Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session G33: Convection and Buoyancy Driven Flows: Rotating Rayleigh-Benard ConvectionConvection
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Chair: Olga Shishkina, Max Planck Institute for Dynamics and Self-Organization, Goettingen Room: 106 |
Monday, November 20, 2017 10:35AM - 10:48AM |
G33.00001: Boundary layers and scaling relations in natural thermal convection Olga Shishkina, Detlef Lohse, Siegfried Grossmann We analyse the boundary layer (BL) equations in natural thermal convection, which includes vertical convection (VC), where the fluid is confined between two differently heated vertical walls, horizontal convection (HC), where the fluid is heated at one part of the bottom plate and cooled at some other part, and Rayleigh--Benard convection (RBC). For BL dominated regimes we derive the scaling relations of the Nusselt and Reynolds numbers (Nu, Re) with the Rayleigh and Prandtl numbers (Ra, Pr). For VC the scaling relations are obtained directly from the BL equations (Shishkina, Phys. Rev. E 93 (2016)), while for HC they are derived by applying the Grossmann--Lohse theory (J. Fluid Mech. 407 (2000)) to the case of VC (Shishkina, Grossmann, Lohse, Geophys. Res. Lett. 43 (2016)). In particular, for RBC with large Pr we derive Nu$\sim$Pr$^0$Ra$^{1/3}$ and Re$\sim$Pr$^{-1}$Ra$^{2/3}$. [Preview Abstract] |
Monday, November 20, 2017 10:48AM - 11:01AM |
G33.00002: Nusselt number and bulk temperature in turbulent Rayleigh--B\'enard convection Eberhard Bodenschatz, Stephan Weiss, Olga Shishkina We present an algorithm to calculate the Nusselt number ($Nu$) in measurements of the heat transport in turbulent Rayleigh--B\'enard convection under general non-Oberbeck--Boussinesq (NOB) conditions (Shishkina, Weiss, Bodenschatz, Phys. Rev. Fluids, 2016). We further critically analyze the different ways to evaluate the dependences of $Nu$ over the Rayleigh number ($Ra$) and show the sensitivity of these dependences to the reference temperatures in the bulk, top and bottom boundary layers (BLs). Finally we propose a method to predict the bulk temperature and a way to calculate the reference temperatures of the top and bottom BLs and validate them against the G\"ottingen measurements (Ahlers, He, Funfschilling, Bodenschatz, New J. Phys., 2012). [Preview Abstract] |
Monday, November 20, 2017 11:01AM - 11:14AM |
G33.00003: Velocity and acceleration statistics in rotating Rayleigh-B\'{e}nard convection: Indicators for transition. Hadi Rajaei, Kim Alards, Rudie Kunnen, Herman Clercx Background rotation causes different flow structures and heat transfer (HT) efficiencies in Rayleigh-B\'{e}nard convection. Three main regimes are known: rotation-unaffected (regime I), rotation-affected (regime II) and rotation-dominated (regime III). Regimes I and II are easily accessible with experiments and simulations, thus they have been extensively studied. Regime III and the transition to this regime are less explored. There are two main hypotheses proposed for the driving mechanisms of the transition to regime III: (i) the relative thicknesses of the viscous and thermal boundary layers (BLs) and (ii) vortical plumes which span throughout the entire domain. These hypotheses are usually examined through different parameters such as viscous and thermal BLs thicknesses and HT efficiency. In this work, we study regime III and these hypotheses from a new perspective: Lagrangian velocity/acceleration fluctuations and autocorrelations of tracers from experiments. We have found that the transition to regime III coincides with three phenomena; suppressed vertical motions, strong penetration of vortical plumes into the bulk and reduced interaction of vortical plumes with their surroundings. These findings allow us to evaluate the available hypotheses and learn more about regime III. [Preview Abstract] |
Monday, November 20, 2017 11:14AM - 11:27AM |
G33.00004: Horizontal motion and distribution of the columnar vortex structures in rotating Rayleigh-Benard convection. Jin-Qiang Zhong, Jun-Qiang Shi, Hao-Yuan Lu, Shan-Shan Ding We report measurements of the horizontal motion of columnar vortex structures in rotating Rayleigh-Benard convection in a range of Rayleigh number $1\ast {10}^{7}\le Ra\le 3.8\ast {10}^{10}$, Ekman number $3.4\ast {10}^{-7}\le Ek\thinspace $and Prandtl number \textit{Pr}$=$4.4. With the reduced Rayleigh number ${Ra}^{\ast }=Ra{Ek}^{4/3}<80$, thermal plumes are vertically straightened to form convective columnar vortices that are advected laterally in a random manner. In the dilute-vortex limit ${Ra}^{\ast }\approx $80, horizontal motion of the columnar vortices possesses the characters of Brownian motions, in terms of a mean-square displacement ${<\Delta r}^{2}\left( t \right)>=4Dt$ linearly dependent on time and a power-spectral density \textbf{\textit{E}}($\omega )$ that follows an $\omega^{-2}$ roll-off. In a