Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection

Molecular hints of two-step transition to convective flow via streamline percolation

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However, its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.

Centrifugal-Force-Induced Flow Bifurcations in Turbulent Thermal Convection

An important and unresolved issue in rotating thermal turbulence is when the flow starts to feel the centrifugal effect. This onset problem is studied here by a novel experiment in which the centrifugal force can be varied over a wide range at fixed Rossby numbers by offsetting the apparatus from the rotation axis. Our experiment clearly shows that the centrifugal force starts to separate the hot and cold fluids at the onset Froude number 0.04. Additionally, this flow bifurcation leads to an unexpected heat transport enhancement and the existence of an optimal state. Based on the dynamical balance and characteristics of local flow structures, both the onset and optimal states are quantitatively explained.

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

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 Ekman number Ek decreases with increasing rotation rate.

On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis

Turbulent Rayleigh-Bénard convection in a 2D square cell is characterized by the existence of a large-scale circulation which varies intermittently. We focus on a range of Rayleigh numbers where the large-scale circulation experiences rapid non-trivial reversals from one quasi-steady (or meta-stable) state to another. In previous work [B. Podvin and A. Sergent, J. Fluid Mech. 766, 172201 (2015); B. Podvin and A. Sergent, Phys. Rev. E 95, 013112 (2017)], we applied proper orthogonal decomposition (POD) to the joint temperature and velocity fields at a given Rayleigh number, and the dynamics of the flow were characterized in a multi-dimensional POD space. Here, we show that several of those findings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of the embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specifically, the embedding theory confirms that the switches among meta-stable states are uncorrelated. It also shows that, despite the large number of degrees of freedom of the turbulent Rayleigh Bénard flow, a low dimensional description of its physics can be derived with low computational efforts, providing that a single global observable reflecting the symmetry of the system is identified. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established.

Jump rope vortex in liquid metal convection

Understanding large-scale circulations (LSCs) in turbulent convective systems is important for the study of stars, planets, and in many industrial applications. The canonical model of the LSC is quasi-planar with additional horizontal sloshing and torsional modes [Brown E, Ahlers G (2009) J Fluid Mech 638:383-400; Funfschilling D, Ahlers G (2004) Phys Rev Lett 92:194502; Xi HD et al. (2009) Phys Rev Lett 102:044503; Zhou Q et al. (2009) J Fluid Mech 630:367-390]. Using liquid gallium as the working fluid, we show, via coupled laboratory-numerical experiments in tanks with aspect ratios greater than unity ([Formula: see text]), that the LSC takes instead the form of a "jump rope vortex," a strongly 3D mode that periodically orbits around the tank following a motion much like a jump rope on a playground. Further experiments show that this jump rope flow also exists in more viscous fluids such as water, albeit with a far smaller signal. Thus, this jump rope mode is an essential component of the turbulent convection that underlies our observations of natural systems.

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long timescales, while the interval between successive crossings on short timescales shows a power-law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and 1/f^{2} power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.

Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence

We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.

Applicability of Taylor's hypothesis in thermally driven turbulence

In this paper, we show that, in the presence of large-scale circulation (LSC), Taylor's hypothesis can be invoked to deduce the energy spectrum in thermal convection using real-space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov's spectrum (k^-5/3). We also record the velocity time series using real-space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov's spectrum (f^-5/3), thus validating Taylor's hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real-space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence.

Ability of a low-dimensional model to predict geometry-dependent dynamics of large-scale coherent structures in turbulence

We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations, which are derived as a function of boundary geometry from the Navier-Stokes equations [Brown and Ahlers, Phys. Fluids 20, 075101 (2008); Phys. Fluids 20, 105105 (2008)]. We test the model using Rayleigh-Bénard convection experiments in a cubic container. The model predicts a mode in which the alignment of a convection roll stochastically crosses a potential barrier to switch between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.

