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We present an experimental study of flow structures in turbulent Rayleigh–Benard convection in annular cells of aspect ratios $$\varGamma =1$$ , 2 and 4, and radius ratio $$\backsimeq $$ 0.5. The convecting fluid is water with Prandtl number $$Pr= 4.3$$ and 5.3. Rayleigh number Ra ranges $$4.8 \times 10^{7} \le Ra \le 4.5 \times 10^{10}$$ . The dipole state (two-roll flow structure) for $$\varGamma = 1$$ and the quadrupole state (four-roll flow structure) for $$\varGamma = 2$$ and 4 are found by multi-temperature-probe measurement. Nusselt number Nu is described by a power-law scaling $$Nu=0.11Ra^{0.31}$$ , which is insensitive to the change of flow structures. However, the Reynolds number Re is influenced by increasing aspect ratios, where Re is found to scale with Ra and $$\varGamma $$ as $$Re\sim Ra^{0.46}\varGamma ^{-0.52}$$ . The normalized amplitudes of two flow structures as a function of Ra exist difference. Based on relative weights of the first four modes using the Fourier analysis, we find that the first mode dominates in $$\varGamma =1$$ cell, but the second mode contains the most energy in $$\varGamma =2$$ and 4 cells. With increasing $$\varGamma $$ , the flow structures exhibit different characteristics.

Spontaneous and stochastic reversal of large scale flow structure is an intriguing and crucial phenomenon in turbulent Rayleigh-Bénard type natural convection. This paper proposes a new control approach to eliminate the reversals through stabilising the corner flows using two small sidewall controllers. Based on a series of direct numerical simulations, it is shown that the control can successfully stop the growth of corner vortices and suppress the reversal of large-scale circulation, if the width of sidewall controllers installed within or near the top of corner vortices is large enough. When the controllers are located around the centre, they can easily break up the large-scale structures or even divide the single roll mode into a double-roll mode for very large widths. Moreover, the influence of sidewall controllers on the heat transport is studied. It is shown that the heat transport efficiency can be slightly enhanced or suppressed when the proper location and width are chosen. The present findings provide a new idea to control the large-scale flow structure and reversals in thermally driven convection through sidewall controlling.

Objectives: The purposes of this work are to investigate the free convective heat transfer in an axis-symmetric open-ended cavity heated from below and to propose useful correlations of Nusselt number. Methods: The governing equations that model the fluid flow and the temperature field are solved using a control volume-based finite differences method. Under steady state condition, the natural convective flow is considered to be laminar, incompressible and axisymmetric. The Boussinesq approximation with constant thermophysical properties is adopted. Numerical experimentations are performed to deduce the optimum sizes of the calculation domain and the mesh grid. Findings: the obtained results indicate that when Rayleigh number (Ra) and aspect ratio (A) are low the heat transfer is weak and mainly conductive. The increase of Ra and A enhances the convective heat transfer mode thereby the heat transfer is ameliorated. Unlike the Rayleigh Bénard convection, the transition from conduction to convection produces at critical value of Rayleigh number (Rac) that is variable dependent on A. Novelty: To the best of authors knowledge, the formula of (Rac) elaborated in this work for the studied cavity is the first attempt. As well, correlation of Nusselt numbers (Nu) for the cold upper plate in terms of Ra and A is performed. Comparisons between Nu at the lower plate given in previous work and Nusselt number at the upper plate is conducted. Keywords: free convection; circular plates; Nusselt number correlations; open ended cavity; critical Rayleigh number

