Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $Γ= 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the detected CS contribute by a third less to the global turbulent heat transport for all investigated $Pr$ compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.
The claim by He et al. [Physical Review Letters 108, 024502 (2012)] that their experiment reached the 'ultimate' regime of turbulent Rayleigh-Bénard convection is not justified by their data.
This letter confirms the existence of heat transfer enhancement (HTE) and reduction (HTR) in turbulent natural convection with polymer additives. HTE and HTR were numerically predicted by Benzi et al.(PRL, 104, 024502, 2010) in homogenous turbulent convection, but experiments by Ahlers & Nikolaenko(PRL, 104, 034503, 2010) in turbulent natural convection observed HTR only. Using direct numerical simulation of natural convection, the present study reconciles earlier numerical and experimental work on the basis of the dominant role of polymer length in the polymer dynamics in extensional flows.
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-Bénard convection in extended cylindrical cells with an aspect ratio $Γ=50$ and $Ra>10^5$. They are uncovered when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $Ra_{\ast}$, that describes the convection…
Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of $10^7 - 10^8$). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant ($A=2 - 2.23$). We found that the change of the sign of the degree of…
We present a fluid dynamics video which illustrates the dynamics of the velocity field in the boundary layer in a turbulent Rayleigh-Benard convection flow. The data are obtained from direct numerical simulation.
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average di…
Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-Bénard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range $ 5\times 10^9 \alt Ra \alt 7 \times 10^{10}$ $Nu$ is smaller than it is for pure water by up to 10%.
Weakly-rotating turbulent Rayleigh-Benard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number an abrupt transition from a turbulent state with nearly rotation-independent heat transport to another turbulent state with enhanced heat transfer is observed at a critical inverse Rossby number $1/Ro_c \simeq 0.4$. Whereas for $1/Ro < 1/Ro_c$ the strength of the large-scale convection-roll is either enhanced or essentially unmodified depending on parameters, its strength is increasingly diminished beyond $1/Ro_c$ where it competes with Ekma…
In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add $ν_\mathrm{ren} \propto Π_u^{1/3} (π/Δ)^{-1/3}$ to the kinematic viscosity; here $Π_u$ is the turbulent kinetic energy flux, and $Δ$ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a $128^3$ grid and compare the results with direct numerical simulation (DNS) on a $512^3$ grid. There is a good agreement between the LES and DNS results…
Multiple chaotic and turbulent regimes in Rayleigh-Bénard convection have been studied and classified from the onset of deterministic chaos to the fully developed turbulence using the distributed chaos approach supported by results of laboratory experiments and numerical simulations. It is shown that the regimes can replace each other depending on value of the Rayleigh number and location in the convection cell (in the bulk of the flow or in the boundary layers). The inertial-buoyancy and helicity based invariants play crucial role in the formation of the regimes. Transition from the classical…
We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.
We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via vortex reconnection of two attracting corner rolls having same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to this flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prand…
Turbulent Rayleigh-Benard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell Gamma is varied between 1 and 12, and the Rayleigh number Ra between 10^7 and 10^9. The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies…
Thermal convection in fluid layers heated from below are usually realized experimentally as well as treated theoretically with fixed boundaries on which conditions for the temperature and the velocity field are prescribed. The thermal and velocity boundary layers attached to the upper and lower boundaries determine to a large extent the properties of turbulent convection at high Rayleigh numbers. Fixed boundaries are often absent in natural realizations of thermal convection. This paper studies the properties of convection driven by a planar heat source below a cooling source of equal size imm…
It is shown that helicity dynamics dominates spectral distribution of the velocity fluctuations in turbulent thermal convection at moderate and large values of the Rayleigh number (distributed chaos and scaling respectively). The large-scale circulation (wind) in the turbulent Rayleigh-Bénard convection is especially sensitive to the helicity dynamics and its chaotic reversals can be associated with the reversals of the mean helicity sign (the ergodic restoration of the reflectional symmetry in a long run). Results of the laboratory experiments and measurements in the free atmospheric convecti…
We conduct direct numerical simulations for turbulent Rayleigh-Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and salt concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann-Lohse theory for traditional RB convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett., 86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theo…
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-…
