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10:45   Turbulent Convection 1 10:45 15 mins #117 Plume statistics in a rough Rayleigh-Bénard convection cell Julien Salort, Laura Guislain, Francesca Chillà Abstract: The Rayleigh-Bénard cell is a useful model system to understand the physics of turbulent thermal convection, because the boundary conditions are well defined. This allows to compare experiments and numerical simulations over a wide range of parameters. However, boundaries in nature or in the industry are seldom hydrodynamically smooth. It is therefore tempting to add roughness at the boundaries of the Rayleigh-Bénard cell, to investigate how the heat transfer and the flow features are modified. Several rough Rayleigh-Bénard cells have been operated in the last decade, in particular in the group of K.-Q. Xia, and in our group in Lyon. These experiments evidence a roughness triggered regime with enhanced heat transfer efficiency when the thickness of the thermal boundary layer matches the roughness size. The enhancement appears to saturate at larger Rayleigh numbers, when the boundary layers are much smaller. These experimental observations have triggered numerical and theoretical works. One open question is the interplay between plume dynamics and turbulence. On the one hand, the generation of plumes at the boundary may be modified by the sharp edges of the roughness elements. On the other hand, the turbulent features of the wind can be enhanced because the threshold Reynolds number is known to be lower over rough surfaces. To investigate this question, we have analysed the plume statistics in a Rayleigh-Bénard cell with a rough hot plate, and a smooth cold plate. This set-up allows direct comparison of rough and smooth configurations within the same apparatus. 11:00 15 mins #126 ELUSIVE TRANSITION TO THE ULTIMATE REGIME OF TURBULENT RAYLEIGH-BÉNARD CONVECTION Pavel Urban, Pavel Hanzelka, Tomáš Králík, Michal Macek, Věra Musilová, Ladislav Skrbek Abstract: One of the key topics in the field of turbulent Rayleigh-Bénard convection (RBC) is the existence of its ultimate regime predicted by R. Kraichnan [1]. Observation of the transition to this ultimate state of RBC has been claimed (based on cryogenic helium experiments [2] and more recently on the SF6 Göttingen experiments at ambient temperature [3]) and disputed [4] several times. To shed more light on this important issue, we have studied the influence of non-Oberbeck-Boussinesq (NOB) effects on the heat transfer experimentally, using cryogenic 4He gas as the working fluid in a cylindrical cell 0.3 m in both height and diameter. We focus on measurements near the saturation vapor curve (SVC) but far away from the critical point (CP), where the first order (vapor/liquid) phase transition represents a much milder problem to the OB conditions [5]. We have chosen the Rayleigh number range 2E12 < Ra < 3E13 for several reasons: Corrections due to the heat conduction in the walls, important at smaller Ra, are already small here while corrections due to the finite heat conductivity and heat capacity of the plates are not yet important; the temperature difference between the bottom and the top plate ∆T=Tb-Tt can be set much bigger than that due to the adiabatic temperature gradient, Prandtl number was nearly constant of order one and the conventional OB criterion α∆T < 0.18 was satisfied. Additionally, as shown in Fig.1, our experimental working points 4He are approximately equally distant from the CP as in Ref. [3] in dimensionless phase diagrams and allow direct comparison with the Göttingen data of Ref. [3]. We see that in the measured data series the mean plate temperature Tm =(Tb+Tt)/2 was kept roughly constant; while the horizontal “blue and red crosses" show the span of internal cell temperature for each particular data point - the blue (red) crosses correspond to Tt (Tb). Figure 1. The 4He (left) and SF6 Goettingen [3] (middle) working points in p -T phase diagrams. The right panel shows the compensated Nu/Ra1/3 versus Ra plots of the Brno data (series A, B and C) shown together with the Göttingen data, obtained under nominally similar conditions. For clarity and simplicity, we calculated the Nu=Nu(Ra) scaling conventionally, based on fluid properties evaluated at Tm and the directly measured pressure p in the cell. Our central result is that the data series A and B, for which Tt closely approaches the SVC, display a strong increase of the Nu(Ra) slope around Ra of order 1E13, similarly as the SF6 data do at 1E14 [3] measured near the SVC, while our control series C closely agree with the SF6 data measured further away from the SVC and do not show any tendency of a transition to the ultimate scaling. Our results clearly demonstrate that for the correct evaluation of heat transfer efficiency of turbulent RBC at high Ra one ought to take into account the non-Oberbeck-Boussinesq (NOB) effects that arise when Tt closely approaches the 4He SVC from the gaseous side of the p-T phase diagram, even if the operating points are