The main objective of the current work is to enhance consistency and capabilities of Moving Particle Semi-implicit (MPS) method for simulating a wide range of free-surface flows and convection heat transfer. For this purpose, two novel high-order gradient and Laplacian operators are derived from the Taylor series expansion and are applied for the discretization of governing equations. Furthermore, the combination of the explicit Third-order TVD Runge-Kutta scheme and two-step projection algorithm is employed to approximate transient terms in the Navier-stokes and energy equations. To further improve the accuracy and performance of the method, a new kernel function is constructed by a combination of the Gaussian and cosine functions and then implemented for modeling the 1D Sod shock tube problem. Validation and verification of the proposed model are conducted through the simulations of several canonical test cases such as: dam break, rotation of a square patch of fluid, two-phase Rayleigh-Taylor instability, oscillating concentric circular drop and good agreement are achieved. The proposed model is then employed to simulate three-phase Rayleigh-Taylor instability and entropy generation due to natural convection heat transfer (Differentially Heated Cavity and Rayleigh-Benard convection). The obtained results reveal that, the newly constructed kernel function provides more reliable results in comparison with two frequently used kernel functions namely; quartic spline and Wendland. Furthermore, it is found that, the enhanced MPS model is capable of handling multiphase flow problems with low and high density contrast.

The magneto-hydrodynamics (MHD) effect is studied at different inclined angles in Rayleigh-Benard (RB) convection inside a rectangular enclosure using the lattice Boltzmann method (LBM). The enclosure is filled with electrically conducting fluids of different characteristics. These characteristics are definedbyPrandtlnumber,Pr. The considered Pr values for this study are 10 and 70. The influence of other dimensionless parameters Rayleigh numbers Ra ¼ 10 ; 10 ; 10 ; 10 and Hartmann numbers Ha = 0, 10, 25, 50, 100, on fluid flow and heat transfer, are also investigated considering different inclined angles φ of magnetic field by analyzing computed local Nusselt numbers and average Nusselt numbers. The results of the study show the undoubted prediction capability of LBM for the current problem. The simulated results demonstrate that the augmentation in heat transfer is directly related to Ra values, but it is opposite while observing the characteristics of Ha values. However, it is also found that φ has a significant impact on heat transfer for different fluids. Besides, isotherms are found to be always parallel to the horizontal axis at Ra ¼ 10 as conduction over-comes the convection in the heat transfer, but this behaviour is not seen at Ra ¼ 10 when Ha > 25. Furthermore,at Ra ¼ 10 , oscillatory instability appears but LBM is still able to provide a complete map of this predicted beha-vior. An appropriate validation with previous numerical studies demonstrates the accuracy of the present approach. 3 4 5 6 3 4 6

In this paper, we make experimental observations of the perturbed Rayleigh-Benard convection to detect the Lagrangian coherent structures (LCSs), which correspond to the invariant manifolds of time-dependent systems and also to investigate the associated fluid transports by numerically integrating the two-dimensional velocity field obtained by Particle Image Velocimetry (PIV). We show the chaotic fluid transports that appear in the system, though some particles are transported almost periodically with time period T or 3T, where T = 17.3 s is the period of the perturbation. We finally propose a novel perturbed Hamiltonian system that enables to recover qualitatively global behaviors observed in experimental results and we also explore the periodic fluid transport that appear in the system.

In this study, we examine the effect of a uniform external magnetic field on Rayleigh-Benard convection in a square cavity filled with a ferrofluid. Numerical simulations are based on the Lattice Boltzmann method. The effects of physical parameters, which are the Rayleigh number, the Hartmann number, and the angle of inclination of the magnetic field are studied. The results obtained are graphically illustrated and discussed for a volume fraction of four percent. These results show that the rate of heat transfer decreases by increasing the Hartmann number. For high Rayleigh number values, the maximum heat transfer rate was obtained for a specific Hartmann number when the Lorentz and buoyancy forces are perpendicular

In the paper, the effect of time-periodic gravity modulation with trigonometric sine, triangular, and square waves-forms on Rayleigh Benard convection in water-alumina nanoliquids and water-alumina-copper hybrid nanoliqiuds is studied by using a single-phase model. Using a perturbation method, linear stability analysis is performed for all the three wave-forms. A generalized Lorenz model that has the influence of nanoliquids and modulation incorporated in it is derived using a truncated Fourier series representation. The Lorenz model is then transformed into a Ginzburg-Landau model using the method of multiscales, and the solution is used to study heat transport. For trigonometric sine, triangular and square wave-forms of modulations comparison are made on their effect on the onset of convection and the heat transport. The linear stability analysis reveals that the critical Rayleigh number obtained in the case of a triangular wave-form is less compared to the value obtained in the cases of trigonometric sine and square wave-forms. This leads to an enhanced heat transfer situation in the case of triangular wave-form compared to that in the other two wave-forms. It is also found that such an enhancement in heat transport increases with amplitude and decreases with the modulation frequency. Thus, the modulation is found to be a regulating mechanism on heat transport. Further, it is observed that water-alumina-copper facilitates maximum heat transport compared to that by water-alumina and water, leading to the conclusion that hybrid nanoliquids facilitate enhanced heat transport compared to that by mono nanoliquids.

