatial correlations of vertical velocity and vertical vorticity, reproducing features of the convective Taylor columns and plumes flow states both part of the geostrophic regime. Additionally, we find in this horizontal plane an organisation into a quadrupolar vortex at higher Rayleigh numbers starting from the plumes state., Comment: 7 pages, 6 figures

The force balance of rotating Rayleigh–Bénard convection regimes is investigated using direct numerical simulation on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive view of the interplay between governing forces both in the bulk and near the walls. We observe, as in other prior studies, regimes of cells, convective Taylor columns, plumes, large-scale vortices (LSVs) and rotation-affected convection. Regimes of rapidly rotating convection are dominated by geostrophy, the balance between Coriolis and pressure-gradient forces. The higher-order interplay between inertial, viscous and buoyancy forces defines a subdominant balance that distinguishes the geostrophic states. It consists of viscous and buoyancy forces for cells and columns, inertial, viscous and buoyancy forces for plumes, and inertial forces for LSVs. In rotation-affected convection, inertial and pressure-gradient forces constitute the dominant balance; Coriolis, viscous and buoyancy forces form the subdominant balance. Near the walls, in geostrophic regimes, force magnitudes are larger than in the bulk; buoyancy contributes little to the subdominant balance of cells, columns and plumes. Increased force magnitudes denote increased ageostrophy near the walls. Nonetheless, the flow is geostrophic as the bulk. Inertia becomes increasingly more important compared with the bulk, and enters the subdominant balance of columns. As the bulk, the near-wall flow loses rotational constraint in rotation-affected convection. Consequently, kinetic boundary layers deviate from the expected behaviour from linear Ekman boundary layer theory. Our findings elucidate the dynamical balances of rotating thermal convection under realistic top/bottom boundary conditions, relevant to laboratory settings and large-scale natural flows.

In RB convection for fluids with Prandtl number $Pr\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $Ro_{c}$ occurs typically in the range $2.3\lesssim Ro_{c}\lesssim 2.9$ (for Rayleigh number $Ra=1.3\times 10^9$, $Pr=6.7$, and a convection cell with aspect ratio $\Gamma=\frac{D}{H}=1$, with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/Ro\lesssim 1/Ro_c$ (slow rotation), the well-known LSC is found: a single domain-filling convection roll made up of many individual thermal plumes. At $1/Ro\gtrsim 1/Ro_c$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, $Ro_{c_2}\approx 2.25$ (different from $Ro_{c_1}\approx 2.7$ for the sharp transition in the Nusselt number $Nu$; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at $Ro_{c_2}$., Comment: 16 pages, 9 Figures

We perform direct numerical simulations of rotating Rayleigh-Bénard convection (RRBC) of fluids with low (Pr=0.1) and high (Pr≈5) Prandtl numbers in a horizontally periodic layer with no-slip bottom and top boundaries. No-slip boundaries are known to actively promote the formation of plumelike vertical disturbances, through so-called Ekman pumping, that control the ambient flow at sufficiently high rotation rates. At both Prandtl numbers, we demonstrate the presence of competing large-scale vortices (LSVs) in the bulk. Strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow that leads to the upscale transfer of kinetic energy that forms the domain-filling LSV condensate. The Ekman plumes from the boundary layers are sheared apart by the large-scale flow, yet we find that their energy feeds the upscale transfer. Our results of RRBC simulations substantiate the emergence of large-scale flows in nature regardless of the specific details of the boundary conditions.

Abstract. The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, $ \tau_{T}$τT, and the thermal expansion coefficient of particles relative to that of the fluid, $ K = \alpha_{p}/\alpha_{f}$K=αp/αf. In particular, the residence time is constant for small thermal response times, $ \tau_{T} \lesssim 1$τT≲1, and increasing with $ \tau_{T}$τT for larger thermal response times, $ \tau_{T} \gtrsim 1$τT≳1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with $ \tau_{T}$τT for larger response times, thus explaining the trends in the DNS data well. Graphical abstract

Recent studies of rotating Rayleigh-B\'enard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction. It has a convoluted structure, illustrated by mean flow fields in horizontal cross-sections of the flow where instantaneous snapshots are compensated for the orientation of the sidewall circulation before averaging. Through separate analysis of the sidewall region and the inner bulk flow, we find that for higher values of the thermal forcing the heat transport in the inner part of the cylindrical domain, outside the sidewall circulation region, coincides with the heat transport on the unconfined periodic domain. Thus the sidewall circulation accounts for the differences in heat transfer between the two considered domains, while in the bulk the turbulent heat flux is the same as that of a laterally unbounded periodic domain. Therefore, experiments, with their inherent confinement, can still provide turbulence akin to the unbounded domains of simulations, and at more extreme values of the governing parameters for thermal forcing and rotation. We also provide experimental evidence for the existence of the sidewall circulation that is in close agreement with the simulation results., Comment: 11 pages, 7 figures

