Flow reversals in thermally driven turbulence

Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation

We perform a bifurcation analysis of the steady states of Rayleigh-Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialization strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this nonlinear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the disconnected branches we find contains an S-shaped curve with hysteresis, which is the origin of a flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyze the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.

Crisis-induced flow reversals in magnetoconvection

We report the occurrence of flow reversals induced by the attractor-merging crisis in Rayleigh-Bénard convection of electrically conducting low-Prandtl-number fluids in the presence of a uniform external horizontal magnetic field. The simultaneous collision of two coexisting chaotic attractors with an unstable fixed point and its associated stable manifold takes place in the higher-dimensional phase space of the system, leading to a single merged chaotic attractor. The effect of strength of the magnetic field on the flow reversal phenomena is also explored in detail.

Rare Event-Triggered Transitions in Aerodynamic Bifurcation

The transitions between two states of a bistable system are investigated experimentally and analyzed in the framework of rare-event statistics. Considering a disk pendulum swept by a flow in a wind tunnel, bistability between two aerodynamic branches is observed, with spontaneous transitions from one branch to the other. The waiting times before spontaneous transition are distributed following a double exponential as a function of the control parameter, spanning 4 orders of magnitude in time, for both transitions. Inspired by a model originally applied to the transition to turbulence, we show that, for the disk pendulum, both transitions are controlled by rare events of the aerodynamic forces acting on the disk which we propose to link in particular to the vortex shedding-induced fluctuations. Beyond the aerodynamic aspects, this work has interesting fundamental outcomes regarding the broad field of rare events in out-of-equilibrium systems.

Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system

Inspired by the experimental and numerical findings, we study the dynamic instabilities of two coupled nonlinear delay differential equations that are used to describe the coherent oscillations between the top and bottom boundary layers in turbulent Rayleigh-Bénard convection. By introducing two sensitivity parameters for the instabilities of the top and bottom boundary layers, we find three different types of solutions, namely in-phase single-period oscillations, multi-period oscillations and chaos. The chaos solution contains rare but large amplitude fluctuations. The statistical properties of these fluctuations are consistent with those observed in the experiment for the massive eruption of thermal plumes, which causes random reversals of the large-scale circulation in turbulent Rayleigh-Bénard convection. Our study thus provides new insights into the origin of rare massive eruptions and sudden changes of large-scale flow pattern that are often observed in convection systems of geophysical and astrophysical scales.

Elliptical Instability and Multiple-Roll Flow Modes of the Large-Scale Circulation in Confined Turbulent Rayleigh-Bénard Convection

The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh-Bénard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each other. The present study reveals the following two important facts: (i) the mechanism which causes the twisting and breaking of a single-roll LSC into multiple rolls is the elliptical instability and (ii) the heat and momentum transport in RBC, represented by the Nusselt (Nu) and Reynolds (Re) numbers, is always stronger (weaker) for smaller (larger) number n of the rolls in the LSC structure. Direct numerical simulations support the findings for n=1,…,4 and the diameter-to-height aspect ratio of the cylindrical container Γ=1/5, the Prandtl number Pr=0.1 and Rayleigh number Ra=5×10^{5}. Thus, Nu and Re are, respectively, 2.5 and 1.5 times larger for a single-roll LSC (n=1) than for a LSC with n=4 rolls.

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.

Robustness of heat transfer in confined inclined convection at high Prandtl number

We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, Pr≃480, and at Rayleigh numbers Ra≃10^{8} and Ra≃5×10^{8} in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle (β) of the convection cell, the character of the flow can be changed from moderately turbulent, for β=0^{∘}, to laminar and steady at β=90^{∘}. The global heat transfer is found to be insensitive to the drastic reduction of turbulent intensity, with maximal relative variations of the order of 20% at Ra≃10^{8} and 10% at Ra≃5×10^{8}, while the Reynolds number, based on the global root-mean-square velocity, is strongly affected with a decay of more than 85% occurring in the laminar regime. We show that the intensity of the heat flux in the turbulent regime can be only weakly enhanced by establishing a large-scale circulation flow by means of small inclinations. However, in the laminar regime the heat is transported solely by a slow large-scale circulation flow which exhibits large correlations between the velocity and temperature fields. For inclination angles close to the transition regime in-between the turbulentlike and laminar state, a quasiperiodic heat-flow bursting phenomenon is observed.

