Abstract Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than layer height once fluctuations temperature velocity are removed. These turbulent superstructures reminiscent patterns close to onset convection. Here we report numerical simulations fluids at different Prandtl number ranging from 0.005 70 for Rayleigh numbers up 10 7 . We identify characteristic scales times that separate fast, small-scale gradually changing...

Significance Since the time Kolmogorov postulated universality of small-scale turbulence, an important research topic has been to experimentally establish it beyond doubt. The likelihood increases with increasing distance (say, in wave number space) from nonuniversal large scales. This as some power flow Reynolds number, and so a great deal emphasis put on creating quantifying very high flows under controlled conditions. present paper shows that universal properties inertial range turbulence...

The global transport of heat and momentum in turbulent convection is constrained by thin thermal viscous boundary layers at the heated cooled boundaries system. This bottleneck thought to be lifted once themselves become fully very high values Rayleigh number [Formula: see text]-the dimensionless parameter that describes vigor convective turbulence. Laboratory experiments cylindrical cells for text] have reported different outcomes on putative law. Here we show, direct numerical simulations...

We present high-resolution direct numerical simulation studies of turbulent Rayleigh–Bénard convection in a closed cylindrical cell with an aspect ratio one. The focus our analysis is on the finest scales convective turbulence, particular statistics kinetic energy and thermal dissipation rates bulk whole cell. fluctuations field can directly be translated into fluctuating local scale which found to develop ever finer increasing Rayleigh number. range these as well probability high-amplitude...

Characteristic properties of turbulent Rayleigh-B\'enard convection in the bulk and boundary layers are summarized for a wide range Rayleigh Prandtl numbers, with specific emphasis on low-Prandtl-number convection.

Abstract We present the results from numerical simulations of turbulent Rayleigh–Bénard convection for an aspect ratio (diameter/height) 1.0, Prandtl numbers 0.4 and 0.7, Rayleigh $1\ensuremath{\times} 1{0}^{5} $ to 1{0}^{9} . Detailed measurements thermal viscous boundary layer profiles are made compared experimental theoretical (Prandtl–Blasius) results. find that disagree by more than 10 % when scaled with similarity variable (boundary thickness) likewise Prandtl–Blasius In contrast,...

Statistical properties of turbulent Rayleigh-Benard convection at low Prandtl numbers (Pr), which are typical for liquid metals such as mercury, gallium or sodium, investigated in high-resolution three-dimensional spectral element simulations a closed cylindrical cell with an aspect ratio one and compared to previous air. We compare the scaling global momentum heat transfer. The exponents found be agreement experiments. Mean profiles root-mean-square velocity well thermal kinetic energy...

We determined the critical Rayleigh numbers ${\text{Ra}}_{c}$ for onset of convection in cylindrical containers with aspect ratios $1\ensuremath{\lesssim}\ensuremath{\Gamma}\ensuremath{\equiv}D/L\ensuremath{\lesssim}9$ ($D$ is diameter and $L$ height) patterns that form just above ${\text{Ra}}_{c}$, both from experiment by direct numerical simulation (DNS). Results agree well linear stability analysis Buell Catton finite sidewall conductivity. For...

Abstract We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh–Bénard convection. These are directly connected to the highly intermittent fluctuations of fluxes momentum and heat at isothermal top bottom walls statistically distributed around corresponding mean thickness scales. The also reflect strong spatial inhomogeneities both layers due large-scale, but complex intermittent, circulation that builds up closed convection cells. Similar layers, we define...

Significance Low-Prandtl-number thermal convection flows in liquid metals for which the temperature diffusivity is much larger than fluid viscosity have been studied less frequently convective air or water, despite many important applications reaching from astrophysics to energy conversion. Currently, turbulence low-Prandtl-number fully accessible only by three-dimensional simulations. Our numerical studies reveal why small-scale more vigorous compared with air. We also find that generation...

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows closed cylindrical cells unit aspect ratio is revisited from a transitional viscous perspective. When Rayleigh number large enough, dynamics at bottom top plates can be separated into an impact region downwelling plumes, ejection upwelling plumes interior away side walls. latter dominated by shear large-scale circulation (LSC) roll which fills whole cell continuously varies its orientation....

Inverse cascades of kinetic energy and thermal variance in the subset vertically homogeneous modes spectral space are found to cause a slow aggregation pair convective supergranules that eventually fill whole horizontally extended, three-dimensional, turbulent Rayleigh-B\'enard convection layer when heat flux is prescribed at top bottom. An additional weak rotation around vertical axis stops this scale smaller than lateral domain extension ceases inverse cascade for variance. The remains...