The angle of directional change of tracer trajectories in rotating Rayleigh-Benard convection is studied as a function of the time increment tau between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change theta(t, tau) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Theta(tau) = with tau shows a transition from the ballistic regime Theta(tau) similar to tau(c) with c = 1] for tau less than or similar to tau(n), with tau(n) the Kolmogorov timescale, to a scaling with smaller exponent c for tau(n) less than or similar to tau less than or similar to T-L, with T-L the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro greater than or similar to 2.5) and is decreasing for increasing rotation rates when Ro less than or similar to 2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro greater than or similar to 2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro less than or similar to 2.5. In the viscous BLs, the PDFs of theta(t, tau) and scaling properties of Theta (tau) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro greater than or similar to 2.5) or of Ekman type (Ro less than or similar to 2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.

Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh–Bénard convection. Three main regimes are known: rotation unaffected, rotation affected and rotation dominated. It has been shown that the transition between rotation-unaffected and rotation-affected regimes is driven by the boundary layers. However, the physics behind the transition between rotation-affected and rotation-dominated regimes are still unresolved. In this study, we employ the experimentally obtained Lagrangian velocity and acceleration statistics of neutrally buoyant immersed particles to study the rotation-affected and rotation-dominated regimes and the transition between them. We have found that the transition to the rotation-dominated regime coincides with three phenomena; suppressed vertical motions, strong penetration of vortical plumes deep into the bulk and reduced interaction of vortical plumes with their surroundings. The first two phenomena are used as confirmations for the available hypotheses on the transition to the rotation-dominated regime while the last phenomenon is a new argument to describe the regime transition. These findings allow us to better understand the rotation-dominated regime and the transition to this regime.

We perform three-dimensional particle tracking measurements on droplets in a turbulent airflow. The droplets display the well-known preferential concentration of inertial particles, with an additional extreme clustering at the smallest scales. We explain this additional clustering phenomenon theoretically based on a Stokes-flow description of two spheres including their mutual hydrodynamic interaction and a perturbative small-inertia expansion.

The geometry of passive tracer trajectories is studied in two different types of rotating turbulent flows; rotating Rayleigh-Bénard convection (RBC; experiments and direct numerical simulations) and rotating electromagnetically forced turbulence (EFT; experiments). This geometry is fully described by the curvature and torsion of trajectories, and from these geometrical quantities we can subtract information on the typical flow structures at different rotation rates. Previous studies, focusing on nonrotating homogeneous isotropic turbulence (HIT), show that the probability density functions (PDFs) of curvature and torsion reveal pronounced power laws. However, the set-ups studied here involve inhomogeneous turbulence, and in RBC the flow near the horizontal plates is definitely anisotropic. We investigate how the typical shapes of the curvature and torsion PDFs, including the pronounced scaling laws, are influenced by this level of anisotropy and inhomogeneity and how this effect changes with rotation. A first effect of rotation is observed as a shift of the curvature and torsion PDFs towards higher values in the case of RBC and towards lower values in the case of EFT. This shift is related to the length scale of typical vortical structures that decreases with rotation in RBC, but increases with rotation in EFT, explainingthe opposite shifts of the curvature (and torsion) PDFs. A second remarkable observation is that in RBC the HIT scaling laws are always recovered, as long as the boundary layer (BL) is excluded. This suggests that these scaling laws are very robust and hold as long as we measure in the turbulent bulk. In the BL of the RBC cell, however, the scaling deviates from the HIT prediction for lower rotation rates. This scaling behavior is found to be consistent with the coupling between the boundary layer dynamics and the bulk flow, which changes under rotation. In particular, it is found that the active coupling of the Ekman-type boundarylayer with the bulk flow suppresses anisotropy in the BL region for increasing rotation rates.