Mechanism of large-scale flow reversals in turbulent thermal convection

It is commonly believed that heat flux passing through a closed thermal convection system is balanced so that the convection system can remain at a steady state. Here, we report a new kind of convective instability for turbulent thermal convection, in which the convective flow stays over a long steady "quiet period" having a minute amount of heat accumulation in the convection cell, followed by a short and intermittent "active period" with a massive eruption of thermal plumes to release the accumulated heat. The rare massive eruption of thermal plumes disrupts the existing large-scale circulation across the cell and resets its rotational direction. A careful analysis reveals that the distribution of the plume eruption amplitude follows the generalized extreme value statistics with an upper bound, which changes with the fluid properties of the convecting medium. The experimental findings have important implications to many closed convection systems of geophysical scale, in which massive eruptions and sudden changes in large-scale flow pattern are often observed.

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.

Controlling Heat Transport and Flow Structures in Thermal Turbulence Using Ratchet Surfaces

In this combined experimental and numerical study on thermally driven turbulence in a rectangular cell, the global heat transport and the coherent flow structures are controlled with an asymmetric ratchetlike roughness on the top and bottom plates. We show that, by means of symmetry breaking due to the presence of the ratchet structures on the conducting plates, the orientation of the large scale circulation roll (LSCR) can be locked to a preferred direction even when the cell is perfectly leveled out. By introducing a small tilt to the system, we show that the LSCR orientation can be tuned and controlled. The two different orientations of LSCR give two quite different heat transport efficiencies, indicating that heat transport is sensitive to the LSCR direction over the asymmetric roughness structure. Through a quantitative analysis of the dynamics of thermal plume emissions and the orientation of the LSCR over the asymmetric structure, we provide a physical explanation for these findings. The current work has important implications for passive and active flow control in engineering, biofluid dynamics, and geophysical flows.

Intermittent direction reversals of moving spatially localized turbulence observed in two-dimensional Kolmogorov flow

We have found that in two-dimensional Kolmogorov flow a spatially localized turbulent state (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of the control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmetry of the internal turbulence we introduce two coarse-grained variables characterizing the internal dynamics. These quantities follow the switching process reasonably. This suggests that the twin attracting invariant sets each of which corresponds to a one-way traveling SLT are embedded in the attractor of the moving SLT and the connection of the two sets is too complicated to be represented by a few degrees of freedom but the motion of an SLT is correlated with the internal turbulent dynamics.

Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh-Bénard convection

We investigate fluctuations of the velocity and temperature fields in two-dimensional (2D) Rayleigh-Bénard (RB) convection by means of direct numerical simulations (DNS) over the Rayleigh number range 10^{6}≤Ra≤10^{10} and for a fixed Prandtl number Pr=5.3 and aspect ratio Γ=1. Our results show that there exists a counter-gradient turbulent transport of energy from fluctuations to the mean flow both locally and globally, implying that the Reynolds stress is one of the driving mechanisms of the large-scale circulation in 2D turbulent RB convection besides the buoyancy of thermal plumes. We also find that the viscous boundary layer (BL) thicknesses near the horizontal conducting plates and near the vertical sidewalls, δ_{u} and δ_{v}, are almost the same for a given Ra, and they scale with the Rayleigh and Reynolds numbers as ∼Ra^{-0.26±0.03} and ∼Re^{-0.43±0.04}. Furthermore, the thermal BL thickness δ_{θ} defined based on the root-mean-square (rms) temperature profiles is found to agree with Prandtl-Blasius predictions from the scaling point of view. In addition, the probability density functions of turbulent energy ɛ_{u^{'}} and thermal ɛ_{θ^{'}} dissipation rates, calculated, respectively, within the viscous and thermal BLs, are found to be always non-log-normal and obey approximately a Bramwell-Holdsworth-Pinton distribution first introduced to characterize rare fluctuations in a confined turbulent flow and critical phenomena.

