Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session AH: Convection and Buoyancy Driven Flows I |
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Chair: Katepalli Sreenivasan, New York University Room: Long Beach Convention Center 103C |
Sunday, November 21, 2010 8:00AM - 8:13AM |
AH.00001: Small-scale turbulent fluctuations beyond Taylor's frozen flow hypothesis Penger Tong, Xiaozhou He, Guowei He The space-time cross-correlation function C(r,t) of local temperature fluctuations in turbulent Rayleigh-Benard convection is obtained from simultaneous two-point time series measurements. The obtained C(r,t) is found to have the scaling form C(r,t) = C(R,0) with R$^2$ = [(r-Ut)$^2$ +(Vt)$^2$], where U and V are two characteristic velocities associated with the mean and rms velocities of the flow. The experiment verifies the theory and demonstrates its applications to a class of turbulent flows in which the requirement of Taylor's frozen flow hypothesis is not met. [Preview Abstract] |
Sunday, November 21, 2010 8:13AM - 8:26AM |
AH.00002: Role of Instability in State and Parameter Estimation of Rayleigh-B\'{e}nard Convection Adam Perkins, Michael Schatz Predictive power in spatiotemporally complex systems is limited by several factors. Foremost among them is inherent system instability that can cause small initial uncertainty to grow rapidly. We address this issue in a Rayleigh-B\'{e}nard convection experiment, in which a novel technique of pattern control provides a tool for the repeatable imposition of a given convection pattern, e.g., a pattern near instability. Selected perturbations are applied to the reference pattern to create an ensemble of systems evolving from nearby initial conditions on both sides of the instability boundary. We employ an efficient forecasting algorithm, the Local Ensemble Transform Kalman Filter (LETKF), to produce system state and parameter estimates from the convection patterns observed experimentally. Preliminary results of applying this state estimation algorithm to diverging pattern trajectories will be discussed. [Preview Abstract] |
Sunday, November 21, 2010 8:26AM - 8:39AM |
AH.00003: Extensive Scaling from Computational Homology and Karhunen-Lo\`{e}ve decomposition: Analysis of Rayleigh-B\'{e}nard Convection Experiments Michael Schatz, H\"{u}seyin Kurtuldu, Konstantin Mischaikow Spatiotemporally-chaotic dynamics in laboratory experiments on convection are characterized using a new dimension, $D_{\rm {CH}}$, determined from computational homology. Over a large range of system sizes, $D_{\rm{CH}}$ scales in the same manner as $D_{\rm{KLD}}$, a dimension determined from experimental data using Karhuenen-Loeve decomposition. Moreover, finite-size effects (the presence of boundaries in the experiment) lead to deviations from scaling that are similar for both $D_{\rm{CH}}$ and $D_{\rm{KLD}}$. In the absence of symmetry, $D_{\rm{CH}}$ can be determined more rapidly than $D_{\rm{KLD}}$. [Preview Abstract] |
Sunday, November 21, 2010 8:39AM - 8:52AM |
AH.00004: Synchronization of Spatiotemporal Chaos in Rayleigh-Benard Convection Alireza Karimi, Mark Paul We study the synchronization of spatiotemporal chaos in Rayleigh-Benard convection using numerical simulations of the Boussinesq equations. We consider one-way coupling between a principal and target convection domain. The principal domain is a large convection layer with no-slip boundaries on all material walls that is exhibiting spatiotemporal chaos. The target domain contains a convection layer that is smaller than the principal domain and is begun from random initial conditions in the temperature field. However, the sidewall boundary conditions of the target domain are given by the time dependent values of the principal domain at the equivalent location. The two domains are considered synchronized when the convection layers exhibit the same dynamics as measured by local and global diagnostics. Using this approach we quantify the length and time scales that describe the synchronization of the two domains over a variety of system parameters. [Preview Abstract] |
Sunday, November 21, 2010 8:52AM - 9:05AM |
AH.00005: Does confined turbulent convection ever attain the `asymptotic scaling' with 1/2--power? Joseph Niemela, Katepalli Sreenivasan We examine turbulent thermal convection for very high Rayleigh numbers using cryogenic helium in a cylindrical container with diameter-to-height aspect ratio $\gamma $ = 1, and confirm that the Nusselt number, Nu, follows approximately the 1/3 power of the Rayleigh number, Ra, for Ra $\le $ $\times $ 2 10$^{14}$: Nu = 0.064 Ra$^{1/3}$. However, when Ra is pushed to higher values by approaching the critical point of helium in the temperature-pressure phase diagram, we observe a new state of enhanced heat transport, corresponding approximately to Nu = 0.078 Ra$^{1/3}$. The transition between the two states of the 1/3-power occurs with a log-log slope of roughly $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $. Comparing experiments in the same apparatus but with $\gamma $ = 4 - as well as slightly different paths through the pressure-temperature phase space with the same aspect ratio - we find that the transition value of Ra is not unique and can vary by an order of magnitude or more depending on experimental conditions. In particular, the transition does not correlate with dynamical parameters such as the Rayleigh number. However, it correlates reasonably well with a non-dimensional parameter related to variability of fluid conductivity and viscosity, occurring when the mean pressures and temperatures approach their critical values closer. No asymptotic transition to a half-power heat transport law was discerned. [Preview Abstract] |
Sunday, November 21, 2010 9:05AM - 9:18AM |