We investigate the anisotropy in turbulent convection in a 3D box using direct numerical simulation. We compute the anisotropic parameter $A = u_\perp^{2}/(2u_{\parallel}^{2})$, where $u_{\perp}$ and $u_{\parallel}$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr} \approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty$, $A \approx 0.3$, thus anisotropy is not very significant even…
This paper deals with determination of turbulent convection velocities from particle image velocimetry (PIV). Turbulent convection velocities are of interest because they can be used to map temporal information into space. Convection velocity can be defined in several different ways. One approach is to use the phase-spectrum of two signals with a time-separation. Obtaining convection velocity per wavenumber involves determining a spatial spectrum. PIV data is limited in spatial resolution and sample length. The influence of truncation of both spatial resolution and frequency resolution is inve…
The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection,…
We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4E8 < Ra < 2E12, while harmonically modulating the temperatures of the plates of our cylindrical cell. We probe the flow by temperature sensors placed in the cell interior and embedded in the highly conducting copper plates and detect thermal waves propagating at modulation frequency in the bulk of the convective flow. We confirm the recent numerical prediction [PRL 125, 154502 (2020)] of the significant enhancement of Nusselt number and report its dependence on the frequency and amplitude of the temperature mo…
Recent findings suggest that wall-bounded turbulent flow can take different statistically stationary turbulent states, with different transport properties, even for the very same values of the control parameters. What state the system takes depends on the initial conditions. Here we analyze the multiple states in large-aspect ratio ($Γ$) two-dimensional turbulent Rayleigh--Bénard flow with no-slip plates and horizontally periodic boundary conditions as model system. We determine the number $n$ of convection rolls, their mean aspect ratios $Γ_r = Γ/n$, and the corresponding transport properties…
A model for the large-scale circulation (LSC) dynamics of turbulent Rayleigh-Benard convection is presented. It consists of two stochastic ordinary differential equations motivated by the Navier-Stokes equation, one each for the strength and the azimuthal orientation of the LSC. Stochastic forces represent phenomenologically the action of the turbulent fluctuations on the LSC. Without adjustable parameters, the model yields a meandering LSC with occasional rotations, and with more rare cessations that occur a few times per day -- differing only by about a factor of two from experiment. Also as…
The boundary layer flow in a Rayleigh-Bénard convection cell of rectangular shape has been visualized in this fluid dynamics video. The experiment has been undertaken in air at a Rayleigh number $Ra=1.3\times 10^{10}$ and a Prandtl number $Pr=0.7$. Various sequences captured at selected positions of the heating plate show that the boundary layer is a very transient flow region characterized by coherent structures that permanently evolve. It becomes fully turbulent in the areas where the large-scale circulation impinge or leave the bottom plate.
In turbulent Rayleigh-Benard convection, a large-scale circulation (LSC) develops in a nearly vertical plane, and is maintained by rising and falling plumes detaching from the unstable thermal boundary layers. Rare but large fluctuations in the LSC amplitude can lead to extinction of the LSC (a cessation event), followed by the re-emergence of another LSC with a different (random) azimuthal orientation. We extend previous models of the LSC dynamics to include momentum and thermal diffusion in the azimuthal plane, and calculate the tails of the probability distributions of both the amplitude an…
Rayleigh--Bénard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing the proper orthogonal decomposition (POD) of numerical data. Instead of the usual POD ansatz of finding modes that describe the energy best, we propose a method that is optimal in describing the heat transport. Thereby, we can determine the modes with the major influence on the heat transport and the coherent structures in the convection cell. We a…
Turbulent Rayleigh-Bénard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and momentum transport, represented by the Nusselt number and Reynolds number, is generally weaker for larger number $n$ of the LSC rolls. This is supported by direct numerical simulations for $Ra=5\times10^5$, $Pr=0.1$, $H=5D$ and $1\leq~n\leq4$.
The spectra of turbulent heat flux $\mathrm{H}(k)$ in Rayleigh-Bénard convection with and without uniform rotation are presented. The spectrum $\mathrm{H}(k)$ scales with wave number $k$ as $\sim k^{-2}$. The scaling exponent is almost independent of the Taylor number $\mathrm{Ta}$ and Prandtl number $\mathrm{Pr}$ for higher values of the reduced Rayleigh number $r$ ($ > 10^3$). The exponent, however, depends on $\mathrm{Ta}$ and $\mathrm{Pr}$ for smaller values of $r$ ($<10^3$). The probability distribution functions of the local heat fluxes are non-Gaussian and have exponential tails.
The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.
We invoke the concepts of magnetic boundary layer and magnetic Rayleigh number and use the magnetic energy dissipation rates in the bulk and the boundary layers to derive some scaling laws expressing how Nusselt number depends on magnetic Rayleigh number, Prandtl number and magnetic Prandtl number for the simple case of turbulent magnetohydrodynamic Rayleigh-Benard convection in the presence of uniform vertical magnetic field.
