In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample as well as a variation in displacements with height (such displacements had been excluded in the original model). Pressure gradients produced by the side wall of the container on average center the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model predicts the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude, and probability distributions of the displacements.
We experimentally test the effects of tilting a turbulent Rayleigh-B{é}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $θ_0$. The probability distribution of $θ_0$ is measured, and used to obtain a tilt-induced potential acting on $θ_0$, which is used in a low-dimensional model of diffusion of $θ_0$ in a potential. The form of the potential is sinusoidal in $θ_0$, and linear in tilt angle for small tilt angles, which is explained by a simple geometric model of the vector direction of the mean buoyancy force acting on the LSC. However, the magnitude of the …
We report Particle Image Velocimetry of the Large Scale Circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-B{é}nard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow to consider a bi-dimensional mean flow. Lots of previous heat flux measurements have shown a Nusselt--Rayleigh regime transition corresponding to an increase of the heat flux in presence of roughness which is highe…
We test the ability of a low-dimensional turbulence model to predict how dynamics of large-scale coherent structures such as convection rolls change in different cell geometries. We performed Rayleigh-Bénard convection experiments in a cubic container, in which there is a single convection roll known as the large-scale circulation (LSC). The model describes the motion of the orientation $θ_0$ of the LSC as diffusion in a potential which is predicted as a function of the shape of the cell from an approximate solutions of the Navier-Stokes equations. The model predicts advected oscillation modes…
Results from direct numerical simulations of vertical natural convection at Rayleigh numbers $1.0\times 10^5$-$1.0\times 10^9$ and Prandtl number $0.709$ support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-B{é}nard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the $-1/2$…
Turbulent Rayleigh-Bénard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and momentum transport, represented by the Nusselt number and Reynolds number, is generally weaker for larger number $n$ of the LSC rolls. This is supported by direct numerical simulations for $Ra=5\times10^5$, $Pr=0.1$, $H=5D$ and $1\leq~n\leq4$.
A possible explanation for the apparent phase stability of the 11.07-year Schwabe cycle of the solar dynamo was the subject of a series of recent papers. The synchronization of the helicity of an instability with azimuthal wavenumber m=1 by a tidal m=2 perturbation played a key role here. To analyze this type of interaction in a paradigmatic set-up, we study a thermally driven Rayleigh-Bénard Convection (RBC) of a liquid metal under the influence of a tide-like electromagnetic forcing. As shown previously, the time-modulation of this forcing emerges as a peak frequency in the m=2 mode of the r…
We present a direct numerical simulation on the dynamics of large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection of air (Pr = 0.7) contained in a cubic cell for Rayleigh number range 2X10^6 < Ra < 10^9 . The strength and orientation of LSC are quantified by the amplitude and phase of the first Fourier mode of the vertical velocity. The plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. However, an abnormal single-roll state with substructures is noted at the face planes for low Ra. In addition to t…
We consider axisymmetric Boussinesq convection in a shallow cylinder radius, L, and depth, H (<< L), which rotates with angular velocity $Ω$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $Ω$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at …
We present a direct numerical simulation to investigate the dynamics and statistics of reorientations of large-scale circulation (LSC) in turbulent rotating Rayleigh-Bénard convection (RRBC) for air ($Pr=0.7$) contained in a cylindrical cell with unit aspect ratio. A wide range of rotation rates ($0\leq Ro^{-1}\leq 30$) is considered for two different Rayleigh numbers $Ra=2\times10^6$ and $2\times10^7$. Using the Fourier mode analysis of time series data obtained from the different probes placed in the azimuthal direction of the container at the mid-plane, the orientation and associated dynami…