This paper investigates the Rayleigh Benard instability of a viscous, Newtonian, Boussinesq fluid with time-periodic boundary temperature modulation using the framework of weakly nonlinear theory. Critical Rayleigh number is computed for asymptotic stability criterion using the energy method accompanied by variational algorithm. Subcritical instability is found to occur under two conditions: when modulation is in anti-phase and when modulation is imposed only on the lower boundary. Supercritical stability is witnessed during in-phase modulation. In all the three cases of the relative phase of two boundary temperatures, the effect of modulation is found to be weaker for infinitesimal disturbances. The findings of the present study could be referred in several applications where appropriate temperature modulation is of prime concern.

Lattice Boltzmann method is used to investigate the Rayleigh–Benard convection of magnetohydrodynamic fluid flow inside a rectangular cavity filled by porous media. The Brinkman–Forchheimer model is considered in the simulation to formulate a porous medium mathematically, and the multi-distribution function model is considered to include the magnetic field effect with different inclination angles. The water is considered as the working fluid, which is electrically conducting. A comprehensive analysis of the impact of governing dimensionless parameters is performed by varying Rayleigh (Ra), Hartmann (Ha), and Darcy (Da) numbers, porosity ( $$\epsilon $$ ), and inclination angles ( $$\phi $$ ) of the applied magnetic field. Numerical results are evaluated in the form of streamlines, isotherms, and the rate of heat transfer in terms of the local and average Nusselt number as well as the entropy generation due to the irreversibility of the fluid friction, temperature gradient, and magnetic field effects. The results imply that increasing Ha and decreasing Da reduce the rate of heat transfer. The average Bejan number $$\hbox {Be}_\mathrm{{avg}}$$ increases for increasing the Hartmann number. On the other hand, augmenting Ra and $$\epsilon $$ improves the heat transfer rate. It is also found that the change of the magnetic field inclination angle $$\phi $$ changes the rate of heat transfer and entropy generation.

Thermal convection is ubiquitous in nature as well as in many industrial applications. The identification of effective control strategies to, e.g., suppress or enhance the convective heat exchange under fixed external thermal gradients is an outstanding fundamental and technological issue. In this work, we explore a novel approach, based on a state-of-the-art Reinforcement Learning (RL) algorithm, which is capable of significantly reducing the heat transport in a two-dimensional Rayleigh-B\'enard system by applying small temperature fluctuations to the lower boundary of the system. By using numerical simulations, we show that our RL-based control is able to stabilize the conductive regime and bring the onset of convection up to a Rayleigh number $Ra_c \approx 3 \cdot 10^4$, whereas in the uncontrolled case it holds $Ra_{c}=1708$. Additionally, for $Ra > 3 \cdot 10^4$, our approach outperforms other state-of-the-art control algorithms reducing the heat flux by a factor of about $2.5$. In the last part of the manuscript, we address theoretical limits connected to controlling an unstable and chaotic dynamics as the one considered here. We show that controllability is hindered by observability and/or capabilities of actuating actions, which can be quantified in terms of characteristic time delays. When these delays become comparable with the Lyapunov time of the system, control becomes impossible., Comment: 24 pages, 10 figures