We report the existence of two new limiting turbulent regimes in horizontal convection (HC) using direct numerical simulations at intermediate to low Prandtl numbers. The flow driven by a horizontal gradient along a horizontal surface, perpendicular to the acceleration of gravity is shown to transition to turbulence in the plume and the core, modifying the rate of heat and momentum transport. These transitions set a sequence of scaling laws blending the theoretical arguments from both the Shishkina, Grossmann & Lohse (SGL) theory with the Hughes, Griffiths & Mullarney (HGM) regime. These resul…
We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, ar…
The corner roll (CR) in the Rayleigh-Bénard (RB) convection accounts for the behaviors of heat transport and convection flow at the corner. Streamlines of the three-dimensional direct numerical simulations for $10^8<Ra<5\times10^9$ show that CR presents well-defined similarity and multi-layer structure. A stream function for CR is developed by homotopy and the structure ensemble dynamics. The model presents the scaling of Reynolds number of corner roll $Re_{cr}\sim Ra^{1/4}$. Scaling of CR scale $r = 0.77 Ra^{-0.085}$ indicates strong near-wall shearing induced by wind and provides a probabili…
We present measurements of the orientation theta_0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in cylindrical cells of aspect ratio 1. theta_0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles Delta theta with a monotonically decreasing probability distribution p(Delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(Delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.
Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophisticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-Bénard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume including part …
We perform direct numerical simulations of rotating Rayleigh--Bénard convection of fluids with low ($Pr=0.1$) and high ($Pr=5$) Prandtl numbers in a horizontally periodic layer with no-slip top and bottom boundaries. At both Prandtl numbers, we demonstrate the presence of an upscale transfer of kinetic energy that leads to the development of domain-filling vortical structures. Sufficiently strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow, despite the formation of plume-like vertical disturbances promoted by so-called Ekman pumping from the viscou…
Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, and Rossby numbers in turbulent rotating Rayleigh-Benard convection are presented. For relatively small $Ra ~ 10^8$ and large Pr modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small Pr = 0.7. there is no heat-transfer enhancement at all. We suggest that the small-Pr behavior is due to the breakdown of the heat-transfer-enhancing Ekman pumping because of larger thermal diffusion.
We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-Bénard convection cell. It is found that thermal plumes are not emitted periodically, but randomly and continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field.
Measurements of the Nusselt number $Nu$ and of temperature variations $ΔT_b$ in the bulk fluid are reported for turbulent Rayleigh-Bénard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra \alt 3\times 10^{14}$ using He (Prandtl number $Pr = 0.67$), N$_2$ ($Pr = 0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 15 bars and near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D = 1.12$m and was located in a new High-Pressure Convection Facility (HPCF) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen,…
The frequency spectra of the entropy and kinetic energy along with the power spectrum of the thermal flux are computed from direct numerical simulations for turbulent Rayleigh-Bénard convection with uniform rotation about a vertical axis in low-Prandtl-number fluids ($\mathrm{Pr} < 0.6$). Simulations are done for convective Rossby numbers $\mathrm{Ro} \ge 0.2$. The temporal fluctuations of these global quantities show two scaling regimes: (i) $ω^{-2}$ at higher frequencies for all values of $\mathrm{Ro}$ and (ii) $ω^{-γ_1}$ at intermediate frequencies with $γ_1 \approx 4$ for $\mathrm{Ro} > 1$…
A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al.(Phys. Rev. Lett., 2012). A multi-layer model is formulated and quantified, whose predictions agree with DNS and experimental data for the Rayleigh-number (Ra) over seven decades. In particular, a thermal buffer layer follows a 1/7 scaling like the previously postulated mixing zone (Procaccia et al, Phys. Rev. A,1991), and yields a Ra-dependent log law constant. A …
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…
For rapidly rotating turbulent Rayleigh--Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the…
The transition to a new turbulent regime in horizontal convection in the case of low Prandtl numbers is analyzed using the Shishkina, Grossmann & Lohse (SGL) theory. The flow driven by the horizontal gradient along a horizontal surface, perpendicular to the acceleration of gravity is shown to transition to turbulence in the plume and the core. This transition to turbulence sets a sequence of heat transfer and momentum transport scalings which are found to follow the SGL prediction for the scaling factors and the prediction of Hughes, Griffith & Mullarney (HGM) for larger forcing amplitudes. Th…