Experimental velocity study of non-Boussinesq Rayleigh-Bénard convection

The effects of strongly varying fluid properties, beyond the validity range of the so-called Boussinesq approximation, were experimentally studied in Rayleigh-Bénard (RB) convection. Two experiments were conducted in the same cubical RB convection cell at similar Rayleigh and Prandtl numbers. In one experiment water was used as working fluid and the imposed temperature difference between the top and bottom plates of the cell was such to ensure non-Boussinesq conditions. In the other experiment, taken as a reference for Boussinesq conditions, methanol was used as working fluid, allowing a smaller temperature difference between the plates. In both experiments the instantaneous and time-averaged flow fields were determined experimentally in a vertical cross section of the cell by using particle image velocimetry. Results show a non-Boussinesq effect that manifests itself as an increase of the time-averaged horizontal velocity component close to the bottom wall of the cell and as a global top-bottom asymmetry of the velocity field. This is an experimental study of the whole velocity field of RB convection at non-Boussinesq conditions.

Surface switching statistics of rotating fluid: Disk-rim gap effects

We examined the influence of internal noise on the irregular switching of the shape of the free surface of fluids in an open cylindrical vessel driven by a bottom disk rotating at constant speed [Suzuki, Iima, and Hayase, Phys. Fluids 18, 101701 (2006)PHFLE61070-663110.1063/1.2359740]. A slight increase in the disk-rim gap (less than 3% of the disk radius) was established experimentally to cause significant changes in this system, specifically, frequent appearance of the surface descending event connecting a nonaxisymmetric shape in strong mixing flow (turbulent flow) and an axisymmetric shape in laminar flow, as well as a shift in critical Reynolds number that define the characteristic states. The physical mechanism underlying the change is analyzed in terms of flow characteristics in the disk-rim gap, which acts as a noise source, and a mathematical model established from measurements of the surface height fluctuations with noise term.

Reorientations of the large-scale flow in turbulent convection in a cube

Large-eddy simulations of turbulent Rayleigh-Bénard convection were conducted for a fluid of Prandtl number Pr=0.7 confined in a cube, for Rayleigh numbers of 10^{6} and 10^{8}. The model solves the unsteady Navier-Stokes equations under the Boussinesq approximation, using a dynamic Smagorinsky model with a Lagrangian averaging technique for the subgrid terms. Under fully developed conditions the flow topology is characterized by a large-scale circulation (LSC) developing in a plane containing one of the diagonals of the cell, while two counter-rotating vortices consequently develop in the other diagonal plane, resulting in a strong inflow at the horizontal midplane. This flow structure is not static, with the LSC undergoing nonperiodic reorientations, or switching, between the two diagonal planes; hence, we supplement the observations of the three-dimensional time-averaged flow structures with single point measurements (time series) to shed light on the dynamics of the reorientations. For all observations, this switching results from a lateral rotation of the LSC in which some finite time spent in a transient state where the large-scale circulation is parallel to one set of side walls; there are, importantly, no observations consistent with so-called cessations of the LSC, in which it decays and then reforms in another plane without such a rotation. The average switching rate for the LSC is in excellent agreement with the results of Bai et al. [K. Bai, D. Ji, and E. Brown, Phys. Rev. E 93, 023117 (2016)PLEEE81539-375510.1103/PhysRevE.93.023117].

Precursor for wind reversal in a square Rayleigh-Bénard cell

We investigate large-scale circulation reversals in a two-dimensional Rayleigh-Bénard cell using a proper orthogonal decomposition (POD)-based, five-mode model. The Rayleigh number considered is Ra=5×10^{7} and the Prandtl number is Pr=4.3. A precursor event, corresponding to the action of a mode L_{*} which disconnects the core region from the boundary layers before the onset of the reversal, is identified in the simulation. The five-mode model predicts correctly the behavior of the POD modes observed in the simulation, and in particular that of mode L_{*}. The presence of mode L_{*}, which was not included in an earlier, lower-dimensional version of the model [Podvin and Sergent, J. Fluid Mech. 766, 172 (2015)JFLSA70022-112010.1017/jfm.2015.15], is found to be instrumental for the reversal dynamics of the model, which suggests that it may also be important for those of the simulation. Reversals can therefore be characterized by three time scales: the transition duration, the interreversal time, and the precursor duration, which separates the precursor event from the onset of the reversal. The distribution of the time scales is found to agree well with the simulation when small-scale intermittency is taken into account through the introduction of noise in the model coefficients.