To enrich the three-dimensional experimental details of vortex structures in rotating Rayleigh–Benard convection, we established a technique visualizing three-dimensional vortex structures using scanning planar particle image velocimetry. Experiments were performed at fixed Rayleigh number, $$\hbox {Ra} = 1.0 \times 10^7$$ and different Taylor numbers from $$\hbox {Ta} = 6.0 \times 10^6$$ to $$1.0 \times 10^8$$ , corresponding to convective Rossby numbers from $$0.1 \le \hbox {Ro} \le 0.5$$ at which gradual transition between vortical plumes and convective Taylor columns regime is observed. Stream function distributions calculated from horizontal velocity vector fields visualize the vortex structure formed in the regimes. As quantitative information extracted from the visualized structures, distances between vortices recognized on the distributions show a good agreement with that evaluated by a theory. With the accumulated planar stream function distributions and vertical velocity component calculated from the horizontal velocity vectors, the three-dimensional representations of vortices indicate that quasi-two-dimensional columnar vortices straighten in the vertical direction with increasing Ta.

PurposeThe study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.Design/methodology/approachThe Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).FindingsResults are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.Originality/valueThe effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

The individual effect of time-periodic gravity modulation, in-phase and out-of-phase temperature modulations and rotational modulation on Rayleigh–Benard convection in twenty-eight nanoliquids is studied in the paper using the two-phase description of the generalized Buongiorno model. The generalized Lorenz model for each modulation problem is derived using the truncated Fourier series representation. The method of multiscales is employed to arrive at the Ginzburg–Landau equations from the Lorenz models, and the solution of Ginzburg–Landau equations is used to quantify the heat transport. The modulation amplitude is considered to be small (of order less than unity) and low frequencies of modulation are considered. The coefficient of the linear term of the algebraic part of the Ginzburg–Landau equations is shown to exclusively hold the information on the amplitude and the frequency of modulation. The influence of nanoparticles (nanotubes) on heat transport in the presence/absence of various modulations is explained. The study reveals that the frequency of modulation is a dominant factor in the case of gravity and rotational modulations whereas in the case of boundary temperature modulation in addition to the frequency of modulation, the phase difference plays an important role. Effect of these three modulations is to enhance/diminish heat transport but depends strongly on the choice of values of frequency of modulation and amplitude. For fixed values of frequency ( $$\omega ^*=5$$ ) and amplitude ( $$\delta _2=0.1$$ ) of various modulations, it is shown that the maximum percentage of heat transport enhancement achieved in glycerin due to 5% of $$\hbox {SWCNTs}$$ is 21.86% for gravity modulation, 17.36% for rotational modulation and 15.63% for boundary temperature modulation (out of phase). The reason for highest heat transport in gravity modulation is explained by finding area under the curves of three modulations. The study reveals that the modulation whose area under the curve is maximum transports maximum heat. The results pertaining to the single-phase model are recovered as a limiting case of the present study. The study shows that the single-phase model under-predicts heat transport compared to the two-phase model. The results obtained in the present study are compared with those of previous investigations and qualitatively good agreement is found.

The paper presents the results of an experimental study of a turbulent convection of liquid sodium in a vertical cylinder with aspect ratio one, heated from one end and cooled from the other. A detailed spectral analysis of temperature signals was carried out for experiments lasting from 1 to 7 hours. It is shown that in the entire range of Rayleigh numbers (0.6÷2.2)·10 7 , the turbulent flow self-organizes into a large-scale circulation (LSC), occupying the entire cavity and having a complex spatio-temporal structure. In addition to the main mode, there are additional modes in the flow structure, such as sloshing and torsion oscillations. The developed experimental data processing algorithm made it possible to isolate these modes and conduct an independent analysis of their characteristics. Long-term measurements made it possible to detect the wandering of the plane of the main LSC mode using the developed algorithm for filtering experimental data. The wandering process is non-periodic in nature and consists in irregular rotation of the LSC plane mainly at angles of the order of 40 – 50° at time scales from units to tens of minutes, and, rarely, at angles of about 90° and even 180° at large time scales. Such rare events were recorded on wavelet diagrams in the form of bursts of spectral energy density.

