Small-Scale Properties of Turbulent Rayleigh-Bénard Convection
TL;DR: In this article, the properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Benard convection are reviewed from an experimental, theoretical, and numerical point of view.
Abstract: The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Benard 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., Sθ(r) ∼ r2/5 for the second-order temperature structure function and Su(r) ∼ r6/5 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 LB and the height of the cell.
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TL;DR: In this article, the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr.
Abstract: The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.
1,372 citations
TL;DR: Key emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers.
Abstract: Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Benard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Benard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.
630 citations
TL;DR: In this paper, the authors derived a lower bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent Rayleigh-Benard (RB) convection, in the thermal and kinetic boundary layer (BL) close to the bottom and top plates.
Abstract: Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Benard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations
321 citations
TL;DR: In this article, the authors provide a critical summary of recent work on turbulent flows from a unified point of view and present a classification of all known transfer mechanisms, including direct and inverse energy cascades.
315 citations
Cites background from "Small-Scale Properties of Turbulent..."
...In 2D, energy dissipation is vanishingly small for large Reynolds numbers, and the energy flux is balanced by the buoyancy term, leading to a Bolgiano scaling (171) as discussed in the section devoted to unstably stratified flows [128,303]....
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...Most numerical investigations of 3D convection point to the Kolmogorov prediction [311,324,325] (see [303] for a discussion)....
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...A channel flow is only one of the many instances where turbulence is fed by multi-scale injections, other paradigmatic examples are given by natural convection [303], turbulence with power-law [595,596] or fractal forcing [597] and atmospheric flowswith simultaneous energy injections due to three dimensional small-scale or two-dimensional large-scale instabilities [174,319,598,599]....
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...bounded flows along homogeneous directions [303,480], in compressible flows [135,481,482] and inmany other systems as...
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TL;DR: In this article, the authors review the recent progress in understanding of fully developed Taylor-Couette turbulence from the experimental, numerical, and theoretical points of view, focusing on the parameter dependence of the global torque and on the local flow organization, including velocity profiles and boundary layers.
Abstract: Taylor-Couette flow, the flow between two coaxial co- or counter-rotating cylinders, is one of the paradigmatic systems in the physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinders, the ratio of the cylinder radii, and the aspect ratio. One key response of the system is the torque required to retain constant angular velocities, which can be connected to the angular velocity transport through the gap. Whereas the low–Reynolds number regime was well explored in the 1980s and 1990s of the past century, in the fully turbulent regime major research activity developed only in the past decade. In this article, we review this recent progress in our understanding of fully developed Taylor-Couette turbulence from the experimental, numerical, and theoretical points of view. We focus on the parameter dependence of the global torque and on the local flow organization, including velocity profiles and boundary layers. Next, we discuss transitions between diff...
297 citations
References
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Book•
01 Jan 1972
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08
8,276 citations
Journal Article•
TL;DR: In this article, the authors consider the problem of finding the components of the velocity at every point of a point with rectangular cartesian coordinates x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8.
Abstract: §1. We shall denote by uα ( P ) = uα ( x 1, x 2, x 3, t ), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1, x 2, x 3. In considering the turbulence it is natural to assume the components of the velocity uα ( P ) at every point P = ( x 1, x 2, x 3, t ) of the considered domain G of the four-dimensional space ( x 1, x 2, x 3, t ) are random variables in the sense of the theory of probabilities (cf. for this approach to the problem Millionshtchikov (1939) Denoting by Ᾱ the mathematical expectation of the random variable A we suppose that ῡ 2 α and (d uα /d xβ )2― are finite and bounded in every bounded subdomain of the domain G .
6,063 citations
TL;DR: A review of these methods can be found in articles by Lauterborn & Vogel (1984), Adrian (1986a), Hesselink (1988), and Dudderar et al..
Abstract: An important achievement of modern experimental fluid mechanics is the invention and development of techniques for the measurement of whole, instantaneous fields of scalars and vectors. These techniques include tomographic interferometry (Hesselink 1988) and planar laser-induced fluorescence for scalars (Hassa et al 1987), and nuclear-magnetic-resonance imaging (Lee et al 1987), planar laser-induced fluorescence, laser-speckle velocimetry, particle-tracking velocimetry, molecular-tracking velocimetry (Miles et al 1989), and particle-image velocimetry for velocity fields. Reviews of these methods can be found in articles by Lauterborn & Vogel (1984), Adrian (1986a), Hesselink (1988), and Dudderar et al (1988), in books written by Merzkirch (1987) and edited by Chiang & Reid (1988) and Gad-el-Hak (1989).
3,413 citations
Book•
01 Jan 1953
TL;DR: In this article, the kinematics of the field of homogeneous turbulence and the universal equilibrium theory of decay of the energy-containing eddies are discussed. But the authors focus on the dynamics of decay and not on the probability distribution of u(x).
Abstract: Preface 1 Introduction 2 Mathematics representation of the field of turbulence 3 The kinematics of homogeneous turbulence 4 Some linear problems 5 General dynamics of decay 6 The universal equilibrium theory 7 Decay of the energy-containing eddies 8 The probability distribution of u(x) Bibliography of research on homogeneous turbulence Index
3,121 citations