Turbulent Rayleigh-Bénard 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 10
. 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.
The physical complexity and the large number of degrees of freedom that can be resolved today by direct numerical simulations of turbulent flows, and by the most sophisticated experimental ...techniques, require new strategies to reduce and analyse the data so generated, and to model the turbulent behaviour. We discuss a few concrete examples for which the turbulence data have been analysed by machine learning tools. We also comment on work in neighbouring fields of physics, particularly astrophysical (and astronomical) work, where Big Data has been the paradigm for some time. We discuss unsupervised, semi-supervised and supervised machine learning methods to direct numerical simulations data of homogeneous isotropic turbulence, Rayleigh-Bénard convection, and the minimal flow unit of a turbulent channel flow; for the last case, we discuss in some detail the application of echo state networks, this being one implementation of reservoir computing. The paper also provides a brief perspective on machine learning applications more broadly.
A new approach to numerical simulation of magnetohydrodynamic flows of liquid metals is presented. It combines the conservative finite-difference discretization with a tensor-product-Thomas solution ...of the elliptic problems for pressure, electric potential, velocity, and temperature. The method is realizable on an arbitrarily clustered structured grid. The main novelty of the approach is the efficient solution of the practically important and computationally challenging elliptic problems for electric potential in flow domains with thin electrically conducting walls. The method is verified via solution of benchmark problems for streamwise-uniform and nonuniform, steady and unsteady magnetohydrodynamic flows in ducts, and for thermal convection in boxes of various aspect ratios. Computational efficiency of the method in comparison to the existing ones is demonstrated.
•Novel method of numerical simulation of magnetohydrodynamic flows with walls of finite electrical conductivity is proposed.•The method is shown accurate and efficient in the case of flows with strong effects of magnetic field and natural convection.•The method is promising for magnetohydrodynamic flow problems in advanced energy and materials processing applications.
Deep learning in turbulent convection networks Fonda, Enrico; Pandey, Ambrish; Schumacher, Jörg ...
Proceedings of the National Academy of Sciences - PNAS,
04/2019, Letnik:
116, Številka:
18
Journal Article
Recenzirano
Odprti dostop
We explore heat transport properties of turbulent Rayleigh–Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. ...Particular attention is paid to the slowly evolving turbulent superstructures—so called because they are larger in extent than the height of the convection layer—which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or “hot spots.” One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.
Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of ...temperature, density and pressure change very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux $J_c(z)$ at the top of the convection zone is reported here by a series of highly resolved three-dimensional direct numerical simulations beyond the Oberbeck–Boussinesq and anelastic limits for dimensionless dissipation numbers, $0.1 \le D\le 0.8$, at fixed Rayleigh number $Ra=10^6$ and superadiabaticity $\epsilon =0.1$. The highly stratified compressible convection regime appears for $D > D_{crit}\approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50 % reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top sublayer deep into the bulk.
Abstract
The entrainment of clear air and its subsequent mixing with a filament of cloudy air, as occurs at the edge of a cloud, is studied in three-dimensional direct numerical simulations that ...combine the Eulerian description of the turbulent velocity, temperature, and vapor fields with a Lagrangian cloud droplet ensemble. Forced and decaying turbulence is considered, such as when the dynamics around the filament is driven by larger-scale eddies or during the final period of the life cycle of a cloud. The microphysical response depicted in nd − 〈r3〉 space (where nd and r are droplet number density and radius, respectively) shows characteristics of both homogeneous and inhomogeneous mixing, depending on the Damköhler number. The transition from inhomogeneous to homogeneous mixing leads to an offset of the homogeneous mixing curve to larger dilution fractions. The response of the system is governed by the smaller of the single droplet evaporation time scale and the bulk phase relaxation time scale. Variability within the nd − 〈r3〉 space increases with decreasing sample volume, especially during the mixing transients. All of these factors have implications for the interpretation of measurements in clouds. The qualitative mixing behavior changes for forced versus decaying turbulence, with the latter yielding remnant patches of unmixed cloud and stronger fluctuations. Buoyancy due to droplet evaporation is observed to play a minor role in the mixing for the present configuration. Finally, the mixing process leads to the transient formation of a pronounced nearly exponential tail of the probability density function of the Lagrangian supersaturation, and a similar tail emerges in the droplet size distribution under inhomogeneous conditions.
Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level ...of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications.
In an attempt to understand the role of the strong radial dependence of thermal diffusivity on the properties of convection in Sun-like stars, we mimic that effect in non-Oberbeck-Boussinesq ...convection in a horizontally extended rectangular domain (aspect ratio 16) by allowing the thermal diffusivity κ to increase with the temperature (as in the case of stars). Direct numerical simulations (i.e., numerical solutions of the governing equations by resolving up to the smallest scales without requiring any modeling) show that, in comparison with Oberbeck-Boussinesq simulations (two of which we perform for comparison purposes), the symmetry of the temperature field about the mid-horizontal plane is broken, whereas the velocity and heat flux profiles remain essentially symmetric. Our choice of κ(T), which resembles the variation in stars, results in a temperature field that loses its fine structures toward the hotter part of the computational domain, but the characteristic large scale of the turbulent thermal "superstructures," which are structures whose size is typically larger than the depth of the convection domain, continues to be largely independent of the depth.
Small-scale universality in fluid turbulence Schumacher, Jörg; Scheel, Janet D.; Krasnov, Dmitry ...
Proceedings of the National Academy of Sciences - PNAS,
07/2014, Letnik:
111, Številka:
30
Journal Article
Recenzirano
Odprti dostop
Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal ...statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 10 ² the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.
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