We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations Rayleigh–Bénard convection for Rayleigh-number range $10^5\leq Ra \leq 10^{11}$ $Pr=0.7$ . Using a Cartesian slab with horizontal periodic conditions an aspect ratio 4, we obtain statistical homogeneity $x$ - $y$ -directions, thus approximating best extended layer relevant most geo- astrophysical flow applications. observe upon canonical use combined long-time area averages,...

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed value largest Lyapunov exponent ${\ensuremath{\lambda}}_{1}$ for a variety aspect ratios and driving strengths. We study particular domain chaos state, which bifurcates supercritically from conducting fluid state involves extended propagating fronts as well point defects. compare our results those Egolf et al., [Nature 404, 733 (2000)], who suggested...

The convection patterns that occur at and slightly above the onset of in cylindrical containers were determined as a function aspect ratio, using simulations Rayleigh-Bénard linear stability analysis. study focused primarily on ratios 6≤Γ≤20, where Γ = diameter/depth, with conducting or insulating, no-slip boundary conditions Prandtl numbers Pr 0.7 28.9. Simulations demonstrate azimuthally pure Fourier mode consistent what is expected from bifurcation theory, an m 1 mode, for even values Γ,...

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects domain-chaos state observed in rotating Rayleigh-B\'enard convection-patterns. In large-aspect-ratio sample, we hybrid consisting domain chaos close to center, surrounded by an annulus nearly stationary radial rolls populated occasional defects reminiscent undulation chaos. Although Coriolis is responsible for chaos, comparing experiment simulation show rolls. Furthermore,...

We study the dynamics of thermal and momentum boundary layers in three-dimensional direct numerical simulations Rayleigh-B\'enard convection for Rayleigh number range $10^5 \le Ra 10^{11}$ $Pr=0.7$. Using a Cartesian slab with horizontal periodic conditions an aspect ratio 4, we obtain statistical homogeneity $x$- $y$-directions, thus approximating infinitely extended system. observe that upon canonical use long-time area averages, coherent mean flow is practically absent. Instead, velocity...

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers Behringer [Phys. Rev. Lett. 40, 712 (1978)] Gollub Benson [J. Fluid Mech. 100, 449 (1980)] in work on a periodic time dependence cells. Our confirms that dynamics these truly chaotic defined positive exponent. evolution of leading...

The amplitude equation for rotating Rayleigh–Bénard convection is derived from the Boussinesq equations with Coriolis force included. vertical boundary conditions are no-slip, and lateral either periodic or rigid. In order to keep track of mean flow, full system considered, instead a potential formulation. A multiple scales perturbation expansion in control parameter ϵ performed, appropriate solvability imposed. This leads usual at ϵ3∕2, but new rotation term enters ϵ7∕4. will cause change...

An extreme dissipation event in the bulk of a closed three-dimensional turbulent convection cell is found to be correlated with strong reduction large-scale circulation flow system that happens at same time as plume emission from bottom plate. The opens possibility for nearly frontal collision down- and upwelling plumes generation high-amplitude thermal layer bulk. This locally connected subsequent energy form shear layer. Our analysis illustrates impact transitions structures on events...

Turbulent convection processes in nature are often found to be organized a hierarchy of plume structures and flow patterns. The gradual aggregation cells or granules supergranule which eventually fills the whole horizontal layer is reported analyzed spectral element direct numerical simulations three-dimensional turbulent Rayleigh-Bénard at an aspect ratio 60. formation proceeds over time span more than 104 convective units for largest accessible Rayleigh number occurs only when turbulence...

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These reproduce traveling waves observed experimentally. Traveling studied near threshold by using complex Ginzburg-Landau equation (CGLE): mode analysis enables CGLE coefficients to be determined. The compared previous experimental theoretical results. Mean flows also computed found more significant as Prandtl number decreases (from sigma=6.4...

We present the results from numerical and theoretical investigations of rotating Rayleigh–Bénard convection for relatively large dimensionless rotation rates, 170 < Ω 274, a Prandtl number 6.4. Unexpected square patterns were found experimentally by Bajaj et al . ( Phys. Rev. Lett. , vol. 81, 1998, p. 806) in this parameter regime near threshold instability bulk. These have not yet been understood theoretically. Sánchez-Álvarez E 72, 2005, 036307) simulations similar parameters when only...

Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-B\'enard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We focused near the threshold supercritical bifurcation from conducting state to a convecting exhibiting domain chaos. A detailed analysis these has carried out is compared with experimental results, as well predictions multiple scale perturbation theory. find that time scaling law agrees theoretical...