The wind in confined thermal convection

2001 ◽  
Vol 449 ◽  
pp. 169-178 ◽  
Author(s):  
J. J. NIEMELA ◽  
L. SKRBEK ◽  
K. R. SREENIVASAN ◽  
R. J. DONNELLY
Keyword(s):  
Rayleigh Number ◽  
Large Scale ◽  
Turnover Time ◽  
Turbulent Convection ◽  
Physical Explanation ◽  
Dynamical Parameter ◽  
Large Scale Circulation ◽  
Wide Range ◽  
Circulation Velocity ◽  
Rayleigh Benard

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Bénard apparatus, which is a closed box with a heated bottom wall. The wind survives even when the dynamical parameter, namely the Rayleigh number, is very large. Over a wide range of time scales greater than its characteristic turnover time, the wind velocity exhibits occasional and irregular reversals without a change in magnitude. We study this feature experimentally in an apparatus of aspect ratio unity, in which the highest attainable Rayleigh number is about 1016. A possible physical explanation is attempted.

Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection

2019 ◽  
Vol 877 ◽  
Author(s):  
Xin Chen ◽  
Shi-Di Huang ◽  
Ke-Qing Xia ◽  
Heng-Dong Xi
Keyword(s):  
Energy Barrier ◽  
Large Scale ◽  
Turnover Time ◽  
Reversal Rate ◽  
Flow Topology ◽  
Large Scale Circulation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Flow Reversals ◽  
Rayleigh Benard

We present an experimental study of the reversal of the large-scale circulation (LSC) in quasi-two-dimensional turbulent Rayleigh–Bénard convection. It is found that there exists a transition in the Rayleigh number ($Ra$) dependence of the reversal rate $f$ with two distinct scalings: for $Ra$ less than a transitional value $Ra_{t}$, the non-dimensionalized reversal rate $ft_{E}\sim Ra^{-1.09}$; however, for higher $Ra$ the scaling changes to $ft_{E}\sim Ra^{-3.06}$, where $t_{E}$ is the turnover time of the LSC. Flow visualization shows that this regime transition originates from a change in flow topology from a single-roll state to a new, less stable, abnormal single-roll state with substructures inside the single roll. The emergence of the substructures inside the LSC lowers the energy barrier for the flow reversals to occur and leads to a slower decay of $f$ with $Ra$. Detailed analysis reveals that, although it is the corner rolls that trigger the reversal event, the probability for the occurrence of reversals mainly depends on the stability of the LSC. This is supported by a model we proposed to predict the critical condition for the transition, which agrees well with the experimental results.

Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 607 ◽  
pp. 119-139 ◽  
Author(s):  
DENIS FUNFSCHILLING ◽  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Small Scale ◽  
Large Scale Circulation ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

Exploring the severely confined regime in Rayleigh–Bénard convection

2016 ◽  
Vol 805 ◽  
Author(s):  
Kai Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Rayleigh Number ◽  
Flow Topology ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Wide Range ◽  
Classical Boundary ◽  
Global And Local ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the effect of severe geometrical confinement in Rayleigh–Bénard convection with a wide range of width-to-height aspect ratio $\unicode[STIX]{x1D6E4}$, $1/128\leqslant \unicode[STIX]{x1D6E4}\leqslant 1$, and Rayleigh number $Ra$, $3\times 10^{4}\leqslant Ra\leqslant 1\times 10^{11}$, at a fixed Prandtl number of $Pr=4.38$ by means of direct numerical simulations in Cartesian geometry with no-slip walls. For convection under geometrical confinement (decreasing $\unicode[STIX]{x1D6E4}$ from 1), three regimes can be recognized (Chong et al., Phys. Rev. Lett., vol. 115, 2015, 264503) based on the global and local properties in terms of heat transport, plume morphology and flow structures. These are Regime I: classical boundary-layer-controlled regime; Regime II: plume-controlled regime; and Regime III: severely confined regime. The study reveals that the transition into Regime III leads to totally different heat and momentum transport scalings and flow topology from the classical regime. The convective heat transfer scaling, in terms of the Nusselt number $Nu$, exhibits the scaling $Nu-1\sim Ra^{0.61}$ over three decades of $Ra$ at $\unicode[STIX]{x1D6E4}=1/128$, which contrasts sharply with the classical scaling $Nu-1\sim Ra^{0.31}$ found at $\unicode[STIX]{x1D6E4}=1$. The flow in Regime III is found to be dominated by finger-like, long-lived plume columns, again in sharp contrast with the mushroom-like, fragmented thermal plumes typically observed in the classical regime. Moreover, we identify a Rayleigh number for regime transition, $Ra^{\ast }=(29.37/\unicode[STIX]{x1D6E4})^{3.23}$, such that the scaling transition in $Nu$ and $Re$ can be clearly demonstrated when plotted against $Ra/Ra^{\ast }$.