Heat transfer enhancement induced by wall inclination in turbulent thermal convection

We present a series of numerical simulations of turbulent thermal convection of air in an intermediate range or Rayleigh numbers (10(6)≤Ra≤10(9)) with different configurations of a thermally active lower surface. The geometry of the lower surface is designed in such a way that it represents a simplified version of a mountain slope with different inclinations (i.e., "Λ"- and "V"-shaped geometry). We find that different wall inclinations significantly affect the local heat transfer by imposing local clustering of instantaneous thermal plumes along the inclination peaks. The present results reveal that significant enhancement of the integral heat transfer can be obtained (up to 32%) when compared to a standard Rayleigh-Bénard configuration with flat horizontal walls. This is achieved through combined effects of the enlargement of the heated surface and reorganization of the large-scale flow structures.

Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection

We report the first experimental study of the influences of the thermal boundary condition on turbulent thermal convection. Two configurations were examined: one had a constant heat flux at the bottom boundary and a constant temperature at the top (CFCT cell); the other had constant temperatures at both boundaries (CTCT cell). In addition to producing different temperature stability in the boundary layers, the differences in the boundary condition lead to rather unexpected changes in the flow dynamics. It is found that, surprisingly, reversals of the large-scale circulation occur more frequently in the CTCT cell than in the CFCT cell, despite the fact that in the former its flow strength is on average 9% larger than that in the latter. Our results not only show which aspects of the thermal boundary condition are important in thermal turbulence, but also reveal that, counterintuitively, the stability of the flow is not directly coupled to its strength.

Long-range ordering of turbulent stresses in two-dimensional flow

Using filter-space techniques, we study the spatial structure of the turbulent stress that couples motion on different length scales in a quasi-two-dimensional laboratory flow. As the length scale increases, we observe the appearance of long-range, system-spanning spatial order of this stress, even though the flow field remains disordered. Suggestively, this ordering occurs only in the range of scales over which we find net inverse energy transfer to larger scales. However, we find that a field built from wave vectors with random phases also displays ordering, suggesting that at least some of the ordering we observe is purely kinematic. Our results help to clarify the role played by geometric alignment in the turbulent energy cascade and highlight the importance of the scale-dependent rate of strain in the energy-transfer process.

Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

Flow reversals in turbulent convection via vortex reconnections

We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via a vortex reconnection of two attracting corner rolls having the same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to the 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 Prandtl numbers.

Breakdown of the large-scale circulation in Γ=1/2 rotating Rayleigh-Bénard flow

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically aligned vortices at strong rotation. For a sample with an aspect ratio Γ=D/L=1 (D is the sample diameter and L is its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for Γ=1/2, Weiss and Ahlers [J. Fluid Mech. 688, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for Γ=1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and nontrivial difference with the Γ=1 sample, where the vertically aligned vortices are distributed randomly.

Spatial distribution of heat flux and fluctuations in turbulent Rayleigh-Bénard convection

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux j ¯(r) in a cylindrical Rayleigh-Bénard cell with aspect ratio Γ=1 for Rayleigh numbers Ra between 2×10^{6} and 2×10^{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, j ¯(r)∝Ra{γ{j}(r)}. The scaling exponent γ{j}(r) decreases monotonically from 0.43 near the axis (r≈0) to 0.29 close to the sidewalls (r≈D/2). The effective exponents near the axis and the sidewall agree well with the measurements of Shang et al. [Phys. Rev. Lett. 100, 244503 (2008)] and the predictions of Grossmann and Lohse [Phys. Fluids 16, 1070 (2004)]. Extrapolating our results to large Rayleigh number would imply a crossover at Ra≈10^{15}, where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down than in plume depleted regions.

Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection

We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio Γ≡D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×10(12)≲Ra≲10(15) for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×10(12), 2×10(11), and 2×10(10), all for Pr=0.7.

Chaotic gas turbine subject to augmented Lorenz equations

Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.

Dynamics and symmetries of flow reversals in turbulent convection

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the "cessation-led" reversals observed earlier in experiments and numerical simulations. We find anomalous fluctuations in the Nusselt number during the reversals. Using the structures of the RBC equations in the Fourier space, we deduce two symmetry transformations that leave the equations invariant. These symmetry transformations help us in identifying the reversing and nonreversing Fourier modes.

