We present a systematic experimental study of geometric and statistical properties of thermal plumes in turbulent Rayleigh-Bénard convection using the thermochromic-liquid-crystal (TLC) technique. The experiments were performed in three water-filled cylindrical convection cells with aspect ratios 2, 1, and 0.5 and over the Rayleigh-number range $5\times10^7 \leq Ra \leq 10^{11}$. TLC thermal images of horizontal plane cuts at various depths below the top plate were acquired. Three-dimensional images of thermal plumes were then reconstructed from the two-dimensional slices of the temperature field. The results show that the often-called sheetlike plumes are really one-dimensional structures and may be called rodlike plumes. We find that the number densities for both sheetlike/rodlike and mushroomlike plumes have power-law dependence on $Ra$ with scaling exponents of $\sim 0.3$, which is close to that between the Nusselt number $Nu$ and $Ra$. This result suggests that it is the plume number that primarily d ermines the scaling exponent of the $Nu$-$Ra$ scaling relation. The evolution of the aspect ratio of sheetlike/rodlike plumes reveals that as $Ra$ increases the plume geometry changes from more-elongated to less-elongated. Our study of the plume area fraction (fraction of coverage over the surface of the plate) further reveals that the increased plume numbers with $Ra$ mainly comes from increased plume emission, rather than fragmentation of plumes. In addition, the area, perimeter, and the shape complexity of the two-dimensional horizontal cuts of sheetlike/rodlike plumes were studied and all are found to obey log-normal distributions.
We report experimental measurements of heat transport in rotating Rayleigh-B{é}nard convection in a cylindrical convection cell with aspect ratio $Γ= 1/2$. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number $4 \times 10^9 < {\rm Ra} < 4 \times 10^{11}$ and Ekman number $2 \times 10^{-7} < {\rm Ek} < 3 \times 10^{-5}$(corresponding to Taylor number $4 \times 10^9 < {\rm Ta} < 1 \times 10^{14}$ and convective Rossby number $0.07 < {\rm Ro} < 5$). We determine the crossover from weakly rotating turbulent convection to rotation dominated geos…
In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample…
We experimentally test the effects of tilting a turbulent Rayleigh-B{é}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $θ_0$. The probability distribution of $θ_0$ is measured, and used to obtain a tilt-induced potential acting on $θ_0$, which is used in a low-dimensional model of diffusion of $θ_0$ in a potential. The form of the potential is sinusoidal in $θ_0$, and linear in tilt angle for small tilt angles, which is explained by a simple geometric model of the vector direction of the mean buoyancy force acting on the LSC. However, the magnitude of the …
We report Particle Image Velocimetry of the Large Scale Circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-B{é}nard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow to consider a bi-dimensional mean flow. Lots of previous heat flux measurements have shown a Nusselt--Rayleigh regime transition corresponding to an increase of the heat flux in presence of roughness which is highe…
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting versus plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at a Rayleigh number of $Ra\approx 3 \times 10^{11}$. This is consistent with the trends observed in 3-…
Two-dimensional simulations of Rayleigh-Bénard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of …
We test the ability of a low-dimensional turbulence model to predict how dynamics of large-scale coherent structures such as convection rolls change in different cell geometries. We performed Rayleigh-Bénard convection experiments in a cubic container, in which there is a single convection roll known as the large-scale circulation (LSC). The model describes the motion of the orientation $θ_0$ of the LSC as diffusion in a potential which is predicted as a function of the shape of the cell from an approximate solutions of the Navier-Stokes equations. The model predicts advected oscillation modes…
We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Bénard convection, at $Ra \sim 10^{10}$. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume t…
Results from direct numerical simulations of vertical natural convection at Rayleigh numbers $1.0\times 10^5$-$1.0\times 10^9$ and Prandtl number $0.709$ support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-B{é}nard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the $-1/2$…
We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octadecane in horizontal layers of several sizes heated from below. This configuration allows to cover a wide range of effective Rayleigh numbers on the liquid PCM phase, up to $\sim 10^9$, without changing any external parameter control. We identify four different regimes as time evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime and (iv) turbulent regime. The first two regimes appear at all domain sizes. However the third and fourth regime require a minimum advance of the …
