Large Scale Structures in Rayleigh-Bénard Convection at High Rayleigh Numbers

Hartlep, T.; Tilgner, A.; Busse, Friedrich H.

doi:10.1103/physrevlett.91.064501

Cited by 113 publications

(160 citation statements)

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“…They also pointed out that the physical process responsible for the formation of these scales does not require that density stratification be taken into account (since it is not included in the Boussinesq approximation). The formation of mesoscale structures in large aspect ratio simulations of turbulent Boussinesq convection was subsequently confirmed by several studies (Hartlep et al, 2003;Parodi et al, 2004;von Hardenberg et al, 2008).…”

Section: Local Hydrodynamic Cartesian Simulations: Mesoscale Dynamicsmentioning

confidence: 63%

The Sun’s Supergranulation

Rincon

Rieutord

2010

Living Rev. Solar Phys.

165

132

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The Sun's supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30,000 km and a lifetime of around 1.8 d. Its most noticeable observable signature is as a fluctuating velocity field of 360 m s -1 rms whose components are mostly horizontal. Supergranulation was discovered more than fifty years ago, however explaining why and how it originates still represents one of the main challenges of modern solar physics.A lot of work has been devoted to the subject over the years, but observational constraints, conceptual difficulties and numerical limitations have all concurred to prevent a detailed understanding of the supergranulation phenomenon so far. With the advent of 21st century supercomputing resources and the availability of unprecedented high-resolution observations of the Sun, a stage at which key progress can be made has now been reached. A unifying strategy between observations and modelling is more than ever required for this to be possible.The primary aim of this review is therefore to provide readers with a detailed interdisciplinary description of past and current research on the problem, from the most elaborate observational strategies to recent theoretical and numerical modelling efforts that have all taken up the challenge of uncovering the origins of supergranulation. Throughout the text, we attempt to pick up the most robust findings so far, but we also outline the difficulties, limitations and open questions that the community has been confronted with over the years.In the light of the current understanding of the multiscale dynamics of the quiet photosphere, we finally suggest a tentative picture of supergranulation as a dynamical feature of turbulent magnetohydrodynamic convection in an extended spatial domain, with the aim of stimulating future research and discussions.

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Section: Local Hydrodynamic Cartesian Simulations: Mesoscale Dynamicsmentioning

confidence: 63%

The Sun’s Supergranulation

Rincon

Rieutord

2010

Living Rev. Solar Phys.

165

132

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“…2͑c͒ and 2͑d͔͒. The growth of convective structures has been observed before, 6,14,15 and goes on long after the process is statistically stationary. Although the details of the field are very unsteady as plumes rise and fall, the large-scale pattern is remarkably steady as Figs.…”

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confidence: 88%

Identification of the wind in Rayleigh–Bénard convection

2005

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Using a symmetry-accounting ensemble-averaging method, we have identified the wind in unbounded Rayleigh-Bénard convection. This makes it possible to distinguish the wind from fluctuations and to identify dynamic features of each. We present some results from processing five independent three-dimensional direct numerical simulations of a ⌫ = 4 aspect-ratio domain with periodic side boundaries at Ra=10 7 and Pr= 1. It is found that the wind boundary layer scales linearly very close to the wall and has a logarithmic region further away. Despite the still noticeable molecular effects, the identification of log scaling and significant velocity and temperature fluctuations well within the thermal boundary layer clearly indicate that the boundary layer cannot be classified as laminar. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1920350͔Recent theories for the prediction of the scaling behavior of the nondimensional heat flux Nu and the Reynolds number Re in the Rayleigh-Bénard convection presume the existence of "wind," 1,2 a large scale circulation that autonomously arises in the system. Indeed, this circulation has been observed by various groups and received quite some attention over the last years. [3][4][5][6][7][8][9] The theories use wind primarily as a conceptual notion; little is known about the actual magnitude of the wind as compared to velocity fluctuations and if it is present for all Rayleigh numbers. 9 But most important, a straightforward definition of wind seems to be missing. The natural candidates are the ensemble average, a time average over a sufficiently long period, a spatial average over a sufficiently large area, and a combination of the three. However, the problem is that all these averages yield a vanishing wind ū = 0. For the ensemble average and the spatial average this may be obvious from symmetry considerations ͑see below͒, but for the time average it is more subtle. In this context the experiments 5,9 are most instructive. Here it is shown that the wind erratically reverses its direction on time scales far exceeding the convective turnover time, Sreenivasan, Bershadskii, and Niemela 9 propose a simple dynamical picture to explain these wind reversals, with two metastable states, i.e., clockwise and counterclockwise mean wind motions; only extreme events, such as ͑a combination of͒ energetic plumes, can flip the system from one state to another. The relevant point here is that the reversals actually conserve the ergodicity of the system: the ͑long͒ time average becomes equal to the ensemble average-which is zero. The purpose of this letter is therefore to come up with a suitable and useful definition of wind. Based on this definition we then determine the wind based on five direct numerical simulations ͑DNS͒ of moderate aspect ratio and with periodic side boundaries. An analysis of the wind field and fluctuations shows evidence of a boundary layer that is not laminar.The Rayleigh-Bénard convection is generated when a layer of fluid with thickness H is subjected to a positive te...