Transition phenomena in unstably stratified turbulent flows

We study experimentally and theoretically the transition phenomena caused by external forcing from Rayleigh-Bénard convection with large-scale circulation (LSC) to the limiting regime of unstably stratified turbulent flow without LSC, where the temperature field behaves like a passive scalar. In the experiments we use the Rayleigh-Bénard apparatus with an additional source of turbulence produced by two oscillating grids located near the sidewalls of the chamber. When the frequency of the grid oscillations is larger than 2 Hz, the LSC in turbulent convection is destroyed, and the destruction of the LSC is accompanied by a strong change of the mean temperature distribution. However, in all regimes of the unstably stratified turbulent flow the ratio [(ℓ{x}∇{x}T)²+(ℓ{y}∇{y}T)² + (ℓ{z}∇{z}T)²]/<θ²> varies slightly (even in the range of parameters where the behavior of the temperature field is different from that of the passive scalar). Here ℓ{i} are the integral scales of turbulence along the x,y,z directions, and T and θ are the mean and fluctuating parts of the fluid temperature. At all frequencies of the grid oscillations we have detected long-term nonlinear oscillations of the mean temperature. The theoretical predictions based on the budget equations for turbulent kinetic energy, turbulent temperature fluctuations, and turbulent heat flux, are in agreement with the experimental results.

Streaks to rings to vortex grids: generic patterns in transient convective spin up of an evaporating fluid

We observe the transient formation of a ringed pattern state during spin up of an evaporating fluid on a time scale of order a few Ekman spin up times. The ringed state is probed using infrared thermometry and particle image velocimetry and it is demonstrated to be a consequence of the transient balance between Coriolis and viscous forces which dominate inertia, each of which are extracted from the measured velocity field. The breakdown of the ringed state is quantified in terms of the antiphasing of these force components which drives a Kelvin-Helmholtz instability and we show that the resulting vortex grid spacing scales with the ring wavelength. This is the fundamental route to quasi-two-dimensional turbulent vortex flow and thus may have implications in astrophysics and geophysics wherein rotating convection is ubiquitous.

Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence

The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process.

Effect of large-scale coherent structures on turbulent convection

We study an effect of large-scale coherent structures on global properties of turbulent convection in laboratory experiments in air flow in a rectangular chamber with aspect ratios A approximately 2 and A approximately 4 (with the Rayleigh numbers varying in the range from 5x10;{6} to 10;{8} ). The large-scale coherent structures comprise the one-cell and two-cell flow patterns. We found that a main contribution to the turbulence kinetic-energy production in turbulent convection with large-scale coherent structures is due to the nonuniform large-scale motions. Turbulence in large Rayleigh number convection with coherent structures is produced by shear rather than by buoyancy. We determined the scalings of global parameters (e.g., the production and dissipation of turbulent kinetic energy, the turbulent velocity and integral turbulent scale, the large-scale shear, etc.) of turbulent convection versus the temperature difference between the bottom and the top walls of the chamber. These scalings are in an agreement with our theoretical predictions. We demonstrated that the degree of inhomogeneity of the turbulent convection with large-scale coherent structures is small.

Azimuthal motion, reorientation, cessation, and reversal of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio one and one-half geometries

We report a systematic experimental study of the orientation and the flow strength of the large-scale circulation (LSC) in water-filled cylindrical Rayleigh-Bénard convection cells with aspect ratios 2.3, 1, and 0.5 by both direct velocity measurement and the indirect multithermal-probe measurement. Unlike its weak effect in the system's global heat transport, the aspect ratio Gamma is found to play an important role in the dynamics of the azimuthal motion of the LSC. It is found that in larger Gamma geometries the azimuthal motion of the LSC's vertical plane is confined in smaller azimuthal region than that in smaller Gamma geometries. The twisting motion between top and bottom parts of the LSC observed in the Gamma=1 geometry is found to be absent in the Gamma=1/2 case. It is found that in the Gamma=1/2 geometry the orientational change mid R:Deltavarphimid R: through a reorientation has an exponential distribution, in contrast to the power-law distribution for the Gamma=1 case. Despite the difference in orientational change, the occurrence of the reorientations is a Poisson process in both geometries. Using the conditional average of the time interval between adjacent cessations or reversals on the rebound flow strength, we demonstrate the possibility to empirically predict when the next cessation or reversal will most likely occur if the rebound flow strength of the preceding cessation or reversal is given.

