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Journal ArticleDOI

New perspectives in turbulent Rayleigh-Bénard convection.

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.
Citations
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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: Numerical simulations of turbulent convection in fluids at different Prandtl number levels suggest a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.
Abstract: Turbulent Rayleigh-Benard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

150 citations

Journal ArticleDOI
TL;DR: A review of recent advances in cloud entrainment can be found in this article, focusing on stratocumulus clouds, and indicating remaining challenges for obtaining accurate data at the required small scales.
Abstract: Cloud entrainment, the mixing between cloudy and clear air at the boundary of clouds, constitutes one paradigm for the relevance of small scales in the Earth system: By regulating cloud lifetimes, meter- and submeter-scale processes at cloud boundaries can influence planetary-scale properties. Understanding cloud entrainment is difficult given the complexity and diversity of the associated phenomena, which include turbulence entrainment within a stratified medium, convective instabilities driven by radiative and evaporative cooling, shear instabilities, and cloud microphysics. Obtaining accurate data at the required small scales is also challenging, for both simulations and measurements. During the past few decades, however, high-resolution simulations and measurements have greatly advanced our understanding of the main mechanisms controlling cloud entrainment. This article reviews some of these advances, focusing on stratocumulus clouds, and indicates remaining challenges.

124 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional simulation of Rayleigh-B\'enard turbulence covering six decades in Rayleigh number Ra up to $1{0}^{14}$ for Prandtl number $\mathrm{Pr}=1} was performed.
Abstract: The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-B\'enard turbulence covering six decades in Rayleigh number Ra up to $1{0}^{14}$ for Prandtl number $\mathrm{Pr}=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely, at ${\mathrm{Ra}}^{*}={10}^{13}$. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling $\mathrm{Nu}\ensuremath{\sim}{\mathrm{Ra}}^{1/3}$ [Proc. R. Soc. A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling $\mathrm{Nu}\ensuremath{\sim}{\mathrm{Ra}}^{0.38}$, corresponding to the effective scaling in the ultimate regime.

115 citations

Journal ArticleDOI
06 Apr 2018
TL;DR: In this article, the authors report the observation of very large-scale and long living coherent structures in highly turbulent Rayleigh-Benard convection up to Rayleigh Ra=109.
Abstract: We report the observation of superstructures, i.e., very large-scale and long living coherent structures in highly turbulent Rayleigh-Benard convection up to Rayleigh Ra=109. We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Γ=128. In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Γ≈4, while horizontally averaged statistics such as standard deviation and kurtosis converge around Γ≈8, the integral scale converges around Γ≈32, and the peak position of the temperature variance and turbulent kinetic energy spectra only converge around Γ≈64.

110 citations


Cites background or methods from "New perspectives in turbulent Rayle..."

  • ...In addition, experiments and simulations agree excellently up to Ra ∼ 1011 due to major developments in experimental and numerical techniques [10,11,13,14]....

    [...]

  • ...However, while heat transfer in industrial applications takes place in confined systems, the aspect ratio in many natural instances of convection is extremely large [10,11,13,14]....

    [...]

References
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Book
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

17,321 citations

Book
01 Jan 1977
TL;DR: In this article, a pipe and channel flow flow past a circular cylinder Free convection between parallel walls Equations of motion further basic ideas Dynamical similarity Low and high Reynolds numbers Some solutions of the viscous flow equations Inviscid flow Boundary layers, wakes, and jets Separation and attachment Lift Convection Stratified flow Flow in rotating fluids Instabilities Transition to turbulence in shear flows Turbulence Homogeneous isotropic turbulence Turbulent shear flow convection in horizontal layers Double diffusive free convection Dynamical chaos Experimental methods Applications of fluid dynamics Not
Abstract: Introduction Pipe and channel flow Flow past a circular cylinder Free convection between parallel walls Equations of motion Further basic ideas Dynamical similarity Low and high Reynolds numbers Some solutions of the viscous flow equations Inviscid flow Boundary layers, wakes, and jets Separation and attachment Lift Convection Stratified flow Flow in rotating fluids Instabilities Transition to turbulence in shear flows Turbulence Homogeneous isotropic turbulence Turbulent shear flows Convection in horizontal layers Double diffusive free convection Dynamical chaos Experimental methods Applications of fluid dynamics Notation Problems Hints and answers to problems Bibliography and references Index.

1,745 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, a new method for obtaining approximate equations for natural convection flows is presented, which allows the specification of the conditions under which the traditional Boussinesq approximation applies to a given Newtonian liquid or gas.

940 citations

Journal ArticleDOI
TL;DR: In this article, a systematic theory for the scaling of the Nusselt number Nu and of the Reynolds number Re in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments.
Abstract: A systematic theory for the scaling of the Nusselt number Nu and of the A systematic theory for the scaling of the Nusselt number Nu and of the Reynolds number Re in strong Rayleigh–Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large-scale convection roll (‘wind of turbulence’) and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number Ra versus Prandtl number Pr phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively, and by whether the thermal or the kinetic boundary layer is thicker. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra [less, similar] 1011) the leading terms are Nu [similar] Ra1/4Pr1/8, Re [similar] Ra1/2Pr[minus sign]3/4 for Pr [less, similar] 1 and Nu [similar] Ra1/4Pr[minus sign]1/12, Re [similar] Ra1/2Pr[minus sign]5/6 for Pr [greater, similar] 1. In most measurements these laws are modified by additive corrections from the neighbouring regimes so that the impression of a slightly larger (effective) Nu vs. Ra scaling exponent can arise. The most important of the neighbouring regimes towards large Ra are a regime with scaling Nu [similar] Ra1/2Pr1/2, Re [similar] Ra1/2Pr[minus sign]1/2 for medium Pr (‘Kraichnan regime’), a regime with scaling Nu [similar] Ra1/5Pr1/5, Re [similar] Ra2/5Pr[minus sign]3/5 for small Pr, a regime with Nu [similar] Ra1/3, Re [similar] Ra4/9Pr[minus sign]2/3 for larger Pr, and a regime with scaling Nu [similar] Ra3/7Pr[minus sign]1/7, Re [similar] Ra4/7Pr[minus sign]6/7 for even larger Pr. In particular, a linear combination of the ¼ and the 1/3 power laws for Nu with Ra, Nu = 0.27Ra1/4 + 0.038Ra1/3 (the prefactors follow from experiment), mimics a 2/7 power-law exponent in a regime as large as ten decades. For very large Ra the laminar shear boundary layer is speculated to break down through the non-normal-nonlinear transition to turbulence and another regime emerges.

933 citations