We report measurements of the temperature frequency spectra $P(\,f, z, r)$ , the variance $\sigma ^2(z,r)$ and the Nusselt number $Nu$ in turbulent Rayleigh–Bénard convection (RBC) over the Rayleigh number range $4\times 10^{11} \underset{\smash{\scriptscriptstyle\thicksim}} { < } Ra \underset{\smash{\scriptscriptstyle\thicksim}} { < } 5\times 10^{15}$ and for a Prandtl number $Pr \simeq ~0.8$ ( $z$ is the vertical distance from the bottom plate and $r$ is the radial position). Three RBC samples with diameter $D = 1.12$ m yet different aspect ratios $\varGamma \equiv D/L = 1.00$ , $0.50$ and $0.33$ ( $L$ is the sample height) were used. In each sample, the results for $\sigma ^2/\varDelta ^2$ ( $\varDelta$ is the applied temperature difference) in the classical state over the range $0.018 \underset{\smash{\scriptscriptstyle\thicksim}} { < } z/L \underset{\smash{\scriptscriptstyle\thicksim}} { < } 0.5$ can be collapsed onto a single curve, independent of $Ra$ , by normalizing the distance $z$ by the thermal boundary layer thickness $\lambda = L/(2 Nu)$ . One can derive the equation $\sigma ^2/\varDelta ^2 = c_1\times \ln (z/\lambda )+c_2+c_3(z/\lambda )^{-0.5}$ from the observed $f^{-1}$ scaling of the temperature frequency spectrum. It fits the collapsed $\sigma ^2(z/\lambda )$ data in the classical state over the large range $20 \underset{\smash{\scriptscriptstyle\thicksim}} { < } z/\lambda \underset{\smash{\scriptscriptstyle\thicksim}} { < } 10^4$ . In the ultimate state ( $Ra \underset{\smash{\scriptscriptstyle\thicksim}} { > } Ra^*_2$ ) the data can be collapsed only when an adjustable parameter $\tilde \lambda = L/(2 \widetilde {Nu})$ is used to replace $\lambda$ . The values of $\widetilde {Nu}$ are larger by about 10 % than the experimentally measured $Nu$ but follow the predicted $Ra$ dependence of $Nu$ for the ultimate RBC regime. The data for both the global heat transport and the local temperature fluctuations reveal the ultimate-state transitions at $Ra^*_2(\varGamma )$ . They yield $Ra^*_2 \propto \varGamma ^{-3.0}$ in the studied $\varGamma$ range.

We present an experimental and theoretical study of Rayleigh–Benard convection in shear-thinning fluids with temperature-dependent properties. Experiments were performed using a cylindrical cell with a radius R=60 mm and height adjustable at d=15 and 20 mm giving a radius-to-height ratio L = 4 and 3, respectively. The fluids used are glycerol (Newtonian fluid) and aqueous xanthan gum solutions (shear-thinning fluids) at 1000 and 1200 ppm. Convection patterns are visualized by the shadowgraph method. In the theoretical part of this study, the weakly nonlinear analysis performed by Vare et al. [J. Fluid Mech. 905, A33 (2020)] is extended to take into account the variation of the thermal expansion coefficient with temperature. For the xanthan gum solutions used, the temperature dependence of the fluid parameters is sufficiently strong to obtain hexagonal cells at the onset of convection. It has been observed that their size decreases with the increase in the temperature difference across the fluid layer above the critical value. This result provides an experimental support to our theoretical study where it is shown that for hexagons, the band of stable wavenumbers is bent toward higher wavenumbers. For the glycerol, Newtonian fluid with a large Prandtl number, a slight increase in the wavelength of rolls is observed in agreement with the literature.