Optimized setup for two-dimensional convection experiments in thin liquid films

We present a novel experimental setup to investigate two-dimensional thermal convection in a freestanding thin liquid film. Such films can be produced in a controlled way on the scale of 5-1000 nm. Our primary goal is to investigate convection patterns and the statistics of reversals in Rayleigh-Bénard convection with varying aspect ratio. Additionally, questions regarding the physics of liquid films under controlled conditions can be investigated, like surface forces, or stability under varying thermodynamical parameters. The film is suspended in a frame which can be adjusted in height and width to span an aspect ratio range of Γ = 0.16-10. The top and bottom frame elements can be set to specific temperature within T = 15 °C to 55 °C. A thickness to area ratio of approximately 10(8) enables only two-dimensional fluid motion in the time scales relevant for turbulent motion. The chemical composition of the film is well-defined and optimized for film stability and reproducibility and in combination with carefully controlled ambient parameters allows the comparison to existing experimental and numerical data.

Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field

Magnetohydrodynamic Rayleigh-Bénard convection was studied experimentally using a liquid metal inside a box with a square horizontal cross section and aspect ratio of five. Systematic flow measurements were performed by means of ultrasonic velocity profiling that can capture time variations of instantaneous velocity profiles. Applying a horizontal magnetic field organizes the convective motion into a flow pattern of quasi-two-dimensional rolls arranged parallel to the magnetic field. The number of rolls has the tendency to decrease with increasing Rayleigh number Ra and to increase with increasing Chandrasekhar number Q. We explored convection regimes in a parameter range, at 2×10^{3}<Q<10^{4} and 5×10^{3}<Ra<3×10^{5}, thus extending the regime diagram provided by Yanagisawa et al. [T. Yanagisawa et al., Phys. Rev. E 88, 063020 (2013)PLEEE81539-375510.1103/PhysRevE.88.063020]. Three regimes were identified, of which the regime of regular flow reversals in which five rolls periodically change the direction of their circulation with gradual skew of the roll axes can be considered as the most remarkable one. The regime appears around a range of Ra/Q=10, where irregular flow reversals were observed in Yanagisawa et al. We performed the proper orthogonal decomposition (POD) analysis on the spatiotemporal velocity distribution and detected that the regular flow reversals can be interpreted as a periodic emergence of a four-roll state in a dominant five-roll state. The POD analysis also provides the definition of the effective number of rolls as a more objective approach.

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.

Flow reversals in low-Prandtl-number Rayleigh-Bénard convection controlled by horizontal circulations

We performed numerical simulations of Rayleigh-Bénard convection of an electrically conductive low-Prandtl-number fluid under a uniform horizontal magnetic field. We reproduced the flow reversals observed in laboratory experiments previously reported by us. The flow pattern is moderately constrained, as the axes of convection rolls tend to align in the direction of the horizontal magnetic field. The flow reversals occur when the intensity of horizontal circulation in a vessel exceeds a certain value, which induces bending and reconnection of convection rolls and causes rearrangement of these rolls. The wave number selection mechanism is responsible for the instability leading to the flow reversals. The total heat flow drastically decreases at the occurrences of reversal, reflecting the reduction of roll flow velocity. The irregularity of the reversal sequence and the change in symmetry in the flow pattern during the reversals are consistent with that in cessation-led flow reversals.

Dynamics of reversals and condensates in two-dimensional Kolmogorov flows

We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate 1/Rh. The linear response to the forcing is a 6×6 square array of counterrotating vortices, which is stable when the Reynolds number Re or Rh are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when Re and Rh are increased, we study the transitions between the different turbulent regimes observed for large Re by varying Rh. A large-scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large-scale drag (Rh large). When Rh is decreased, the condensate becomes unstable and a regime with random reversals between two large-scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large-scale velocity that continuously bifurcates to a Gaussian distribution when Rh is decreased further.

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.

Recurrent bursts via linear processes in turbulent environments

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly periodic and self-sustained burst cycles. Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.

