Intermittency of velocity fluctuations in turbulent thermal convection

Ching, Emily S. C.; Leung, Chi Kin Randolph; Qiu, Xin; Tong, Penger

doi:10.1103/physreve.68.026307

Cited by 15 publications

(13 citation statements)

References 20 publications

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“…Using experimental data of Libchaber at the University of Chicago [25,26], Ching and Kwok [27] found that local temperature dissipation in high Rayleigh number convection satisfy a similar SL hierarchy, and Ching [28] showed that the scaling behavior of the temperature structure functions for length scales below and above the Bolgiano scale are both well described by the SL hierarchical symmetry. Both velocity fluctuations [29] and temperature fluctuations [30] were confirmed to be welldescribed by the SL hierarchical symmetry. Xia et al [31] made a direct multipoint measurements of the velocity and temperature fields, and showed that in the central region, velocity and temperature both have excellent SL scaling with different model parameters.…”

Section: Experimental Verifications Of the Hierarchical Symmetrymentioning

confidence: 74%

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

She

Zhang

2009

Acta Mech Sin

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Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque (SL) hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.

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Section: Experimental Verifications Of the Hierarchical Symmetrymentioning

confidence: 74%

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

She

Zhang

2009

Acta Mech Sin

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“…The method, plotting (logarithms of) SFs of different orders p against each other and not against the scale r, is usually effective in revealing mutual scaling relations and in particular intermittency. In the context of RB convection, it has first been applied by Benzi et al (1994) and later by Cioni et al (1995), Ching (2000), Zhou & Xia (2001), Skrbek et al (2002), Ching et al (2003b), and Kunnen et al (2008). Independent of the scaling of the second-order velocity SF (K41, BO59, shear flow scaling), dimensional scaling implies S ( p) u (r) ∼ (S (2) u (r)) p/2 .…”

Section: Further Obstacles In Identifying Bo59 Scalingmentioning

confidence: 98%

Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

Lohse¹,

Xia

2010

Annu. Rev. Fluid Mech.

814

631

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The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Bénard convection are reviewed, from an experimental, theoretical, and numerical point of view. In particular, we address the question of whether, and if so where in the flow, the so-called Bolgiano-Obukhov scaling exists, i.e., S θ (r) ∼ r 2/5 for the second-order temperature structure function and S u (r) ∼ r 6/5 for the second-order velocity structure function. Apart from the anisotropy and inhomogeneity of the flow, insufficiently high Rayleigh numbers, and intermittency corrections (which all hinder the identification of such a potential regime), there are also reasons, as a matter of principle, why such a scaling regime may be limited to at most a decade, namely the lack of clear scale separation between the Bolgiano length scale L B and the height of the cell. 335 Annu. Rev. Fluid Mech. 2010.42:335-364. Downloaded from www.annualreviews.org by Indiana University -Purdue University Indianapolis -IUPUI on 10/04/12. For personal use only.

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“…It was found that the two horizontal velocity components are characterized by the same value of β but the vertical velocity component is characterized by a smaller value of β. This distinction was attributed [10] to the presence of the plumes which makes the vertical velocity component more intermittent. As a further test of our scheme of plume extraction, we analyze v b (t) at the cell center to check whether its horizontal and vertical components will now be characterized by the same value of β.…”

mentioning

confidence: 99%

“…In a recent study [10], the three velocity components at the cell center were found to possess the She-Leveque hierarchical structure [11]:…”

mentioning

confidence: 99%

Extraction of Plumes in Turbulent Thermal Convection

et al. 2004

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We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence of the plume velocity and understand the results using the equations of motion. We further obtain the average local heat flux in the vertical direction at the cell center. Our result shows that heat is not mainly transported through the central region but instead through the regions near the sidewalls of the convection cell. where v is the velocity field, p the pressure divided by density, T the temperature field, andẑ is the unit vector in the vertical direction. Furthermore, δT = T − T 0 where T 0 is the mean temperature of the bulk fluid, g is the acceleration due to gravity and α, ν, and κ are respectively the volume expansion coefficient, kinematic viscosity and thermal diffusivity of the fluid. The state of fluid motion is characterized by the geometry of the cell and two dimensionless parameters: the Rayleigh number, Ra = αg∆L 3 /(νκ), which measures how much the fluid is driven and the Prandtl number, Pr = ν/κ, which is the ratio of the diffusivities of momentum and heat of the fluid. Here ∆ is the maintained temperature difference between the bottom and the top, and L is the height of the cell. When Ra is sufficiently large, the convective motion becomes turbulent. In turbulent convection, local velocity and temperature measurements taken at a point within the convection cell display complex fluctuations in time. On the other hand, visualization of the flow reveals recurring coherent structures. One prominent coherent structure is a plume, which is a mushroom-like flow generated by buoyancy. Thus at least two strategies can be employed to study turbulent thermal convection or turbulent flows in general. One is to analyze and understand the fluctuations of the local measurements. The other is to characterize the coherent structures and study and understand their dynamics. These two approaches are not independent but provide complementary knowledge of turbulent flows. In particular, there is the natural question of whether and how information about the coherent structures can be extracted from the local measurements.For turbulent flows not driven by buoyancy, various methods including proper orthogonal decomposition, conditional sampling and wavelet analysis have been proposed to identify coherent vortical structures from local velocity measurements [2]. On the other hand, much less work has been done in identifying plumes or extracting information about plumes in turbulent thermal convection [3,4,5]. Belmonte and Libchaber[3] used the skewness of the temperature derivative as a signature of the plumes. Zhou and Xia[4] associated the difference in the skewness of the positive and negative parts of the temperature difference with the presence of plumes and identified the plumes whenever the temperature difference becomes larger than a chosen threshold [6]. In Ref.[5], plu...

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Intermittency of velocity fluctuations in turbulent thermal convection

Cited by 15 publications

References 20 publications

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

Extraction of Plumes in Turbulent Thermal Convection

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