We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Γ=D/L=1/2 and Γ=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Γ=1 sample at $Ra=1\times10^8$ and $5\times10^8$ the obtained LSC orientation …
We study the connection between extreme events of thermal and kinetic energy dissipation rates in the bulk of three-dimensional Rayleigh-Bénard convection and the wall shear stress patterns at the top and the bottom planes that enclose the layer. Zero points of this two-dimensional vector field stand for detachments of strong thermal plumes. If their position at the opposite planes and a given time is close then they can be considered as precursors for high-amplitude bulk dissipation events triggered by plume collisions or close passings. This scenario requires a breaking of the synchronicity …
The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-Bénard turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we performed three-dimensional simulations of Rayleigh-Bénard turbulence in a slim-box without the front and back walls with aspect ratio, $L:D:H=1:1/6:1$, in the Rayleigh number $Ra=[1\times10^8, 1\times10^{10}]$ for Prandtl number $Pr=0.7$. The velocity profile is successfully quantified by a two-layer function of a st…
Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection. The conservation equations of mass, momentum and energy of fluid are discretized into SPH equations. The body force due to the change of density in a temperature field is considered by the Boussinesq approximation. The numerical method is validated by comparing numerical results with experimental results from literature. The numerical and experimental results reach a good agreement. Then the SPH method is applied to study the nat…
Turbulent convection systems are known to give rise to prominent large scale circulation. At the same time, the `background' (or `small-scale') turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh-Bénard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($Γ=32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of smal…
The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio $Γ=1$ and focused on the critical points of the skin friction field. We identify…
This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh-Bénard setup, filled with an oil-water mixture. For oleophilic walls, e.g. using only $10\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is then only about $20\%$ as compared to pure water. The physical explanation of the highly-efficient he…
We consider axisymmetric Boussinesq convection in a shallow cylinder radius, L, and depth, H (<< L), which rotates with angular velocity $Ω$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $Ω$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at …
We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, a…
Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because t…
We investigate the miscible Rayleigh-Taylor (RT) instability in both 2 and 3 dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: We identify three distinct evolutionary phases in the development of the mixed layer, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the o…
We present a numerical study of Rayleigh-Bénard convection disturbed by a longitudinal wind. Our results show that under the action of the wind, the vertical heat flux through the cell initially decreases, due to the mechanism of plumes-sweeping, and then increases again when turbulent forced convection dominates over the buoyancy. As a result, the Nusselt number is a non-monotonic function of the shear Reynolds number. We provide a simple model that captures with good accuracy all the dynamical regimes observed. We expect that our findings can lead the way to a more fundamental understanding …
The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely a…
We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux $\bar{j}(r)$ in a cylindrical Rayleigh-Bénard cell with aspect ratio Γ=1 for Rayleigh numbers Ra between $2 \times 10^6$ and $2\times 10^{9}$ at a fixed Prandtl number Pr = 5.2. The numerical results reveal that the heat flux close to the sidewall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, $\bar{j}(r)\propto Ra^{γ_j(r)}$. The scaling exponent $γ_j(r)$ decreases monotonical…
The structure of the boundary layers in turbulent Rayleigh-Benard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at an aspect ratio one for Rayleigh numbers of Ra=3e+9 and 3e+10 at fixed Prandtl number Pr=0.7. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of the Prandtl-Blasius-Pohlhausen theory. Deviations decrease when a dynamical rescaling of the dat…
Influence of plume activity on thermal convection in a rectangular cell
Indian Institute of Technology Roorkee（印度技术学院罗尔基分校）；New York University Abu Dhabi（纽约大学阿布扎比分校）；Technische Universität Ilmenau（伊尔梅瑙工业大学）；New York University（纽约大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
We conducted a three-dimensional numerical simulation of bioconvection generated by oxygen-reactive chemotactic bacteria. This study investigated the bioconvection patterns, interference between plumes, and the wavelength of bioconvection patterns. In addition, we clarified the transport characteristics of cells and oxygen in the bioconvection. Multiple plumes occur in the suspension and three-dimensional bioconvection is formed around the plumes by the cells with vortex rings arising around the plumes. Even if bioconvection at a high Rayleigh number is disturbed, the bioconvection is strongly…