Bounds are derived for rotating Rayleigh–Bénard convection with free slip boundaries as a function of the Rayleigh, Taylor and Prandtl numbers ${\textit {Ra}}$ , ${\textit {Ta}}$ and ${\textit {Pr}}$ . At infinite ${\textit {Pr}}$ and ${\textit {Ta}} > 130$ , the Nusselt number ${\textit {Nu}}$ obeys ${\textit {Nu}} \leqslant \frac {7}{36} \left ({4}/{{\rm \pi} ^2} \right )^{1/3} {\textit {Ra}} {\textit {Ta}}^{-1/3}$ , whereas the kinetic energy density $E_{kin}$ obeys $E_{kin} \leqslant ({7}/{72 {\rm \pi}}) \left ({4}/{{\rm \pi} } \right )^{1/3} {\textit {Ra}}^2 {\textit {Ta}}^{-2/3}$ in the frame of reference in which the total momentum is zero, and $E_{kin} \leqslant ({1}/{2{\rm \pi} ^2})({{\textit {Ra}}^2}/{{\textit {Ta}}})({\textit {Nu}}-1)$ . These three bounds are derived from the momentum equation and the maximum principle for temperature and are extended to general ${\textit {Pr}}$ . The extension to finite ${\textit {Pr}}$ is based on the fact that the maximal velocity in rotating convection at infinite ${\textit {Pr}}$ is bound by $1.23 {\textit {Ra}} {\textit {Ta}}^{-1/3}$ .

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 $\eta = {R_i}/{R_o} \in [0.3,0.9]$ ( $R_i$ and $R_o$ are the radius of the inner and outer cylinders, respectively). This study focuses on the dependence of flow dynamics, heat transport and asymmetric mean temperature fields on the radius ratio $\eta$ . For the inverse Rossby number $Ro^{-1} = 1$ , as the Coriolis force balances inertial force, the flow is in the inertial regime. The mechanisms of zonal flow revolving in the prograde direction in this regime are attributed to the asymmetric movements of plumes and the different curvatures of the cylinders. The number of roll pairs is smaller than the circular roll hypothesis as the convection rolls are probably elongated by zonal flow. The physical mechanism of zonal flow is verified by the dependence of the drift frequency of the large-scale circulation (LSC) rolls and the space- and time-averaged azimuthal velocity on $\eta$ . The larger $\eta$ is, the weaker the zonal flow becomes. We show that the heat transport efficiency increases with $\eta$ . It is also found that the bulk temperature deviates from the arithmetic mean temperature and the deviation increases as $\eta$ decreases. This effect can be explained by a simple model that accounts for the curvature effects and the radially dependent centrifugal force in ACRBC.

The present study investigates the flow and thermal fields of Rayleigh-Bénard convection (RBC) in a rectangular channel with an internal circular cylinder. The parameters considered are Rayleigh number (104≤Ra≤106), Prandtl number (Pr = 0.7), and irreversibility distribution ratio (φ = 1). The vertical distance (δ) in the range of -0.2 ≤ δ ≤ 0.2 is the major simulation parameter in present study. The results are analyzed based on the iso-surface of temperature, vortical structure with orthogonal enstrophy distribution, and entropy generations. Additionally, Nusselt number (Nu) and Bejan number (Be) are obtained to analyze the heat transfer characteristics and irreversibility, respectively. The Rayleigh number and the vertical distance significantly influence the flow and thermal characteristics within the channel. Besides, an artificial neural network (ANN) model is used to predict the distribution of local Nusselt number. The performance of present ANN model is evaluated by comparing the tendency and quantitative values with the direct numerical simulation (DNS) results. The results show that the ANN model used in this study can precisely predict the correlation between the input parameters and output parameter with lesser computational time and cost compared to the DNS.

This paper investigates the effect of time-periodic temperature modulation on Rayleigh-Benard convection using rigid isothermal boundary conditions. The time-periodic temperature modulation has been considering in three different modes, out-of-phase (OPM), lower boundary (LBMO), and in-phase modulation (IPM). Heat transfer results are calculated in terms of the Nusselt and mean Nussult numbers through the finite amplitude of convection which is derived from the Ginzburg-Landau equation (GLE). The Ginzburg-Landau equation has been derived from the Fredholm solvability condition at third. The GLE is a function of the system parameters and solved numerically. The present study shows that heat transfer results are controlled effectively by out-of-phase and lower boundary modulations. The modulated amplitude of convection enhances heat transfer for low frequencies and diminishes for high frequencies. Further, it is found that rigid boundary conditions are diminishing heat transfer than free boundaries. Finally, it is concluded that heat transfer results are controlled by rigid isothermal boundary conditions and modulation.