far away from the CP. Considering the NOB effects is crucial for all experiments aiming to observe the transition to the ultimate regime of RBC. In particular, our analysis suggests that the crossover to the ultimate regime claimed in [3], is most likely caused by the NOB effects in the SF6 used in the close vicinity of the SVC [5]. Thus, the important question of the transition to the ultimate state of RBC remains open. This research is funded by the Czech Science Foundation under project GA ČR 17-03572S. References [1] R. H. Kraichnan. Turbulent thermal convection at arbitrary Prandtl numbers. Phys. Fluids 5: 1374–1379, 1962. [2] P. E. Roche, F. Gauthier, R. Kaiser, J. Salort. Roche. On the triggering of the ultimate regime of convection New J. Phys. 12 085014, 2010. [3] X. He, D. Funfschilling, H. Nobach, E. Bodenschatz, G. Ahlers. Transition to the ultimate state of turbulent Rayleigh–Bénard convection, Phys. Rev. Lett 108, 024502, 2012. [4] L. Skrbek and P. Urban. Has the ultimate state of turbulent thermal convection been observed? J. Fluid Mech. 785: 270–282, 2015. [5] P. Urban, P. Hanzelka, T. Králík, M. Macek, V. Musilová. Elusive transition to the ultimate regime of turbulent Rayleigh-Bénard convection. Physical Review E 99, 011101(R), 2019. 11:15 15 mins #256 The Ultimate state of convection without the hot air Philippe-E. Roche Abstract: Over the last 2 decades, the ultimate state (or ultimate regime) has become the most debated topic in the field of convection. More than a dozen of Rayleigh-Bénard experiments conducted at very large Rayleigh numbers (Ra) are often presented as in contradiction, due to diverging heat transfer efficiencies (Nusselt number Nu), as illustrated by the figure. Some experiments experience a more or less pronounced heat transfer enhancement at large Ra while others don’t. Over the years, three different views have emerged in Grenoble/Lyon, Brno/Prague/Trieste and Gottingen/Twente/Santa Barbara to account for the results. These views are based on variants of Kraichnan’s 1962 prediction of a fully-turbulent asymptotic state of convection, or on Boussinesq approximation effects. Taken separately, the respective datasets and/or model are certainly fair and self-consistent, but no proposed interpretation is yet able to account for all existing observations. We conducted a meta-analysis of all the experiments performed at very high Ra assuming that (1) all data are correct (2) the various biases that inevitably alter measurements cannot fully account for the onset of scatter right above Ra~ 1e12 (knowing that all data agree over decades of lower Ra). Among all the experiments reporting a strong heat transfer enhancement, we identify few robust signatures for the ultimate state (dependence with the cell aspect ratio, scaling exponent, etc …) and the conditions for its occurrence. Based on these observations, a focused exploration of the other datasets allows to spot weak signs of transitions, and in one case where a finite size artefact can explain the absence of such sign. We argue that most very-high-Rayleigh numbers experiments could be described in a unified fashion, stating that a transition to the ultimate state takes place but that a mechanism can damp the increase of heat transfer. Although a first model emerges for this mechanism, it is yet to be understood in details. 11:30 15 mins #261 Direct numerical simulations towards ultimate turbulence Richard Stevens, Roberto Verzicco, Detlef Lohse Abstract: Both in experiments and simulations of Rayleigh-B\'enard (RB) convection it is a major challenge to reach the ultimate regime in which the boundary layers transition from laminar to turbulent \cite{ahl09}. In the ultimate regime the scaling exponent $\gamma$ in the relation $Nu \sim Ra^{\gamma}$, where Nusselt $Nu$ is the dimensionless heat transport and Rayleigh $Ra$ is the dimensionless temperature difference between the plates, increases. The critical Rayleigh number ($Ra^{*}$) for the transition to the ultimate regime has been observed in the G\"ottingen experiments around $Ra^{*} \approx 2 \times 10^{13}$. So far, the highest $Ra$ obtained in direct numerical simulations (DNS) is $Ra=2 \times 10^{12}$ for aspect ratio $\Gamma=0.5$ \cite{ste11}. Here we present a comparison between the G\"ottingen experiments and DNS up to $Ra=10^{13}$ \cite{he12,ahl17}. We find perfect agreement between experiments and simulations, both for the heat transfer, see figure \ref{figure1}a and for the mean and temperature variance profiles close to the sidewall, see figure \ref{figure1}b and figure \ref{figure1}c. In addition, we discuss simulations for $\Gamma=0.23$ up to $Ra=10^{14}$, which are performed on grids with almost $100 \times 10^9$ nodes. The preliminary results from these simulations are in good agreement with measurements by Roche et al. \cite{roc10}. 