We present a simple, new criterion to extract line plumes from the velocity fields, without using the temperature field, in a horizontal plane close to the plate in turbulent convection. The existing coherent structure detection criteria from velocity fields, proposed for shear driven wall turbulence, are first shown to be inadequate for turbulent convection. Based on physical arguments, we then propose that the negative values of $\overline{\nabla_H}\cdot\overline{u}$, the horizontal divergence of the horizontal velocity field extracts the plume regions from the velocity field. The $\overline…
We investigate the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in a large box of aspect ratio $Γ=32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($Γ\appr…
Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated…
The role of polymers additives on the turbulent convective flow of a Rayleigh--Taylor system is investigated by means of direct numerical simulations (DNS) of Oldroyd-B viscoelastic model. The dynamics of polymers elongation follow adiabatically the self-similar evolution of the turbulent mixing layer, and shows the appearance of a strong feedback on the flow which originate a cut off for polymer elongations. The viscoelastic effects on the mixing properties of the flow are twofold. Mixing is appreciably enhanced at large scales (the mixing layer growth-rate is larger than that of the purely N…
We study the fractionation of two components between a well-mixed gas and a saturated convecting porous layer. Motivated by geological carbon dioxide (CO$_2$) storage we assume that convection is driven only by the dissolved concentration of the first component, while the second acts as a tracer with increased diffusivity. Direct numerical simulations for convection at high Rayleigh numbers reveal that the partitioning of the components, in general, does not follow a Rayleigh fractionation trend, as commonly assumed. Initially, increases in tracer diffusivity also increase its flux, because th…
The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is…
The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough, the dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region away from the side walls. The latter is dominated by the shear of the large-scale circulation (LSC) roll which fills the whole cell and continuously varies i…
We analyse the entrainment and energetics of equal and opposite axisymmetric turbulent air plumes in a vertically confined space at a Rayleigh number of $1.24\times 10^{7}$ using theory and direct numerical simulation. On domains of sufficiently large aspect ratio, the steady state consists of turbulent plumes penetrating an interface between two layers of approximately uniform buoyancy. As described by Baines and Turner (J. Fluid Mech. vol. 37, 1969, pp. 51-80), upon penetrating the interface the flow in each plume becomes forced and behaves like a constant-momentum jet, due to a reduction in…
In this numerical study on Rayleigh-Bénard convection we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers $10^5 \leq Ra \leq 10^9$ for a fixed Prandtl number of $Pr=4.3$. We find that the global heat transfer can be enhanced up to $18\%$, and locally around $800\%$. The averaged Reynolds number is always dec…
We study the dynamics of line plumes on the bottom plate in turbulent convection over six decades of Rayleigh number $(10^5<Ra_w<10^{11})$ and two decades of Prandtl number $(0.7<Pr<600)$. We qualitatively identify the main dynamics as motion along the plumes, lateral merging of the plumes and initiation of the plumes; various other minor types of motion also occur along with these main dynamics. The mean velocity along the length of the plumes scales as the large scale flow velocity, with the fraction of the length of the plumes affected by shear increasing with $Ra_w$ as $L_{ps}/L_p\sim Ra_w…
The heat transport in rotating Rayleigh-Bénard convection is considered in the limit of rapid rotation (small Ekman number $E$) and strong thermal forcing (large Rayleigh number $Ra$). The analysis proceeds from a set of asymptotically reduced equations appropriate for rotationally constrained dynamics; the conjectured range of validity for these equations is $Ra \lesssim E^{-8/5}$. A rigorous bound on heat transport of $Nu \le 20.56Ra^3E^4$ is derived in the limit of infinite Prandtl number using the background method. We demonstrate that the exponent in this bound cannot be improved on using…
The arrangement of brine above water across a micro porous permeable membrane is used to study high Rayleigh Number($10^{11}- 10^{10}$) high Schmidt number(650)turbulent convection. The flux shows 4/3$^{rd}$ scaling with line plume as the near wall coherent structures. Shifting of multiple large scale flow cells result in changing near membrane mean shear directions for large aspect ratios. Lower aspect ratios show single large scale flow cell and constant sense of mean shear.