Rapidly rotating Rayleigh-Bénard convection is studied using time-resolved particle image velocimetry and three-dimensional particle tracking velocimetry. Approaching the geostrophic regime of rotating convection, where the flow is highly turbulent and at the same time dominated by the Coriolis force, typically requires dedicated setups with either extreme dimensions or troublesome working fluids (e.g. cryogenic helium). In this study, we explore the possibilities of entering the geostrophic regime of rotating convection with classical experimental tools: a table-top conventional convection cell with a height of 0.2 m and water as the working fluid. In order to examine our experimental measurements, we compare the spatial vorticity autocorrelations with the statistics from simulations of geostrophic convection reported earlier in [D. Nieves et al., Phys. Fluids 26, 086602 (2014)]. Our findings show that we have indeed access to the geostrophic convection regime and can observe the signatures of the typical flow features reported in the aforementioned simulations.

8th Symposium on Turbulence & Shear Flow Phenomena (TSFP8) Heat transfer in a Rayleigh-Bénard configuration consisting of a vertical cylinder, which is rotating about its axis, can be intensified considerably when the rotation rate is modulated harmonically in time. Such time-dependent rotation introduces an Euler force into the governing equations which leads to a particular modification of the flow that is shown to support a Nusselt number (Nu) that is considerably higher than in case of constant rotation. We use direct numerical simulation of the incompressible Navier–Stokes equations to perform a comprehensive parameter study of the flow-structuring and associated heat transfer investigating primarily the effect of variations in the frequency with which the rotation rate varies.We consider flow in an upright cylinder of unit aspect ratio which is heated from below and cooled at the top. At sufficiently strong Euler forces the temporal variation of Nu shows a striking dynamics with periods of gradual increase in Nu with more rapid oscillations superimposed, next to rather catastrophic events in which the entire flow-structure that supported high levels of Nu collapses entirely and it returns to a value more similar to that attained at steady rotation. During periods of oscillatory build-up of Nu, high levels of turbulence gradually become more pronounced from the outer cylinder wall inward and a gradually stronger thermal column arises along the centreline of the cylinder. This flow structure can support Nu up to 250% larger than without rotation, a value otherwise achievable only by employing phase transition.

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = $10^9$ and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/$Ro^*$ = 1 while various modulation frequencies 0.1 ≤ $Ro_\omega$ ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.

We propose that the collision rates of non-spherical particles settling in a turbulent environment are significantly higher than those of spherical particles of the same mass and volume. The theoretical argument is based on the dependence of the particle drag force on the particle orientation, thus varying gravitational settling velocities, which can remain different until contact due to the particle inertia. Therefore, non-spherical particles can collide with large relative velocities. Direct numerical simulations (DNS) of streamwise decaying isotropic turbulence seeded with small, heavy, rotationally symmetric ellipsoids of five different aspect ratios are performed to confirm these arguments. The motion of 21 million ellipsoids is tracked by a Lagrangian particle solver assuming creeping flow conditions and neglecting the influence of the particles on the flow. We find that ellipsoids collide considerably more often than spherical particles of the same volume and mass due to a drastically increased mean relative velocity at contact.

Motivated by applications in engineering as well as in other disciplines where the motion of particles in a turbulent flow field is important, the orientation and settling velocity of ellipsoidal particles in a spatially decaying isotropic turbulent flow are numerically investigated. With respect to cloud microphysics ellipsoidal particles of various shapes are interpreted as archetypes of regular ice crystals, i.e., plates and columns approximated by oblate and prolate ellipsoids. The motion of 19 million small and heavy ellipsoidal particles is tracked by a Lagrangian point-particle model based on Stokes flow conditions. Five types of ellipsoids of revolution such as prolates, spheres, and oblates are considered. The orientation and settling velocity statistics are gathered at six turbulence intensities characterized by the turbulent kinetic energy dissipation rate ranging from 30 to 250 cm2s-3. It is shown that the preferential orientation of ellipsoids is disturbed by the turbulent fluctuations of the fluid forces and moments. As the turbulence intensity increases the orientation probability distribution becomes more and more uniform. That is, the settling velocity of the ellipsoids is influenced by the turbulence level since the drag force is dependent on the orientation. The effect is more pronounced, the longer the prolate or the flatter the oblate is. The theoretical settling velocity based on the orientation probability of the non-spherical particles is smaller than that found in the simulation. The results show the existence of the preferential sweeping phenomenon also for non-spherical particles. These two effects of turbulence on the motion of ellipsoids change the settling velocity and as such the swept volume, that is expected to result in modified collision probabilities of ellipsoid-shaped particles.

Small-scale isotropy of turbulence is an assumption required for most theoretical descriptions. A combined experimental-numerical approach shows how buoyant forcing and rotation affects the small- and large-scale isotropy in thermally driven turbulence.

Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotating while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier–Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\times 10^{10}$, at constant Prandtl number $Pr=1$, and vary the Ekman number in the range $Ek=1.3\times 10^{-7}$ to $Ek=2\times 10^{-6}$, which satisfies both requirements of supercriticality and strong rotation. We focus on the differences between the application of no-slip versus stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at $Ek\approx 9\times 10^{-7}$ for $Ra=1\times 10^{10}$ and at $Ek\approx 3\times 10^{-7}$ for $Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in $Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat-transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions, the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

When the classical Rayleigh-B\'enard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large scale circulation (LSC) is the dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at $Ra \sim 10^8-10^9$ ($Pr=4-6$) and $0 \lesssim 1/Ro \lesssim 25$ we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regime II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part., Comment: 21 pages, 12 figures

The strongly-modified turbulence statistics of Rayleigh–Bénard convection subject to various rotation rates is addressed by numerical investigations. The flow is simulated in a domain with periodic boundary conditions in the horizontal directions, and confined vertically by parallel no-slip isothermal walls at the bottom and top. Steady rotation is applied about the vertical. The rotation rate, or equivalently the Rossby number $Ro,$ is varied such that $Ro$ ranges from $\infty$ (no rotation) to $Ro=0.1$ (strong rotation). Two different Rayleigh numbers are used, viz. $Ra=2.5\times 10^6$ and $2.5\times 10^7,$ characterising buoyancy due to temperature differences. The Prandtl number $\sigma=1,$ close to the value for air. Horizontally averaged statistics show that rotation reduces the turbulence intensity, although probability density functions clearly show that considerable (preferably cyclonic) vorticity is added to the flow by the Ekman boundary layers on the solid walls. Rotation changes the balance of the turbulent kinetic energy budget. It is found that for a range of rotation rates the buoyant production is higher than without rotation. Therefore, at appropriate rotation rates the heat flux through the fluid layer is increased relative to the non-rotating case. At sufficiently rapid rotation, however, the heat flux through the fluid layer is strongly attenuated.

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 number) is increased. Furthermore, a close inspection of local turbulent length scales (Kolmogorov and Bolgiano lengths) 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.

Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra = $10^9$ and Prandtl number $\sigma$ = 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 $\leq 1.2$ 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 = $\infty.$ Since the LSC is no longer present at this Rossby value we conclude that the peak heat transfer is independent of the LSC.

Buoyant convection and the Coriolis force caused by the rotation of our Earth are important forces in the flows in the atmosphere and the oceans. A convenient model for such flows, although not fully compatible, is the rotating Rayleigh‐Benard setting: A horizontally infinite layer of fluid is vertically confined by solid walls rotating around a vertical axis, the bottom wall being at a higher temperature than the top wall. Although the lack of a top wall in the geophysical flows makes the model not directly applicable, the general behavior of the model flow shows considerable similarities to real flow in the atmosphere. Furthermore, in the atmosphere the tropopause can be regarded as a “top wall” to a certain extent. Especially for the large-scale flows in the atmosphere, the effect of the rotation is dominant. The Rossby number, the ratio between inertial and Coriolis forces, is rather small O0.1. A well-known theorem valid in rotation-dominated flows was formulated by Proudman 1 and experimentally proven by Taylor; 2 it is known as the Taylor‐Proudman theo

Using measurements of Lagrangian acceleration in turbulent rotating convection and accompanying direct numerical simulations, we show that the transition between turbulent states reported earlier [e.g., S. Weiss et al., Phys. Rev. Lett. 105, 224501 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.224501] is a boundary-layer transition between the Prandtl-Blasius type (typical of nonrotating convection) and Ekman type.

Collisions of small and heavy non-spherical particles settling in a turbulent environment are very important to various fields of physics and engineering. However, in contrast to spherical particles the collision probabilities are virtually unknown. In this study we focus on a very important condition for the numerical determination of collision probabilities: the collision detection. We discuss the need for efficient strategies to narrow down the number of possible collision pairs and compare three collision detection methods for ellipsoidal particles. We derive an analytical formula for the collision probability in the case of gravitational settling and validate the collision detection methods with this. Finally, we present statistics of the accuracy and efficiency of the methods. For the case of ellipsoidal particles in turbulence we find that the continuous collision detection with neglected rotation within a time step is the optimal trade-off between accuracy and efficiency.Copyright © 2014 by ASME

The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 μm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm 2 s − 3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to gravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature.