We investigate the effect of weak rotation on the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection, using the theory for cessations in a low-dimensional stochastic model of the flow previously studied. We determine the cessation frequency of the LSC as a function of rotation, and calculate the statistics of the amplitude and azimuthal velocity fluctuations of the LSC as a function of the rotation rate for different Rayleigh numbers. Furthermore, we show that the tails of the reorientation probability distribution function remain unchanged for rotating systems, while the di…
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 …
The aspect ratio (Γ) dependence of the heat transfer (Nusselt number Nu in dimensionless form) in turbulent (two-dimensional) Rayleigh-Bénard convection is numerically studied in the regime $0.4 \le Γ\le 1.25$ for Rayleigh numbers $10^7 \le Ra \le Ra^{9}$ and Prandtl numbers Pr =0.7 (gas) and 4.3 (water). Nu (Γ) shows a very rich structure with sudden jumps and sharp transitions. We connect these structures to the way the flow organizes itself in the sample and explain why the aspect ratio dependence of Nu is more pronounced for small Pr. Even for fixed Γdifferent turbulent states (with differ…
We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of convective--stably-stratified fluids. We demonstrate that in the limit of large Rayleigh number ($Ra\in [4\times 10^7,10^9]$) and large stratification (Brunt-Väisälä frequencies $f_N \gg f_c$, where $f_c$ is the convective frequency), simulations are in good agreement with a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region (Lecoanet \& Quataert 2013 MNRAS 430 (3) 2363-2376). Specific…
Rayleigh-Bénard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised setup to study thermal convection. Of special interest are the statistics of the turbulent temperature field, which we are investigating and comparing for three different geometries, namely convection with periodic horizontal boundary conditions in three and two dimensions as well as convection in a cylindrical vessel, in order to work out similarities and differences. To this end, we derive an exact evolution equation for the temperature probability densit…
By tailoring the geometry of the upper boundary in turbulent Rayleigh-Bénard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude and varying boundary wavelength $λ$, we find that the exponent $β$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \propto Ra^β$, is maximized at $λ\equiv λ_{\text{max}} \approx (2 π)^{-1}$, but decays to the planar value in both the large ($λ\gg λ_{\text{max}}$) and small ($λ\ll λ_{\text{max}}$) wavelength limits. The changes in the exponent originate in the …
We measured Reynolds numbers R_e of turbulent Rayleigh-Benard convection over the Rayleigh-number range 2 times 10^8 < R < 10^11 and Prandtl-number range 3.3 < sigma < 29 for cylindrical samples of aspect ratio Gamma = 1. For R < R_c = 3 times 10^9 we found R_e ~ R^beta_eff with beta_eff = 0.46 < 1/2. Here both the sigma- and R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > R_c we found R_e = 0.106 sigma^-3/4 R^1/2, which differs from the GL prediction. The relatively sharp transition at R_c to the large-R regime suggests a qualitative and sudden ch…
We analyze the Prandtl number (Pr) dependence of spectra and fluxes of kinetic energy, as well as the energy injection rates and dissipation rates, of turbulent thermal convection using numerical data. As expected, for a flow with $ \mathrm{Pr} \lessapprox 1 $, the inertial-range kinetic energy flux is constant, and the kinetic energy spectrum is Kolmogorov-like ($ k^{-5/3} $). More importantly, we show that the amplitudes of the kinetic energy fluxes and spectra and those of structure functions increase with the decrease of Pr, thus exhibiting stronger nonlinearity for flows with small Prandt…
High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Ra…
We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-Bénard convection in a cylindrical sample of aspect ratio $Γ\equiv D/L = 0.50$ ($D = 1.12$ m is the diameter and $L = 2.24$ m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range $3\times 10^{12} \alt \Ra \alt 10^{15}$ and for Prandtl numbers \Pra\ between 0.79 and 0.86. For $\Ra < \Ra^*_1 \simeq 1.4\times 10^{13}$ we find $\Nu = N_0 \Ra^{γ_{eff}}$ with $γ_{eff} = 0.312 \pm 0.002…
Using direct numerical simulations of turbulent thermal convection for Rayleigh number ($\mathrm{Ra}$) between $10^6$ and $10^8$ and unit Prandtl number, we derive scaling relations for viscous dissipation in the bulk and in the boundary layers. We show that contrary to the general belief, the total viscous dissipation in the bulk is larger, albeit marginally, than that in the boundary layers. The bulk dissipation rate is similar to that in hydrodynamic turbulence with log-normal distribution, but it differs from $(U^3/d)$ by a factor of $\mathrm{Ra}^{-0.18}$. Viscous dissipation in the bounda…