11:45 15 mins #152 Velocity structure functions of thermal convection and hydrodynamic turbulence follow similar scaling Shashwat Bhattacharya, Shubhadeep Sadhukhan, Anirban Guha, Mahendra K. Verma Abstract: We compute the velocity structure functions of Rayleigh-Bénard Convection using high-resolution simulation data with Rayleigh number Ra = 1.1 x 10^11 and unit Prandtl number. We show that similar to hydrodynamic turbulence, the scaling exponents of structure functions of thermal convection fit well with the hierarchy model of She and Leveque. Our results are consistent with Kolmogorov's energy spectrum observed in turbulent convection; they also agree with a modified version of Kolmogorov's theory for hydrodynamic turbulence to thermal convection. Further, like in hydrodynamic turbulence, the probability density functions of velocity increments in thermal convection follow stretched exponential distribution and are close to Gaussian at large separations. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate, which is unlike in hydrodynamic turbulence where both are equal. 12:00 15 mins #488 Unifying view on heat transport enhancement behaviour in confined Rayleigh-Bénard, rotating Rayleigh-Bénard, double diffusive convection and quasi-static magnetoconvection Kai Leong Chong, Yantao Yang, Zi Li Lim, Shi-Di Huang, Jin-Qiang Zhong, Richard J.A.M. Stevens, Roberto Verzicco, Detlef Lohse, Ke-Qing Xia Abstract: Rayleigh-Bénard (RB) flow under geometrical confinement, RB under rotation and double diffusive convection (DDC) are the three canonical models where turbulent flow is simultaneously subjected to a driving and a stabilizing force. Intuitively, one thinks that weaker flow should result in weaker scalar transport. However, previous researches have independently show a hallmark feature for such kind of flow which is the existence of scalar transport enhancement compared to the pure RB convection [1,2,3,4,5]. In this work, we study the three systems side-by-side in order to provide a more fundamental perspective. It is found that rather than the global transport responses, the three systems are actually similar in some local quantities such as the increase in plume coherency and relative boundary layer thicknesses. Furthermore, we reveal that the coupling between the normal stress and scalar fluctuations plays a key role in the optimal transport. The implication of this work leads us to the study of quasi-static magnetoconvection which in principle belongs to the same class of stabilized turbulent flow. Indeed, there exists an intermediate regime of heat transport enhancement and it can be understood by our proposed concept. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view to understand the scalar transport enhancement for the seemingly different turbulent flows and this concept could be potentially extended to other situations with similar stabilization. 12:15 15 mins #111 Transition to the ultimate regime in 2D Rayleigh-Benard convection Detlef Lohse, Xiaojue Zhu, Varghese Mathai, Richard Stevens, Roberto Verzicco Abstract: In ref. [1] we revealed the onset of a transition to the ultimate regime in 2D DNS of Rayleigh-Bénard turbulence beyond Ra ≈ 1013. Here we have further extended the DNS of ref. [1] to even larger Ra, namely now up to Ra = 4.64 × 1014, sticking to the same strict numerical resolution criteria of both boundary layer (BL) and bulk. The simulation at the highest Ra was performed with a grid resolution of 31200 × 25600 with 28 points in the boundary layer. The evidence for the transition to the ultimate regime is overwhelming: 1. On the global heat transfer: Nu(Ra), compensated with Ra0.357, is shown in figure 1a. An objective least squares fit of an effective power law Nu ∼ Raγ to the last 6 data points gives a scaling exponent γ = 0.345; the last 5 data points give γ = 0.345, last four data points give γ = 0.352, last 3 data points give γ = 0.357, and last 2 points give γ = 0.358; i.e. no matter how the data is interpreted, the scaling exponent is always larger than 1/3 and monotonously increasing with Ra. 2. On the local heat flux: In the plume ejecting regime, beyond 1013 the effective scaling exponents is close to γ = 0.38, see figure 1. In contrast, it remains ≤ 1/3 in the plume impacting regime, which therefore with increasing Ra looses more and more relevance for the overall heat transfer. 3. Beyond 1013, the horizontal velocity profiles u+(y+) in the BLs become logarithmic (see fig. 2 of the Ref. [1]), signaling a turbulent BL, which is characteristic for the ultimate regime, rather than one of laminar type as in the classical regime. 4. Finally, the transition to ultimate RB turbulence in the numerical data of [1] has also been confirmed through an extended self-similarity (ESS) analysis of the temperature structure functions, see ref. [2]. We find no ESS scaling before the transition. However, beyond the transition and for large enough wall distance y+ > 100, we find clear ESS behaviour, as expected for a scalar in a turbulent boundary layer. Therefore also that analysis provides strong evidence that the observed transition in the global Nusselt number around Ra = 1013 indeed is the transition from a laminar type BL to a turbulent type BL.