AH.00006: Transition to the ultimate regime in two-dimensional turbulent Rayleigh-B\'enard convection Richard Stevens, Kazuyasu Sugiyama, Detlef Lohse The heat transfer in a RB system is determined by the Rayleigh number $Ra$ and the Prandtl number $Pr$. Various natural heat transfer phenomenon involve $Ra \ga 10^{20}$ and thus extrapolations to this high Ra number regime are required. Here we present results from DNS for two-dimensional RBC with $Pr = 1$ in an aspect ratio $\Gamma=D/L=0.23$, where $D$ and $L$ are the width and height of the box, respectively and achieve $Ra$ up to about $10^{13}$. For $Ra<1\times10^{10}$ the Nusselt number varies nearly as the $1/3$ power of $Ra$. However, for $Ra>1\times10^{10}$ we find a sharp transition towards a regime where the Nusselt number varies nearly as the $1/2$ power of $Ra$. A visualization of the simulation results reveals that the transition in the $Nu$ number scaling are caused by a break-up of the large scale structures that are observed at lower $Ra$ numbers. [Preview Abstract] |
Sunday, November 21, 2010 9:18AM - 9:31AM |
AH.00007: A low dimensional model for Rayleigh-Benard convection in rectangular domains Jorge Bailon-Cuba, Joerg Schumacher A low dimensional model ({\bf LDM}) for Rayleigh-B\'enard ({\bf R-B}) convection in rectangular boxes, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from Proper Orthogonal Decomposition ({\bf POD}) of the field using the Snapshot Method. The most energetic {\bf POD} modes give us a hint on the dynamic dominance of coherent flow patterns, and how well the original inhomogeneous flow can be modeled with a reduced number of modes. A quadratic non-homogeneous {\bf ODE} system is obtained for the evolution of the modal amplitudes. A solution which considers the additional dissipation due to the neglected less energetic modes is considered in terms of a parameter $e \ge 0$, fixed at a value where the ensemble average of the total viscous and thermal dissipation in the model is the same as in the full simulation ({\bf DNS}). We discuss first results of the evolution of the {\bf LDM} and compare it with the {\bf DNS} data of the {\bf R-B} problem. [Preview Abstract] |
Sunday, November 21, 2010 9:31AM - 9:44AM |
AH.00008: Measuring the departures from the Boussinesq approximation in Rayleigh-B\'{e}nard convection experiments H\"{u}seyin Kurtuldu, Michael Schatz, Konstantin Mischaikow Algebraic topology (homology) is used to characterize quantitatively non-Oberbeck-Boussinesq (NOB) effects in weakly turbulent Rayleigh-B\'{e}nard convection patterns from laboratory experiments. For fixed parameter values, homology analysis yields a set of Betti numbers that can be assigned to hot upflow and, separately, to cold downflow in a convection pattern. Analysis of data acquired under a range of experimental conditions where NOB effects are systematically varied indicates the difference between time-averaged Betti numbers for hot and for cold flow can be used as an order parameter to measure the strength of NOB-induced pattern asymmetries. This homology-based measure not only reveals NOB-effects that Fourier methods and measurements of pattern curvature fail to detect, but also permits distinguishing pattern changes caused by modified lateral boundary conditions from NOB pattern changes. These results suggest a new approach to characterizing data from either experiments or simulations where NOB effects are expected to play an important role. [Preview Abstract] |
Sunday, November 21, 2010 9:44AM - 9:57AM |
AH.00009: Conservative bounds on Rayleigh-B\'enard convection with mixed thermal boundary conditions Ralf Wittenberg In studies of turbulent Rayleigh-B\'enard convection, the potential effects of imperfectly conducting plates bounding the fluid on convective heat transport have been receiving increasing attention. We investigate the influence of boundaries of finite Biot number on variational upper bounds on the Nusselt number as a function of the Rayleigh number, using the background flow method in a formulation that interpolates between the extremes of fixed temperature (perfectly conducting) and fixed heat flux (perfectly insulating) boundary conditions. For finite Prandtl number convection, fixed temperature conditions are a singular limit of the full problem; we discuss this result and extensions to related contexts such as infinite Prandtl number and porous medium convection. [Preview Abstract] |
Sunday, November 21, 2010 9:57AM - 10:10AM |
AH.00010: Generation of vertical convective vortex in the transition from anomalous to normal steady-state convection Albert Sharifulin, Anatoly Poludnitsin This phenomenon was discovered in the framework of experimental attempt[1] to define form of bifurcation curve in enclosed cavity with boulders temperature state of which could slowly deviate from condition of directly from bottom heating. In order to verify the discovered regularity experiment with slow cubic cell inclination form direct form bottom heat position was performed. The transition process from abnormal convection flow(When heated, and therefore more light, fluid moves down) to normal one during bifurcation curve crossing appeared to be completely unexpected and in radical contrast to served one in our 2D calculations and of other authors. The transition process appears as a fast, for 1-2 seconds, the rotation around the vertical axis of the entire mass of fluid filling the cavity. In the presentation the effect theoretical investigations results are discussed. Series of new problems concerned with the effect of existence borders definition and with possibility to control the effect through fluid properties and heat conditions is formulated Possibility of spontaneous vertical convective vortex generation application to atmospheric behavior explanation and to Earth's mantle one is discussed. [1] A.N. Sharifulin, A.N. Poludnitsin A.N., A.S. Kravchuk Laboratory Scale Simulation of Nonlocal Generation of a Tropical Cyclone. Journal of Experimental and Theoretical Physics, 2008, Vol.107, No.6, pp.1090-1093. [Preview Abstract] |
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