dense-vortex regime${\thinspace Ra}^{\ast }<$ 30, we find $<{\Delta r}^{2}\left( t \right)>=4Dt^{\alpha }$. With decreasing \textit{Ek} the constant $ D$ decreases, but the exponent $\alpha $ increases and exceeds 1.0. The PDF of the displacement $P(\Delta r(t))$, however, remains Gaussian with a variance $\sigma^{2}\propto t^{\alpha }$ for various \textit{Ek}. Horizontal distribution of the columnar vortices is quantified by applying Voronoi analysis to the vortex-core position data. In the dense-vortex regime the PDF of the Voronoi areas shows larger (smaller) probability of having large (small) Voronoi areas than that of randomly distributed vortices, indicating vortex clustering effect and the formation of vortex-grid structures. [Preview Abstract] |
Monday, November 20, 2017 11:27AM - 11:40AM |
G33.00005: Temperature fluctuations and thermal plume dynamics in turbulent rotating Rayleigh-Bénard convection. Shan-Shan Ding, Wen-Dan Yan, Hui-Min Li, Jin-Qiang Zhong We present measurements of the temperature fluctuations in rotating Rayleigh-Bénard convection that are taken at fluid heights 0 $\le z\le 20\lambda $ ($\lambda $ being the thermal boundary layer thickness) above the bottom plate, with a Prandtl number \textit{Pr}$=$6.0, varied Rayleigh numbers in the range $5.8\ast {10}^{8}\le Ra\le 6.3\ast {10}^{9}$ and inversed Rossby numbers $1/Ro\le 8.0$. The temperature variance profile exhibits a power-low dependence $\sigma \left( z \mathord{\left/ {\vphantom {z \lambda }} \right. \kern-\nulldelimiterspace} \lambda \right)=\sigma_{0}\left( z \mathord{\left/ {\vphantom {z \lambda }} \right. \kern-\nulldelimiterspace} \lambda \right)^{-\beta (Ro)}\thinspace $when $z>\lambda $. For various \textit{Ra} the exponents $\beta (Ro)$ follow a single curve and decrease rapidly with increasing 1/\textit{Ro}. Profiles of the temperature skewness $Sk(z \mathord{\left/ {\vphantom {z \lambda }} \right. \kern-\nulldelimiterspace} \lambda )$ and kurtosis $Ku\left( z \mathord{\left/ {\vphantom {z \lambda }} \right. \kern-\nulldelimiterspace} \lambda \right)$ are also independent on\textit{ Ra}, both decrease with increasing 1/\textit{Ro}. The dynamical properties of thermal plumes are analyzed using their temperature time series. Over the \textit{Ro} range studied, both the plume temperature amplitude $A$ and the time width $w$ are in log-normal distributions. When $z>\lambda $ the means of $A$ and the plume time fraction are dictated by power functions of $z$, both increase with stronger rotations. The variance of log($A)$, however, follows a logarithm function of $z$, and decreases at larger 1/\textit{Ro}. With these findings we elucidate that under the influences of rotation thermal plumes produce more pronounce and persistent thermal disturbances, leading to stronger but more symmetrically distributed temperature fluctuations in the interior fluid. [Preview Abstract] |
Monday, November 20, 2017 11:40AM - 11:53AM |
G33.00006: TROCONVEX: An extreme laboratory approach to geostrophic turbulence Jonathan Cheng, Rudie Kunnen Many celestial bodies contain vast fluid layers of turbulent, massively-multiscale flows, driven by buoyant instabilities and constrained by Coriolis forces. The canonical problem of rotating Rayleigh-B\'{e}nard convection (RRBC) provides a fundamental framework for understanding such flows, but even in this simplified setting, many geophysical behaviors remain inaccessible to current studies. Here we present the first results from a new 4-meter high cylindrical RRBC device, TROCONVEX, designed to characterize rotating convection in far more extreme conditions than previously possible: it can attain Ekman numbers as low as 5x10$^{\mathrm{-9}}$ and Rayleigh numbers as high as 10$^{\mathrm{14}}$ in water, both nearly an order of magnitude more extreme than other RRBC experiments. We examine a suite of nonrotating and rapidly-rotating convection cases by measuring the Rayleigh, Ekman, and Nusselt numbers. Scaling trends between these parameters show the heat transfer evolution over many behavioral regimes, ranging from rotationally-constrained convective plumes to nonrotating-style turbulence. Future measurements of temperature statistics at the boundaries of the fluid layer will specify the flow morphology. In combination with future velocity measurements, these extreme laboratory results will expand our understanding of rotating convection toward geophysical settings. [Preview Abstract] |
Monday, November 20, 2017 11:53AM - 12:06PM |
