Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KU: Convection and Buoyancy Driven Flows IV |
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Chair: Andreas Haselbacher, University of Illinois at Urbana-Champaign Room: Hilton Chicago Marquette |
Monday, November 21, 2005 4:10PM - 4:23PM |
KU.00001: Test of the steady-state fluctuation theorem in turbulent Rayleigh-B{\'e}nard convection Penger Tong, Xiaodong Shang, Keqing Xia Local entropy production rate $\sigma({\bf r},t)$ in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. The statistical properties of the time-averaged $\sigma({\bf r},t)$ are analyzed and the results are compared with the predictions of the steady state fluctuation theorem (SSFT) of Gallavotti and Cohen. The experiment reveals that the SSFT can indeed be extended to the local variables, but further development is needed in order to incorporate the common dynamic complexities of far-from-equilibrium systems into the theory. *Work supported by the Research Grants Council of Hong Kong SAR under Grant Nos. HKUST603504 (P.T.) and CUHK403003 (K.Q.X.). [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KU.00002: Structure of thermal and velocity boundary layers in turbulent thermal convection Andre Thess, Ronald du Puits, Christian Resagk, Friedrich Busse, Andreas Tilgner We report a series of experimental investigations of the
structure of thermal and velocity boundary layers in turbulent
Rayleigh-Benard convection. Our measurements are conducted
for Rayleigh numbers $10^8 |
Monday, November 21, 2005 4:36PM - 4:49PM |
KU.00003: The Reynolds number of the large-scale circulation in turbulent Rayleigh-Benard convection Denis Funfschilling, Eric Brown, Alexei Nikolaenko, Guenter Ahlers We measured Reynolds numbers $R_e$ of the large-scale circulation of turbulent Rayleigh-B\'enard convection over the Rayleigh-number range $2\times 10^8 \alt R \alt 10^{11}$ and Prandtl-number range $3.3 \alt \sigma \alt 29$ for cylindrical samples of aspect ratio $\Gamma = 1$. For $R \alt R_c \simeq 3times 10^9$ we found $R_e \sim R^{\beta_{eff}}$ with $beta_{eff} \simeq 0.46 < 1/2$. Here both the $\sigma$- and $R$- dependences are quantitatively consistent with the Grossmann- Lohse (GL) prediction. For $R > R_c$ we found $R_e = 0.106~ sigma^{-3/4} R^{1/2}$, which differs from the GL prediction. The relatively sharp transition at $R_c$ to the large-$R$ regime suggests a qualitative and sudden change that renders the GL prediction inapplicable. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KU.00004: Complex patterns in rotating Rayleigh-B\'{e}nard convection. Eric Serre, Jos\'{e}-Joaquim Sanchez-Alvarez, Emilia Crespo del Arco, Friedrich Busse Flows induced by thermal buoyancy in rotating systems play an important role in many industrial processes as well as in numerous problems in geophysical and astrophysical fluid dynamics. Thermal convection in a horizontal fluid layer heated from below and rotating about a vertical axis has also become a prime example in theories of pattern formation and of the transition to spatio-temporal chaos. The K\"{u}ppers-Lortz instability occurs in a rotating Rayleigh-B\'{e}nard convection and is a paradigmatic example of spatiotemporal chaos [G. K\"{u}ppers and D. Lortz, J. Fluid Mech. 35, 609 (1969)]. Surprisingly and contrary to this established scenario, Bajaj et al. 1998 [K. Bajaj, et al., Phys. Rev. Lett. 81 (1998)] observed experimentally in a cylinder square patterns in the range of parameters where K\"{u}ppers-Lortz instability was expected. In this work we study numerically square patterns properties by taking into account realistic boundary conditions. The Navier-Stokes and heat transport equations have been solved in the Oberbeck-Boussinesq approximation using an efficient pseudo-spectral technique. All the characteristics of the pattern show that it appears when the flow is laterally confined. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KU.00005: Re-orientations of the large-scale circulation in turbulent Rayleigh-B{\'e}nard convection Eric Brown, Alexei Nikolaenko, Guenter Ahlers We present measurements of the orientation $\theta_0(t)$ of the large-scale circulation (LSC) of turbulent Rayleigh-B{\'e}nard convection in cylindrical cells of aspect ratio 1. The orientation undergoes irregular reorientations. It contains two types of reorientation events to be called rotation and cessation. Rotation through angles $\Delta \theta$ has a monotonically decreasing probability distribution $p(\left| \Delta \theta \right|) \propto \left| \Delta \theta \right|^{- \gamma}$ with $\gamma \simeq 4$ reminiscent of heavy-tail distributions in many other systems. Cessations involve a brief vanishing of the LSC, followed by a new spontaneous re- organization of the LSC with a randomly chosen new orientation. Thus the probability distribution for cessation is uniform: $p( \left| \Delta \theta \right|) = 1/\pi$. Both rotations and cessations have Poissonian statistics in time. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KU.00006: Convectons Edgar Knobloch, Oriol Batiste Simulations of $^3$He-$^4$He mixtures with a negative separation ratio in two-dimensional containers, heated from below, with realistic boundary conditions and moderately large aspect ratio reveal, at supercritical Rayleigh numbers, the existence of 'convectons', i.e., localized states of stationary convection, separated by regions of no convection (O. Batiste and E. Knobloch, Phys. Fluids 17, 064102, 2005). These states exist over a well-defined range of Rayleigh numbers, and different numerically stable convectons may exist at fixed parameter values. When the Rayleigh number is reduced the convectons shrink by eliminating rolls at the edges; if the Rayleigh number is reduced too far no stable convectons are present and the convecton decays to the conduction state before a new convecton regrows in its place. Similar behavior occurs with periodic boundary conditions in the horizontal. The origin and properties of these states will be described. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KU.00007: Organized flow structures is turbulent thermal convection Chao Sun, Ke-Qing Xia, Penger Tong The technique of particle image velocimetry is used to study the velocity field in turbulent Rayleigh-B\'{e}nard convection in an aspect-ratio-1 cylindrical cell filled with water. By measuring the 2D velocity vector map in different cross-sections of the cell, we investigate the 3D flow structures and dynamics of the synchronized plume motions. The experiment reveals how thermal plumes synchronize their emissions and organize their motions spatially between the top and bottom plates, which generate highly coherent velocity oscillations in the entire convection box. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KU.00008: Local temperature fluctuations in turbulent Rayleigh-B{\'e}nard convection with wide-ranging aspect ratios Ke-Qing Xia, Chao Sun, Li-Yuan Ren We report measurements of the local temperature fluctuations in 1-meter diameter cylindrical convection cells with aspect ratio $\Gamma$ ranging from 0.67 to 20 and the Rayleigh number Ra varying from 10$^7$ to 4$\times$10$^{12}$, at the Prandtl number Pr $\approx$ 4.3. Measurements are made at both cell center and the sidewall positions. The results show that the normalized temperature rms has a power-law dependence on Ra for all positions and aspect ratios, i.e. $\sigma/\Delta T\sim$ Ra$^{\alpha}$, where $\Delta T$ is the temperature difference across the convection cell. It is found that for sidewall positions $\alpha$ is approximately the same for most values of $\Gamma$, while it generally increases with $\Gamma$ for the center positions. We also found that the magnitude of the normalized temperature rms at both the center and sidewall is approximately the same for large $\Gamma$ ($\agt$ 10), while for small values of $\Gamma$ the sidewall fluctuations are roughly a factor of 2 larger than the center ones. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KU.00009: Azimuthal Motion of the Mean Wind in Turbulent Thermal Convection Heng-Dong Xi, Quan Zhou, Ke-Qing Xia We report an experimental study of the azimuthal motion of the circulation plane of the mean wind in turbulent Rayleigh-B{\'e} nard convection in water. Measurements were made in both aspect ratio $\Gamma = 1$ and $0.5$ cylindrical cells. The results show that for $\Gamma = 1$ the orientation of the wind fluctuates over an azimuthal angular range of $\sim \pm 100$ degrees about a preferred direction for over 90$\%$ of the time. In contrast, for $\Gamma =0.5$ the orientation of the wind shows no preferred direction. For $\Gamma = 1$ the observed azimuthal motion of the wind is a superposition of a periodic oscillation in short timescale and chaotic fluctuation in longtime scale. For both $\Gamma =$ 1 and 0.5 the apparently stochastic azimuthal motion of the wind generates a net-rotation on average, with the $\Gamma =$ 0.5 cell having a much larger net-rotation rate. Measurements with varying values of the Rayleigh number Ra is made for the $\Gamma =0.5$ case, and it is found that the net rotation rate diminishes with increasing Ra, reaching a vanishing value around $Ra = 1\times 10^{11}$. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KU.00010: Turbulent Thermal Convection in Liquid Sodium Kaveri Joshi, Daniel Lathrop, K.R. Sreenivasan We investigate heat transport in a low Prandtl number (Pr=0.0096) fluid in a cylindrical cell of aspect ratio $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ heated from below. We measure temperature fluctuations and velocity (using ultrasonic velocimetry). In this talk we will discuss the velocity and heat flux dependence on temperature drop. We will also present measurements of plate temperature fluctuations stemming from the large fluid thermal conductivity relative to that of the plate. [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KU.00011: Entropy cascade and Bolgiano-Obukhov scaling in turbulent thermal convection Emily S.C. Ching, W.C. Cheng It is interesting to understand the scaling behavior of velocity and temperature fields in turbulent thermal convection. Theoretical ideas suggest Bolgiano-Obukhov scaling when the turbulent dynamics are governed by a cascade of entropy. On the other hand, there were experimental and numerical studies of confined convection which showed results that are inconsistent of Bolgiano-Obukhov scaling. To help shedding light on this issue, we have studied a shell model of turbulent convection whose stationary dynamics are, by construction, governed by a cascade of entropy when buoyancy is significant. We have indeed observed Bolgiano-Obukhov scaling plus corrections. We have further found that the corrections are due to intermittent variations of the entropy transfer rate. By assuming that the moments of the entropy transfer rate have a hierarchical structure, we are able to understand the observed scaling behavior and predict the velocity and temperature scaling exponents. [Preview Abstract] |
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