scholarly journals Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

2016 ◽  
Vol 791 ◽  
Author(s):  
Xiaozhou He ◽  
Eberhard Bodenschatz ◽  
Guenter Ahlers
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Cylindrical Sample ◽  
Ultimate State ◽  
Large Scale Circulation ◽  
Classical State ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present measurements of the orientation ${\it\theta}_{0}$ and temperature amplitude ${\it\delta}$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh–Bénard convection (RBC) with aspect ratio ${\it\Gamma}\equiv D/L=1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr\simeq 0.8$. The results for ${\it\theta}_{0}$ revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth’s Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity $D_{{\it\theta}}$ and a corresponding Reynolds number $Re_{{\it\theta}}$ for Rayleigh numbers over the range $2\times 10^{12}\lesssim Ra\lesssim 1.5\times 10^{14}$. In the classical state ($Ra\lesssim 2\times 10^{13}$) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351–386) for $Ra\lesssim 10^{11}$ and $Pr=4.38$, which gave $Re_{{\it\theta}}\propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_{{\it\theta}}\propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_{V}$ (He et al., New J. Phys., vol. 17, 2015, 063028). At larger $Ra$ the data for $Re_{{\it\theta}}(Ra)$ revealed a transition to a new state, known as the ‘ultimate’ state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_{V}(Ra)$ at $Ra_{1}^{\ast }\simeq 2\times 10^{13}$ and $Ra_{2}^{\ast }\simeq 8\times 10^{13}$. In the ultimate state we found $Re_{{\it\theta}}\propto Ra^{0.40\pm 0.03}$. Recently, Skrbek & Urban (J. Fluid Mech., vol. 785, 2015, pp. 270–282) claimed that non-Oberbeck–Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as ‘ultimate’.

scholarly journals The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection

2009 ◽  
Vol 638 ◽  
pp. 383-400 ◽  
Author(s):  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Large Scale ◽  
Lateral Displacement ◽  
Torsional Oscillation ◽  
Restoring Force ◽  
Large Scale Circulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Sloshing Mode ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In agreement with a recent experimental discovery by Xi et al. (Phys. Rev. Lett., vol. 102, 2009, paper no. 044503), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling & Ahlers (Phys. Rev. Lett., vol. 92, 2004, paper no. 1945022004). We show that both modes can be described by an extension of a model developed previously Brown & Ahlers (Phys. Fluids, vol. 20, 2008, pp. 105105-1–105105-15; Phys. Fluids, vol. 20, 2008, pp. 075101-1–075101-16). The extension consists of permitting a lateral displacement of the LSC circulation plane away from the vertical centreline of the sample as well as a variation of the displacement with height (such displacements had been excluded in the original model). Pressure gradients produced by the sidewall of the container on average centre the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model yields the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude and probability distributions of the displacements.

Thermal convection in inclined cylindrical containers

2016 ◽  
Vol 790 ◽  
Author(s):  
Olga Shishkina ◽  
Susanne Horn
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Large Scale ◽  
Direct Numerical Simulations ◽  
Large Scale Circulation ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Small Inclination

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle ${\it\beta}$, $0\leqslant {\it\beta}\leqslant {\rm\pi}/2$, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number $\mathit{Nu}$ and Reynolds number $\mathit{Re}$. The considered Rayleigh numbers $\mathit{Ra}$ range from $10^{6}$ to $10^{8}$, the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the $\mathit{Nu}\,({\it\beta})/\mathit{Nu}(0)$ dependence is not universal and is strongly influenced by a combination of $\mathit{Ra}$ and $\mathit{Pr}$. Thus, with a small inclination ${\it\beta}$ of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small $\mathit{Pr}$, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to ${\it\beta}={\rm\pi}/2$, $\mathit{Nu}$ and $\mathit{Re}$ decrease with increasing ${\it\beta}$ in all considered cases. Generally, the $\mathit{Nu}({\it\beta})/\mathit{Nu}(0)$ dependence is a complicated, non-monotonic function of ${\it\beta}$.