A combined numerical–experimental investigation on the scaling of velocity structure functions in turbulent rotating Rayleigh–B´enard convection is carried out. Direct numerical simulations in a cylindrical domain and a horizontally periodic domain are compared with experiments using a cylindrical tank in which stereoscopic particle image velocimetry is employed. The turbulent length scales that govern the scaling of the structure functions are evaluated directly in the numerical simulations. They provide a framework for the interpretation of the structure functions. The composition of the domain (cylinder/periodic) has a quantitative effect on the length scales even in the fluid bulk. At lower rotation rates an additional scaling range due to rotation is found. At higher rotation rates a direct transition is observed from dissipation-range scaling at small separations to an uncorrelated state at larger separations.

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.

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. ©2006 The American Physical Society

The existence of a buoyancy-dominated scaling range in convective turbulence is a longstanding open question. We investigate this issue by considering the scale-by-scale energy budget in direct numerical simulations of Rayleigh-B\'enard convection. We try to minimize the so-called Bolgiano length scale, the length scale at which buoyancy becomes dominant for scaling. Therefore, we deliberately choose modest Rayleigh numbers $\mathrm{Ra}=2.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ and $2.5\ifmmode\times\else\texttimes\fi{}{10}^{7}$. The budget reveals that buoyant forcing, turbulent energy transfer, and dissipation are contributing significantly over a wide range of scales. Thereby neither Kolmogorov-like (balance of turbulent transfer and dissipation) nor Bolgiano-Obukhov-like scaling (balance of turbulent transfer and buoyancy) is expected in the structure functions, which indeed reveal inconclusive scaling behavior. Furthermore, we consider the calculation of the Bolgiano length scale. To account for correlations between the dissipation rates of kinetic energy and thermal variance we propose to average the Bolgiano length scale directly. This gives an estimate, which is one order of magnitude larger than the previous estimate, and actually larger than the domain itself. Rather than studying the scaling of structure functions, we propose that the use of scale-by-scale energy budgets resolving anisotropic contributions is appropriate to consider the energy cascade mechanisms in turbulent convection.

Vortical columns are key features of rapidly rotating turbulent Rayleigh-Benard convection. In this work we probe the structure of the sidewall boundary layers experimentally and show how they affect the spatial vortex distribution in a cylindrical cell. The cell has a diameter-to-height aspect ratio 1/2 and is operated at Rayleigh number $5.9 \times 10^9$ and Prandtl number 6.4. The vortices are detected using particle image velocimetry. We find that for inverse Rossby numbers 1/Ro > 3 (expressing the rotation rate in a dimensionless form) the sidewall boundary layer exhibits a rotation-dependent thickness and a characteristic radial profile in the root-mean-square azimuthal velocity with two peaks rather than a single peak typical for the non-rotating case. These properties point to Stewartson-type boundary layers, which can actually cover most of the domain for rotation rates just above the transition point. A zonal ordering of vortices into two azimuthal bands at moderate rotation rates 3 < 1/Ro < 7 can be attributed to the sidewall boundary layer. Additionally, we present experimental confirmation of the tendency of like-signed vortices to cluster on opposite sides of the cylinder for 1 < 1/Ro < 5. At higher rotation rates and away from the sidewall the vortices are nearly uniformly distributed.

A simple model for many geophysical and astrophysical flows, such as oceanic deep convection and the convective outer layer of the Sun, is found in rotating Rayleigh.BeLenard convection: a horizontal fluid layer heated from below and cooled from above is rotated about a vertical axis. Three dimensionless parameters characterise this flow: the Rayleigh number Ra describes the strength of the destabilising temperature gradient, the Prandtl number relates the diffusion coefficients for heat and momentum of the fluid, and the Rossby number Ro is the ratio of buoyancy and Coriolis forces ( \(Ro = \infty \) when rotation is absent and Ro 1 for rotation-dominated flow). We investigate the effect of rotation on the flow anisotropy in turbulent convection in an upright cylinder of equal height and diameter, with experiments and numerical simulations.

In this Letter we report experimental evidence that rotation enhances vertical inhomogeneity in turbulent convection, in spite of the increased columnar flow ordering under rotation. Measurements using stereoscopic particle image velocimetry have been carried out on turbulent rotating convection in water. At constant Rayleigh number Ra = 1.11$\times 10^9$ several rotation rates have been used, so that the Rossby number takes values from Ro = $\infty$ (no rotation) to 0.09 (strong rotation). The three component velocity data, obtained at two vertical positions, are used to investigate the anisotropy of the flow through the invariants of the Reynolds-stress anisotropy tensor and the Lumley triangle, as well as to correlate the vertical velocity and vorticity. In the center plane rotation causes the turbulence to be ‘‘rodlike,’’ while closer to the top plate a trend toward isotropy is observed.