In this paper, we present results from an experimental study into turbulent Rayleigh-Benard convection forced externally by periodically modulated unidirectional rotation rates. We find that the azimuthal rotation velocity $\dotθ$(t) and thermal amplitude $δ$(t) of the large-scale circulation (LSC) are modulated by the forcing, exhibiting a variety of dynamics including increasing phase delays and a resonant peak in the amplitude of $\dotθ$(t). We also focus on the influence of modulated rotation rates on the frequency of occurrence $η$ of stochastic cessation/reorientation events, and on the …
It is shown that helicity dynamics dominates spectral distribution of the velocity fluctuations in turbulent thermal convection at moderate and large values of the Rayleigh number (distributed chaos and scaling respectively). The large-scale circulation (wind) in the turbulent Rayleigh-Bénard convection is especially sensitive to the helicity dynamics and its chaotic reversals can be associated with the reversals of the mean helicity sign (the ergodic restoration of the reflectional symmetry in a long run). Results of the laboratory experiments and measurements in the free atmospheric convecti…
Rayleigh-Benard convection is not only a classical problem in fluid dynamics but plays also an important role in many metallurgical and crystal growth applications. The measurement of the flow field and of the dynamics of the emerging large-scale circulation in liquid metals is a challenging task due to the opaqueness and the high temperature of the melts. Contactless inductive flow tomography is a technique to visualize the mean three-dimensional flow structure in liquid metals by measuring the flow induced magnetic field perturbations under the influence of one or several applied magnetic fi…
Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study
University of Virginia（弗吉尼亚大学）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Indiana University（印第安纳大学）；Texas A&M University（德克萨斯农工大学）；Weizmann Institute of Science（魏茨曼科学研究所）
In Rayleigh-Bénard convection, it has been found that the amount of heat passing through the fluid has a power law dependence on the imposed temperature difference. Modifying this dependence, either enhancing or reducing the heat transfer capability of fluids, is important in many scientific and practical applications. Here, we present a simple means to control the vertical heat transfer in Rayleigh-Bénard convection by injecting heat through one lateral side of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates the large-scale c…
We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-B{é}nard convection. Temperature measurements are broken down into Fourier moments as a function of $θ-θ_0$, where $θ$ is the azimuthal angle in a horizontal plane at mid-height, and $θ_0$ is the LSC orientation. The oscillation structure is dominated by a 3rd order sine moment and 3rd order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a model…
For rapidly rotating turbulent Rayleigh--Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the…
The effects of a vertical static magnetic field on the flow structure and global transport properties of momentum and heat in liquid metal Rayleigh-Bénard convection are investigated. Experiments are conducted in a cylindrical convection cell of unity aspect ratio, filled with the alloy GaInSn at a low Prandtl number of $\mathit{Pr}=0.029$. Changes of the large-scale velocity structure with increasing magnetic field strength are probed systematically using multiple ultrasound Doppler velocimetry sensors and thermocouples for a parameter range that is spanned by Rayleigh numbers of $10^6 \le \m…
High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Ra…
We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh-Bénard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} \le Ra \le 10^{8}$ and Prandtl number ($Pr$) range $2.0 \le Pr \le 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the to…
We present measurements of the orientation $θ_0$ and temperature amplitude $δ$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio $Γ\equiv D/L = 1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr \simeq 0.8$. Results for $θ_0$ revealed a preferred orientation with upflow in the West, consistent with a broken azimuthal invariance due to Earth's Coriolis force [see \cite{BA06b}]. They yielded the azimuthal diffusivity $D_θ$ and a corresponding Reynolds number $Re_θ$ for Rayleigh numbers o…
Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction…
We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number $Ra=10^6$. The numerical studies are conducted for single flow trajectories up to $10^5$ convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number $Pr$ of the flui…
We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh-Bénard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range Ra $ \in [{10^6},{10^8}]$ and radius ratio range $η= {R_i}/{R_o} \in [0.3,0.9]$. This study focuses on the dependence of flow properties on the radius ratio $η$. The temperature and velocity fields reveal that different curvatures of the inner and outer cylinders of the ACRBC system lead to asymmetric movements of hot and cold plumes …
Two types of spontaneous breaking of the space translational symmetry in distributed chaos have been considered for turbulent thermal convection at large values of Rayleigh number. First type is related to boundaries and second type is related to appearance of inertial range of scales. The first type is dominated by vorticity correlation integral: $\int_{V} \langle {\boldsymbol ω} ({\bf x},t) \cdot {\boldsymbol ω} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by stretched exponential spectrum $\exp-(k/k_β)^{β}$ with $β=1/2$. The second type is dominated by energy correlation…
Turbulent convection systems are known to give rise to prominent large scale circulation. At the same time, the `background' (or `small-scale') turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh-Bénard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($Γ=32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of smal…
We investigate the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in a large box of aspect ratio $Γ=32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($Γ\appr…
Local boundary layer scales in turbulent Rayleigh-Benard convection
本文计算了三维湍流Rayleigh-Benard对流中的局部边界层尺度。这些尺度与等温顶壁和底壁处的动量通量和热量通量的高度间歇性波动直接相关，并且在统计上分布在相应的平均厚度尺度周围。局部边界层尺度也反映了两个边界层的强烈空间不均匀性，这是由于在封闭的对流单体中建立的大尺度但复杂且间歇的环流造成的。类似于湍流边界层，我们定义的内部尺度的基础上，局部剪切应力，可以一直扩展到经典的粘性尺度在散装湍流，例如Kolmogorov规模，和外部尺度的基础上，在墙上的斜坡。我们讨论的后果，我们的推广，特别是缩放我们的内部和外部边界层厚度和由此产生的剪切雷诺数相对于瑞利数。温度场的平均外厚度尺度接近热边界层厚度的标准定义。在速度场的情况下，在某些条件下，外尺度遵循类似的比例作为普朗特-布拉修斯型定义相对于瑞利数，但不同的定量。摩擦系数c_（max）标度正好落在层流和湍流极限之间，表明边界层具有转捩特性。此外，我们进行了分析，最近建议的耗散层厚度尺度与瑞利数，并找到一个过渡的缩放。我们还进行了一项研究，在Ra= 1 e +8的情况下，纵横比等于3。
Horizontal Convection (HC) at large Rayleigh and Prandtl numbers, is studied experimentally in a regime up to seven orders of magnitude larger in terms of Rayleigh numbers than previously achieved. To reach Rayleigh up to $10^{17}$, the horizontal density gradient is generated using differential solutal convection by a differential input of salt and fresh water controlled by diffusion in a novel experiment where the zero-net mass flux of water is ensured through permeable membranes. This setup allows for measuring accurately the Nusselt number in solutal convection by carefully controlling the…
Inspired by the hemispherical asymmetry observed in the Earth's inner core, we perform direct numerical simulations to study the effect of the gravity center offset in spherical Rayleigh-Bénard convection. We find that even a minimal shift of the gravity center has a pronounced influence on the flow structures. When the gravity center is shifted towards the South, the co-latitudinal buoyancy component creates an energetic jet on the Northern side of the inner sphere that is directed towards the outer sphere. As a result, a large-scale meridional circulation is formed. However, surprisingly, th…
The heat transfer and flow structure in rotating Rayleigh-Bénard convection are strongly influenced by the Rayleigh ($Ra$), Prandtl ($Pr$), and Rossby ($Ro$) number. For $Pr\gtrsim 1$ and intermediate rotation rates, the heat transfer is increased compared to the non-rotating case. We find that the regime of increased heat transfer is subdivided into a low and a high $Ra$ number regime. For $Ra\lesssim 5\times10^8$ the heat transfer at a given $Ra$ and $Pr$ is highest at an optimal rotation rate, at which the thickness of the viscous and thermal boundary layer is about equal. From the scaling …
The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough, the dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region away from the side walls. The latter is dominated by the shear of the large-scale circulation (LSC) roll which fills the whole cell and continuously varies i…