Self-induced cyclic reorganization of free bodies through thermal convection

We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of interactions between many free bodies mediated by thermal convection, which gives rise to surprising robust oscillations between different large-scale circulations. Once begun, this process repeats cyclically, with the collection of objects (solid spheres) entrained and packed from one side of the convection cell to the other. The cyclic frequency is highest when the spheres occupy about half of the cell bottom and their size coincides with the thickness of the thermal boundary layer. Our work shows that a deformable mass stimulates a thermally convecting fluid into oscillation, a collective behavior that may be found in nature.

Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection

We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at Ra approximately 10;{10} . Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e., both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time domain, i.e., the Bolgiano time scale t_{B} , above which buoyancy effects are significant. Above t_{B} , temperature is active and is found to be more intermittent than concentration, which is passive. This suggests that the active scalar possesses a higher level of intermittency in turbulent thermal convection. It is further found that the mixing of both scalar fields are isotropic for scales larger than t_{B} even though buoyancy acts on the fluid in the vertical direction. Below t_{B} , temperature is passive and is found to be more anisotropic than concentration. But this higher degree of anisotropy is attributed to the higher diffusivity of temperature over that of concentration. From the simultaneous measurements of temperature and concentration, it is shown that two scalars have similar autocorrelation functions and there is a strong and positive correlation between them.

Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point

As shown in earlier work [Ahlers, J. Fluid Mech. 569, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient. If the working fluid is ethane close to the critical point, the origin of non-Oberbeck-Boussinesq corrections is very different, as will be shown in the present paper. Namely, the main origin of NOB corrections then lies in the strong temperature dependence of the isobaric thermal expansion coefficient beta(T). More precisely, it is the nonlinear T dependence of the density rho(T) in the buoyancy force that causes another type of NOB effect. We demonstrate this through a combination of experimental, numerical, and theoretical work, the last in the framework of the extended Prandtl-Blasius boundary-layer theory developed by Ahlers as cited above. The theory comes to its limits if the temperature dependence of the thermal expension coefficient beta(T) is significant. The measurements reported here cover the ranges 2.1<or similar to Pr<or similar to 3.9 and 5x10(9)<or similar to Ra<or similar to 2x10(12) and are for cylindrical samples of aspect ratios 1.0 and 0.5.

Wind and boundary layers in Rayleigh-Bénard convection. I. Analysis and modeling

The aim of this paper is to contribute to the understanding of and to model the processes controlling the amplitude of the wind of Rayleigh-Bénard convection. We analyze results from direct simulation of an L/H=4 aspect-ratio domain with periodic sidewalls at Ra=(10(5), 10(6), 10(7), 10(8)) and at Pr=1 by decomposing independent realizations into wind and fluctuations. It is shown that, deep inside the thermal boundary layer, horizontal heat fluxes exceed the average vertical heat flux by a factor of 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the direct numerical simulation results to parametrize the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude.

Numerical and experimental investigation of structure-function scaling in turbulent Rayleigh-Bénard convection

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

Modeling the dynamics of a free boundary on turbulent thermal convection

Based on our previous experimental study, we present a one-dimensional phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations.