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“…The results described in this study are based on the linearized mean-field equations, and therefore, they cannot describe detail features of the turbulent convection observed in the numerous laboratory experiments [13,14,15,16,17,18,19,20,21,22] and in direct numerical simulations [24,25]. In particular, we made the following assumptions about the turbulent convection.…”

Section: Discussionmentioning

confidence: 99%

“…However, some aspects related to the origin of large-scale coherent structures in non-rotating turbulent convection are not completely understood. Hartlep et al (2003) noted that there are two points of view on the origin of large-scale circulation in turbulent convection [24]. According to one point of view, the rolls which develop at low Rayleigh numbers near the onset of convection continually increase their size as Rayleigh number is increased and continue to exist in an average sense at even the highest Rayleigh numbers reached in the experiments [29].…”

Section: Introductionmentioning

confidence: 99%

“…They usually embrace the entire convective boundary layer (of the order of 1-3 km in height) and include pronounced convergence flow patterns close to the surface. In the sheared convective flows, the structures represent largescale rolls (cloud streets) stretched along the mean wind [1,2,12] Coherent structures in convective turbulent flows were comprehensively studied theoretically, experimentally and in numerical simulations [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. However, some aspects related to the origin of large-scale coherent structures in non-rotating turbulent convection are not completely understood.…”

Section: Introductionmentioning

confidence: 99%

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Large-scale instabilities in a nonrotating turbulent convection

2006

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A theoretical approach proposed in Phys. Rev. E 66, 066305 (2002) is developed further to investigate formation of large-scale coherent structures in a non-rotating turbulent convection via excitation of a large-scale instability. In particular, the convective-wind instability that causes formation of large-scale coherent motions in the form of cells, can be excited in a shear-free regime. It was shown that the redistribution of the turbulent heat flux due to non-uniform large-scale motions plays a crucial role in the formation of the coherent large-scale structures in the turbulent convection. The modification of the turbulent heat flux results in strong reduction of the critical Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the excitation of the convective-wind instability. The large-scale convective-shear instability that results in the formation of the large-scale coherent motions in the form of rolls stretched along imposed large-scale velocity, can be excited in the sheared turbulent convection. This instability causes the generation of convective-shear waves propagating perpendicular to the convective rolls. The mean-field equations which describe the convective-wind and convective-shear instabilities, are solved numerically. We determine the key parameters that affect formation of the large-scale coherent structures in the turbulent convection. In particular, the degree of thermal anisotropy and the lateral background heat flux strongly modify the growth rates of the large-scale convective-shear instability, the frequencies of the generated convective-shear waves and change the thresholds required for the excitation of the large-scale instabilities. This study elucidates the origins of the large-scale circulations and rolls in the atmospheric convective boundary layers and the meso-granular structures in the solar convection.

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Large Scale Structures in Rayleigh-Bénard Convection at High Rayleigh Numbers

Cited by 113 publications

References 14 publications

The Sun’s Supergranulation

The Sun’s Supergranulation

Identification of the wind in Rayleigh–Bénard convection

Large-scale instabilities in a nonrotating turbulent convection

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