G33.00007: Rotating Rayleigh-Bénard convection at low Prandtl number Andres Aguirre Guzman, Rodolfo Ostilla-Monico, Herman Clercx, Rudie Kunnen Most geo- and astrophysical convective flows are too remote or too complex for direct measurements of the physical quantities involved, and thus a reduced framework with the main physical constituents is beneficial. This approach is given by the problem of rotating Rayleigh-B\'enard convection (RRBC). For large-scale systems, the governing parameters of RRBC take extreme values, leading to the geostrophic turbulent regime. We perform Direct Numerical Simulations to investigate the transition to this regime at low Prandtl number ($Pr$). In low-$Pr$ fluids, thermal diffusivity dominates over momentum diffusivity; we use $Pr=0.1$, relevant to liquid metals. In particular, we study the convective heat transfer (Nusselt number $Nu$) as a function of rotation (assessed by the Ekman number $Ek$). The strength of the buoyant forcing (Rayleigh number $Ra$) is $Ra=1\times10^{10}$ to ensure turbulent convection. Varying $Ek$, we observe a change of the power-law scaling $Nu\propto Ek^\beta$ that suggests a transition to geostrophic turbulence, which is likely to occur at $Ek=9\times10^{-7}$. The thermal boundary layer thickness, however, may suggest a transition at lower Ekman numbers, indicating that perhaps not all statistical quantities show a transitional behaviour at the same $Ek$. [Preview Abstract] |
Monday, November 20, 2017 12:06PM - 12:19PM |
G33.00008: The effect of centrifugal buoyancy on the heat transport in rotating Rayleigh-B\'enard convection Susanne Horn, Jonathan Aurnou In a rapidly rotating and differentially heated fluid, the centrifugal acceleration can play a similar role to that of gravity in generating convective motion. However, in the paradigm system of rotating Rayleigh-B\'enard convection, centrifugal buoyancy is typically not considered in theoretical studies and, thus, usually undesired in laboratory experiments, despite being unavoidable. How centrifugal buoyancy affects the turbulent flow, including the heat transport, is still largely unknown, in particular, when it can be considered negligible. We study this problem by means of direct numerical simulations. Unlike in experiments, we are able to systematically vary the Froude number Fr (ratio of centrifugal to gravitational acceleration) and the Rossby number Ro (dimensionless rotation rate) independently, and even set each to zero exactly. We show that the centrifugal acceleration simultaneously leads to contending phenomena, e.g. reflected by an increase and a decrease of the center temperature, or a suppression and an enhancement of the heat transfer efficiency. Which one prevails as net effect strongly depends on the combination of Fr and Ro. Furthermore, we discuss implications for experiments of rapidly rotating convection. [Preview Abstract] |
Monday, November 20, 2017 12:19PM - 12:32PM |
G33.00009: Magnetoconvection and universality of heat transport enhancement Zi Li Lim, Kai Leong Chong, Ke-Qing Xia We numerically investigate how a vertical external magnetic field affects the convective flow in a Rayleigh-Benard turbulent convection. We observed an enhancement of heat transport under certain range of the Hartmann number Ha that characterizes the strength of the stabilizing Lorentz force. Heat transport enhancement caused by a stabilizing force is also observed in several other systems [1]. We find that the heat transport behaviour in the present system may also be understood in terms of an interplay between the stabilizing and destabilizing forces of the system and the observed optimum heat transport enhancement can be explained by an optimal coupling between thermal boundary layer and the momentum boundary layer. Therefore, the observed behaviour in magnetoconvection appears to belong to the same universality class of stabilizing-destabilizing (SD) flows reported recently [1]. [1] K. L. Chong, et al. Confined Rayleigh-Benard, Rotating Rayleigh-Benard, and Double Diffusive Convection: A unifying view on turbulent transport enhancement through coherent structure manipulation, Phys. Rev. Lett. (in press). [Preview Abstract] |
Monday, November 20, 2017 12:32PM - 12:45PM |
G33.00010: Logarithmic temperature and velocity profiles in Rayleigh-B\'enard turbulence Xiaojue Zhu, Varghese Mathai, Richard Stevens, Roberto Verzicco, Detlef Lohse In this study, we present results from two-dimensional DNS for the temperature and velocity profiles in Rayleigh-B\’enard convection. The mean temperature profiles, averaged both vertically and horizontally, are logarithmic in the boundary layers. The logarithmic region extends wider with increasing Rayleigh number and reaches one and half decades at $Ra = 10^{14}$. Similarly, there is also a logarithmic dependence of the mean velocity profile when the shear Reynolds number $Re_s \approx 420$ , as suggested by Grossmann-Lohse theory. We further separate the boundary into plume emitting and impacting regions and show that the heat transport has different scalings in the two regions. From low to high Rayleigh number, the system undergoes a transition from the impacting dominant regime to the emitting dominant regime with respect to the heat transport. [Preview Abstract] |
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