We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, $Ra_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number $Ra_d = H/α_t$ and the dispersivity ratio $r = α_l/α_t$, where $H$ is the domain height, $α_t$ and $α_l$ are the transverse and longit…
We have found a multi-scale steady solution of the Boussinesq equations for Rayleigh-Bénard convection in a three-dimensional periodic domain between horizontal plates with a constant temperature difference by using a homotopy from the wall-to-wall optimal transport solution given by Motoki et al. (J. Fluid Mech., vol. 851, 2018, R4). The connected steady solution, which turns out to be a consequence of bifurcation from a thermal conduction state at the Rayleigh number $Ra\sim10^{3}$, is tracked up to $Ra\sim10^{7}$ by using a Newton-Krylov iteration. The exact coherent thermal convection exhi…
Rotating Rayleigh--Bénard 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 …
We experimentally and numerically investigated the generation of plumes from a local heat source (LHS) and studied the interaction of these plumes with cellular convective motion (CCM) in a rectangular cavity filled with silicon oil at a Prandtl number (Pr) of approximately two thousand. The LHS is generated using a 0.2-W green laser beam. A roll-type CCM is generated by vertically heating one side of the cavity. The CCM may lead to the formation of an unusual spiral convective plume that resembles a vertical Archimedes spiral. A similar plume is obtained in a direct numerical simulation. We d…
We study the velocity field in a horizontal (x-y) plane 1.5 mm above the hot plate in turbulent natural convection using PIV at a Rayleigh number Raw=106 and Prandtl number Pr=5.2. The plane of measurement is inside the velocity boundary layer estimated from the natural convection boundary layer equations[7] as well as inside the velocity boundary layer due to the large scale flow[2, 5].The boundary layer comprises of line plumes with sinking fluid between them. The instantaneous velocity variation from the center of the sinking fluid to the line plumes is found to deviate with the classical P…
We study the structure of the thermal boundary layer (BL) in Rayleigh-Bénard convection for Prandtl number ($Pr$) 0.021 by conducting direct numerical simulations in a two-dimensional square box for Rayleigh numbers ($Ra$) up to $10^9$. The large-scale circulation in the flow divides the horizontal plates into three distinct regions, and we observe that the local thermal BL thicknesses in the plume-ejection region are larger than those in the plume-impact and shear-dominated regions. Moreover, the local BL width decreases as $Ra^{-β(x)}$, with $β(x)$ depending on the position at the plate. We …
A fluid between two spheres, concentric or not, at different temperatures will flow in the presence of a constant gravitational force. Although there is no possible hydrostatic state, energy transport is dominated by diffusion if temperature difference between the spheres is small enough. In this conductive regime the average Nusselt number remains approximately constant for all Rayleigh numbers below some critical value. Above the critical Rayleigh number, plumes appear and thermal convection takes place. We study this phenomenon, in particular the case where the inner sphere is displaced fro…
We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperatu…
Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number $Ra \approx 1708$ has been calculated up to $Ra\approx 5. 10^6$ and shows heat flux $Nu \sim 0.143\, Ra^{0.28}$ with a delicate spiral structure in the temperature field. Another solution that maximizes $Nu$ over the horizontal wavenumber has been calculated up to $Ra=10^9$ and its heat flux scales as $Nu \sim 0.115\, Ra^{0.31}$ for $10^7 < Ra \le 10^9$, quite similar to 3D tur…
We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh-Bénard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range Ra $ \in [{10^6},{10^8}]$ and radius ratio range $η= {R_i}/{R_o} \in [0.3,0.9]$. This study focuses on the dependence of flow properties on the radius ratio $η$. The temperature and velocity fields reveal that different curvatures of the inner and outer cylinders of the ACRBC system lead to asymmetric movements of hot and cold plumes …