Cessations and reversals of the large-scale circulation in turbulent thermal convection

We present an experimental study of cessations and reversals of the large-scale circulation (LSC) in turbulent thermal convection in a cylindrical cell of aspect ratio (Gamma) 1/2 . It is found that cessations and reversals of the LSC occur in Gamma = 1/2 geometry an order-of-magnitude more frequently than they do in Gamma=1 cells, and that after a cessation the LSC is most likely to restart in the opposite direction, i.e., reversals of the LSC are the most probable cessation events. This contrasts sharply to the finding in Gamma=1 geometry and implies that cessations in the two geometries are governed by different dynamics. It is found that the occurrence of reversals is a Poisson process and that a stronger rebound of the flow strength after a reversal or cessation leads to a longer period of stability of the LSC. Several properties of reversals and cessations in this system are found to be statistically similar to those of geomagnetic reversals. A direct measurement of the velocity field reveals that a cessation corresponds to a momentary decoherence of the LSC.

Large-scale circulation model for turbulent Rayleigh-Bénard convection

A model for the large-scale-circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical samples is presented. It consists of two physically motivated stochastic ordinary differential equations, one each for the strength and the azimuthal orientation of the LSC. Stochastic forces represent phenomenologically the influence of turbulent fluctuations. Consistent with measurements, the model yields an azimuthally meandering LSC with occasional rotations, and with more rare cessations. As in experiment, cessations have a uniform distribution of LSC orientation changes.

Azimuthal motion of the mean wind in turbulent thermal convection

We present an experimental study of the azimuthal motion of the mean wind in turbulent thermal convection. The experiments were conducted with cylindrical convection cells of unity aspect ratio and over the range of the Rayleigh number from 1 x 10(9) to 1 x 10(10). The azimuthal angle of the circulation plane of the mean wind was measured using both the particle image velocimetry and flow-visualization techniques. It is found that the azimuthal motion consists of erratic fluctuations and a time-periodic oscillation. The orientation of the wind is found to be "locked," i.e., it fluctuates about a preferred direction most of the time with all other orientations appearing as "transient states," and large excursions of the azimuthal angle often result in a net rotation which takes the wind back to the preferred orientation. The rate of erratic rotation of the circulation plane is found to have a strong dependence on Ra. Our result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.

Bifurcation analysis of multiple steady flow patterns for Rayleigh-Bénard convection in a cubical cavity at Pr = 130

The bifurcation diagram of steady convective flow patterns inside a cubical cavity with adiabatic lateral walls heated from below and filled with silicone oil (Pr = 130) was determined for values of the Rayleigh number (Ra) up to 1.5 x 10(5). A continuation procedure based on the Galerkin spectral method was used to determine the steady convective solutions as a function of Ra. Bifurcations leading to either new steady or time-dependent solutions were identified and new steady solution branches were also continued. A total of fifteen steady solutions were tracked and the stability analysis predicted that six flow patterns were stable and that two, three, or even four of these patterns coexisted over certain ranges of Ra in the studied domain. Predicted flow patterns and transitions are in agreement with flow visualizations previously reported in the literature. The variation of the Nusselt number (Nu) as a function of Pr was investigated for three of the stable flow patterns identified: a x or y roll, a diagonal oriented roll and a pattern formed by four connected half rolls. It was found that whereas the Nusselt changes within the region 0.71 < or = Pr < or = 10 it tends to an asymptotic value with increasing Pr.

Clustering of polarity reversals of the geomagnetic field

Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of polarity reversals of the geomagnetic field. In spite of the commonly used underlying hypothesis, we show that this process strongly departs from a Poisson statistics, the origin of this failure stemming from the presence of temporal clustering. We find that a Lévy statistics is able to reproduce paleomagnetic data, thus suggesting the presence of long-range correlations in the underlying dynamo process.

Scaling of the Reynolds number in turbulent thermal convection

A riddle in turbulent thermal convection is the apparent dispersion from 0.42 to 0.5 in the value of the scaling exponent of experimentally measured Reynolds number Re approximately Ragamma, where Ra is the Rayleigh number. The measured Re may be divided into two groups: one based on the circulation frequency of the mean wind and the other based on a directly measured velocity. With new experimental results we show that in frequency measurements the dispersion in gamma is a result of the evolution in the circulation path of the wind, and that in the velocity measurements it is caused by the inclusion of a counterflow in the mean velocity. When these factors are properly accounted for both groups give gamma=0.5, which may imply that a single mechanism is driving the flow for both low and high values of Ra.