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 an effort to achieve very large Rayleigh numbers when studying turbulence on a Rayleigh--Baposenard configuration, one can carry out simulations and experiments in as high convection cells as possible which involves using convection cells with the smallest possible aspect ratio. However, with the increasing height of the cell, the Rayleigh number grows much slower than the critical Rayleigh number for the onset of convection in the same container. This article discusses how to estimate accurately the critical Rayleigh number for the onset of convection in confined geometries and the optimal shape of the container.

Numerical simulations of a Rayleigh-Benard turbulent convective flow are examined to determine the optical and mechanical turbulence properties and resulting index of refraction and temperature structure function fields with the goal of understanding the propagation characteristics of a laser beam carrying orbital angular momentum. Beams carrying orbital angular momentum are a topic of interest for secure high data density free-space communications systems in both the atmosphere and underwater environment. The choice of Rayleigh-Benard convection provides a highly controllable configuration for studying optical turbulence and once the flow reaches a steady state, it may be treated as homogeneous. With a well characterized turbulent state provided by the simulations, attention is focused on the mechanics of beam propagation through the turbulence. Simulations are performed using the open source computational fluid dynamics package OpenFoam, a finite volume solver, and an in-house developed code that uses spectral methods. In the case of each solver, the Boussinesq approximation is used to model buoyancy and both the Navier-Stokes equations and the thermal energy equation are simultaneously solved. The outcome from the two computational schemes will be cross compared for result fidelity, spatial resolution, and computation time. The initial effort will examine air as the working medium in a domain with dimensions of 0.5 m on a side and a height of 0.1 m.

It is well known that Rayleigh-Benard convection with perturbations yields Lagrangian chaotic transport, and the mechanism of inducing chaotic transport has been numerically clarified by lobe dynamics [2]. On the other hand, the mechanism of such Lagrangian transport has not been enough studied by experiments. In our previous work [16], we made an experimental study to investigate the Lagrangian transport appeared in the two-dimensional Rayleigh-Benard convection by giving oscillation on the velocity fields and showed that there exist Lagrangian Coherent Structures (LCSs) which correspond to invariant manifolds of non-autonomous systems. We also showed that the LCSs entangle with each other around cell boundaries. In this paper, we further explore the global invariant structures of the perturbed Rayleigh-Benard convection by clarifying the details on the LCSs and explain how the fluid transport obeys lobe dynamics. Finally, we propose a novel Hamiltonian model for the two-dimensional perturbed Rayleigh-Benard convection that enables to elucidate the global structures detected by experiments.

To study the flow topology and temperature distribution of Rayleigh-Benard convection in a highly slender cell, measurement of the simultaneous velocity and temperature in the 3-D domain is required. For this aim, implementing a simultaneous time-resolved 3-D PTV and two-colour PLIF is planned. As a part of this development, for both PTV and two-colour PLIF techniques, the experimental setup has been implemented separately to measure time-resolved 2-D velocity and temperature and is presented in this paper. For PTV, a scanning system is also utilized to scan the flow field to capture the planar velocity in different depths of the flow domain. Progress on calculation of the out-of-plane velocity component including the theory is discussed. Finally, results of the time-resolved 2-D PTV and PLIF systems are presented.

It is known that some fluid particles may be transported chaotically in Lagrangian description although the velocity field seems to be stable in Eulerian description. A typical example can be found in the system of two-dimensional Rayleigh-Benard convection with perturbed velocity fields, which has been investigated as a low dimensional mechanical model of fluid phenomena associated with natural convection in order to clarify the mechanism of fluid transport (see, for instance, [2]). In this study, we make an experimental study on the global structures of chaotic mixing appeared in the two-dimensional perturbed Rayleigh-Benard convection by analyzing Lagrangian coherent structures (LCSs), which correspond to the invariant manifolds of time-dependent mechanical systems. We develop an apparatus to measure the velocity field by Particle Image Velocimetry (PIV) and then show the LCSs which can be numerically detected from the experimental data by computing Finite-time Lyapunov exponent (FTLE) fields. Finally, we show the global structures of chaotic mixing appeared in the perturbed Rayleigh-Benard convection as well as the steady convection by experiments. In particular, we clarify how the LCSs are entangled with each other around the cell boundaries to carry out chaotic Lagrangian transports.