scholarly journals Understanding the uncertainty in global forest carbon turnover

2020 ◽  
Vol 17 (15) ◽  
pp. 3961-3989 ◽  
Author(s):  
Thomas A. M. Pugh ◽  
Tim Rademacher ◽  
Sarah L. Shafer ◽  
Jörg Steinkamp ◽  
Jonathan Barichivich ◽  
...  
Keyword(s):  
Large Scale ◽  
Tree Mortality ◽  
Forest Biomass ◽  
Turnover Time ◽  
Biomass Carbon ◽  
Carbon Turnover ◽  
Turnover Rates ◽  
Wide Range ◽  
The Future ◽  
Total Turnover

Abstract. The length of time that carbon remains in forest biomass is one of the largest uncertainties in the global carbon cycle, with both recent historical baselines and future responses to environmental change poorly constrained by available observations. In the absence of large-scale observations, models used for global assessments tend to fall back on simplified assumptions of the turnover rates of biomass and soil carbon pools. In this study, the biomass carbon turnover times calculated by an ensemble of contemporary terrestrial biosphere models (TBMs) are analysed to assess their current capability to accurately estimate biomass carbon turnover times in forests and how these times are anticipated to change in the future. Modelled baseline 1985–2014 global average forest biomass turnover times vary from 12.2 to 23.5 years between TBMs. TBM differences in phenological processes, which control allocation to, and turnover rate of, leaves and fine roots, are as important as tree mortality with regard to explaining the variation in total turnover among TBMs. The different governing mechanisms exhibited by each TBM result in a wide range of plausible turnover time projections for the end of the century. Based on these simulations, it is not possible to draw robust conclusions regarding likely future changes in turnover time, and thus biomass change, for different regions. Both spatial and temporal uncertainty in turnover time are strongly linked to model assumptions concerning plant functional type distributions and their controls. Thirteen model-based hypotheses of controls on turnover time are identified, along with recommendations for pragmatic steps to test them using existing and novel observations. Efforts to resolve uncertainty in turnover time, and thus its impacts on the future evolution of biomass carbon stocks across the world's forests, will need to address both mortality and establishment components of forest demography, as well as allocation of carbon to woody versus non-woody biomass growth.

Turbulent convection and large scale circulation in a cube with rough horizontal surfaces

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
N. Foroozani ◽  
J. J. Niemela ◽  
V. Armenio ◽  
K. R. Sreenivasan
Keyword(s):  
Large Scale ◽  
Turbulent Convection ◽  
Large Scale Circulation

Dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation

2015 ◽  
Vol 778 ◽  
Author(s):  
Jin-Qiang Zhong ◽  
Sebastian Sterl ◽  
Hui-Min Li
Keyword(s):  
Large Scale ◽  
Modulation Frequency ◽  
Rotation Velocity ◽  
Viscous Drag ◽  
Phase Lag ◽  
Large Scale Circulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present measurements of the azimuthal rotation velocity $\dot{{\it\theta}}(t)$ and thermal amplitude ${\it\delta}(t)$ of the large-scale circulation in turbulent Rayleigh–Bénard convection with modulated rotation. Both $\dot{{\it\theta}}(t)$ and ${\it\delta}(t)$ exhibit clear oscillations at the modulation frequency ${\it\omega}$. Fluid acceleration driven by oscillating Coriolis force causes an increasing phase lag in $\dot{{\it\theta}}(t)$ when ${\it\omega}$ increases. The applied modulation produces oscillatory boundary layers and the resulting time-varying viscous drag modifies ${\it\delta}(t)$ periodically. Oscillation of $\dot{{\it\theta}}(t)$ with maximum amplitude occurs at a finite modulation frequency ${\it\omega}^{\ast }$. Such a resonance-like phenomenon is interpreted as a result of optimal coupling of ${\it\delta}(t)$ to the modulated rotation velocity. We show that an extended large-scale circulation model with a relaxation time for ${\it\delta}(t)$ in response to the modulated rotation provides predictions in close agreement with the experimental results.

Sign in / Sign up

Export Citation Format

Share Document