Confinement-induced heat-transport enhancement in turbulent thermal convection

We report an experimental and numerical study of the effect of spatial confinement in turbulent thermal convection. It is found that when the width of the convection cell is narrowed, the heat-transfer efficiency increases significantly despite the fact that the overall flow is slowed down by the increased drag force from the sidewalls. Detailed experimental and numerical studies show that this enhancement is brought about by the changes in the dynamics and morphology of the thermal plumes in the boundary layers and in the large-scale flow structures in the bulk. It is found that the confined geometry produces more coherent and energetic hot and cold plume clusters that go up and down in random locations, resulting in more uniform and thinner thermal boundary layers. The study demonstrates how changes in turbulent bulk flow can influence the boundary layer dynamics and shows that the prevalent mode of heat transfer existing in larger aspect ratio convection cells, in which hot and cold thermal plumes are carried by the large-scale circulation along opposite sides of the sidewall, is not the most efficient way for heat transport.

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.

Effect of weak rotation on large-scale circulation cessations in turbulent convection

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 PDF remain unchanged for rotating systems, while the distribution of the LSC amplitude and correspondingly the cessation frequency are strongly affected by rotation. Our results are in close agreement with experimental observations.

Oscillations, cessations, and circulation reversals of granular convection in a densely filled rotating container

We study spontaneously forming convection in a container that is almost completely filled with a bidisperse granular mixture. The container with an aspect ratio close to 1 rotates slowly about a horizontal axis. In this geometry, single vortex rolls are observed in the cell plane, after a spontaneous symmetry breaking. The circulation of grains produces nonuniform segregation patterns of the mixture that in turn interact with the convective flow. We describe oscillatory modulations of the convection velocity, cessations and spontaneous reversals of the circulation. All these features are absent in multiroll granular convection.

Connecting flow structures and heat flux in turbulent Rayleigh-Bénard convection

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≤Γ≤1.25 for Rayleigh numbers 10(7)≤Ra≤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 Γ different turbulent states (with different resulting Nu) can exist, between which the flow can or cannot switch. In the latter case the heat transfer thus depends on the initial conditions.

Statistical analysis of global wind dynamics in vigorous Rayleigh-Bénard convection

Experimental and numerical studies of thermal convection have shown that sufficiently vigorous convective flows exhibit a large-scale thermal wind component sweeping along small-scale thermal boundary layer instabilities. A characteristic feature of these flows is an intermittent behavior in the form of irregular reversals in the orientation of the large-scale circulation. There have been several attempts toward a better understanding and description of the phenomenon of flow reversals, but so far most of these models are based on a statistical analysis of few-point measurements or on simplified theoretical assumptions. The analysis of long-term data sets (>5×10(5) turnover times τ(t)=d/u(rms)) obtained by numerical simulations of turbulent two-dimensional Rayleigh-Bénard convection allows us to get a more comprehensive view of the spatio-temporal flow behavior. By means of a global statistical analysis of the characteristic spatial modes of the flow we extract information about the stability of dominant large-scale modes as well as the reversal paths in state subspace. We examine probability density functions and drift vector fields of two-dimensional state subspaces spanned by different large-scale spatial modes. This also provides information about the coexistence of dominant modes.

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.

Coherent oscillations of turbulent Rayleigh-Bénard convection in a thin vertical disk

A well-defined oscillation is observed in the power spectrum of several fluctuating signals in turbulent Rayleigh-Bénard convection occurring in a thin vertical disk filled with water. The experiment reveals that the coherent oscillations are produced by periodic emission of thermal plumes, which gives rise to periodic pulses of forcing, resulting in a pulsed large-scale circulation in the thin cell. The experimental results agree well with the theoretical predictions made from two coupled nonlinear delayed equations.

Spontaneous flow reversals in Rayleigh-Bénard convection of a liquid metal

We report a finding of spontaneous flow reversals of roll-like patterns in liquid gallium Rayleigh-Bénard convection. The vessel has a square geometry with an aspect ratio of 5, and a horizontal magnetic field is applied to align the rolls. The flow patterns were visualized by ultrasonic velocity measurements, and the processes of the reversal were clearly observed. The basic flow pattern observed in the vessel is a four-roll structure with its axis parallel to the magnetic field. Emergence of a new circulation at a corner of the vessel causes flow reversal with reorganization of the whole pattern. The flow keeps relatively steady four-roll structure for most of the duration, while the reversal of it is over in a short time. The reversals of the flow occur randomly with the interval time between reversals being much longer than the circulation time.