In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Benard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection.

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

The linear Rayleigh-Benard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$.

The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-B\'enard 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-B\'enard 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 stress length, $\ell_u^+\approx \ell_0^+(z^+)^{3/2}\left[1+\left({z^+}/{z_{sub}^+}\right)^4\right]^{1/4}$, as proposed by She et al. (She 2017), though neither a Prandtl-Blasius-Pohlhausen type nor the log-law is seen in the viscous boundary layer. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, $A$ can be described by composition of the thermal stress length $\ell^*_{\theta}$ and the thicknesses of thermal boundary layer $z^*_{sub}$ and $z^*_{buf}$, i.e. $A\simeq z^*_{sub}/\left(\ell^*_{\theta 0}{z^*_{buf}}^{3/2}\right)$. The adverse pressure gradient responsible for turning the wind direction contributes to thermal plumes gathering at the ejecting region and thus the log-law of temperature profile. The Nusselt number scaling and local heat flux of the present simulations are consistent with previous results in confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation on a fixed plane., Comment: 16 pages, 37 figures

In laboratory experiments, horizontal translational motion of columnar vortices formed in rotating Rayleigh–Bénard convection was investigated. Two types of measurements, vertical velocity fields and horizontal temperature fields, were conducted with water as the test fluid. Using particle image velocimetry, the vertical velocity fields determined the parameter range at which the quasi-two-dimensional columnar vortices emerged. Locally, the duration characteristics of the columns, evaluated with their vertical coherence, indicate the minimum time scale of translational motion of the vortices in the horizontal plane. Vortex tracking of the horizontal temperature fields over long observation periods (${>}10^{3}~\text{s}$) was conducted using encapsulated thermochromic liquid crystal visualization. Two cylindrical vessels with different radii showed the emergence of the centrifugal effect in $O({>}10^{2}~\text{s})$ despite the small Froude number ($Fr). Further, in the horizontal plane the columnar vortices behaved in a random-walk-like diffusive motion. The statistically calculated mean-squared displacements indicated anomalous diffusive motion of the columns; displacement increasing with time as $t^{\unicode[STIX]{x1D6FE}}$ with $\unicode[STIX]{x1D6FE}\neq 1$. We discuss the causes of this anomaly in both the instantaneous and long-term statistical data gathered from experimental observations over different time scales. The enclosure effect from the repulsion of up-welling and down-welling vortices ensures that vortices diffuse only little, resulting in a sub-diffusive (decelerated) motion $\unicode[STIX]{x1D6FE} in $O(10^{1}~\text{s})$. With this weak centrifugal contribution, the translational motion of the columns slowly accelerates in the radial direction and thereby yields a super-diffusive (accelerated) motion $\unicode[STIX]{x1D6FE}>1$ in $O(10^{2}~\text{s})$.

The bifurcations of penetrative Rayleigh-Benard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4°C, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θm. The relationship between the normalized critical Rayleigh number (Rac(θm)/Rac(0)) and θm is formulated, which is in good agreement with the stability results within a large range of θm. The aspect ratio has a minor effect on Rac(θm)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.

The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet (J. Fluid Mech., vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing.

In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, $\ell _{c}^{u}$ for the velocity field and $\ell _{c}^{\unicode[STIX]{x1D703}}$ for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length $\ell _{F}$ on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when $\ell _{F}$ is smaller than the minimum values of the cross-over scales given by $\ell _{c,min}^{\unicode[STIX]{x1D703}\ast }=\ell _{c,min}^{\unicode[STIX]{x1D703}}Nu/H=0.8$, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of $\ell _{F}\approx 3\ell _{c,min}^{\unicode[STIX]{x1D703}}$ or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.