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 NU: Convection and Buoyancy Driven Flows VI |
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Chair: Guenter Ahlers, University of California, Santa Barbara Room: Hilton Chicago Marquette |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NU.00001: 2D Chaotic Mixing with Natural Convection Luis M. de la Cruz, Eduardo Ramos In this work chaotic mixing inside a two dimensional cavity achieved with time dependent natural convection is investigated. The motion of flow is induced by imposing alternating hot and cold temperatures on opossite walls, with this set up no moving walls are required to mix the fluid inside the container. This idea is illustrated by numerically solving the governing equations of natural convection in a two dimensional square cavity with sections of its upper and lower horizontal walls cooled and heated in a periodic manner. These conditions generate a vortex of time dependent intensity that moves its center in a closed loop around the geometrical center of the container. The mixing properties of the flow are visualized by Lagrangian tracking of a collection of points located in arbitrary positions inside of the domain. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NU.00002: Localized Resonances due to Spatial Forcing Jonathan McCoy, Will Brunner, Werner Pesch, Eberhard Bodenschatz Periodic forcing provides a basic tool for probing the response of a spatially extended system to changes in its external environment. We report experimental results on spatially periodic forcing of thermally driven convection in a large aspect ratio fluid layer. This system displays a number of two-dimensional resonant pattern formation phenomena in which the system spontaneously breaks a symmetry in order to accommodate the forcing. A novel form of spatiotemporal chaos, consisting of localized resonance structures which mediate the transition from forced straight rolls to the generic state of spiral defect chaos, will be the focus of this presentation. This work is supported by the National Science Foundation under grant no. DMR-0305151 and by the Max Planck Society. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NU.00003: Rise Heights of Lazy Fountains Gary Hunt, Nigel Kaye The initial rise height $z_m$ of turbulent Boussinesq fountains is determined analytically for small and large source Froude numbers $Fr_0$. Solutions were obtained after recasting the plume conservations equations of Morton, Taylor \& Turner (1956) in terms of the inverse square of a local Froude number and a local dimensionless fountain width. For large $Fr_0$, the fountain is `forced' and the well-established linear increase of the rise height with $Fr_0$ is obtained, i.e. $z_m/r_0 \sim Fr_0$; $r_0$ denoting the source radius. However, for small $Fr_0$ the fountain is `lazy' and the dependence $z_m/r_0 \sim Fr_0^2$ more sensitive. Additionally, the rise height for lazy fountains is predicted to be independent of the entrainment coefficient $\alpha$. Comparison of our solutions with existing experimental and numerical results of fountain rise height, as well as with our own experimental results, show good agreement and support the derived scalings. Experimental results suggest that the entrainment coefficient for highly-forced fountains is $\alpha_f\approx0.058$, i.e. closer to that of a jet than of a plume. \\ Morton, B. R., Taylor, G. I. \& Turner, J. S. (1956), ‘Turbulent gravitational convection from maintained and instantaneous sources’, \it{Proc. Roy. Soc. A} \textbf{234}, 1–23. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NU.00004: Chaos near the onset of electroconvection of a homeotropic nematic liquid crystal Sheng-Qi Zhou, Guenter Ahlers We report on shadowgraph measurements of spatio-temporal chaos patterns of electro-convection in the homeotropically aligned nematic liquid crystal MBBA. The cell had a thickness of $27$ $\mu\rm m $ and a conductivity of $7.3\times10^{-8}\, (\Omega\,{\rm m})^{- 1}$. An AC voltage of amplitude $V$ and frequency $f$ with $20 \leq f \leq 200$ Hz was applied orthogonal to the cell plane. We found oblique (normal) rolls for $f < f_L$ ($f > f_L$) with $f_L \simeq 75$ Hz. From the structure factor (square of the modulus of the Fourier transform) of the images we determined a correlation length $\xi$ (inverse half-width) and maximum $S_0$. For small $\epsilon \equiv V^2/ V_c^2 -1 > 0$ fits of power laws to the results for $\xi$ ($S_0$) yielded an exponent smaller (larger) than that predicted from Ginzburg-Landau equations. The departure from theory is similar to that found previously for domain chaos in rotating Rayleigh-Benard convection\footnote{Y. Hu, R. E. Ecke and G. Ahlers, Phys. Rev. Lett. {\bf 74}, 5040 (1995).} and recent electro-convection measurements in a planar nematic liquid crystal.\footnote{X.-C. Xu and G. Ahlers, unpublished.} [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NU.00005: Homological Characterization of Spiral Defect Chaos Michael Schatz, Marcio Gameiro, Konstantin Mischaikow, Kapil Krishan, Santiago Madruga, Hermann Riecke Relating the global structure of patterns to underlying dynamics is an important aspect of the study of complex systems. We use the mathematics of homology to characterize data from laboratory experiments and numerical simulations of spiral defect chaos, a weakly turbulent state of Rayleigh-Benard convection. We note observations implying asymmetries between hot and cold flows, novel measures of boundary influence and indicators of system control parameters. We also find the evolution of the global structure of the flow to be primarily stochastic unlike the locally chaotic signatures reported previously. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NU.00006: Anchoring entrained tendrils in thermally convecting stratified fluids Laura Schmidt, Wendy Zhang When two stratified, miscible fluid layers undergo vigorous thermal convection, a thin tendril of one fluid can become entrained in the other. A typical tendril is anchored to the interface at one spot and can persist for long times [1]. The persistence of these tendrils may be related to the mechanism anchoring stationary hotspots in the Earth's mantle. We devised a simple model to examine the steady-state entrainment dynamics. The thermal convection is approximated by an axial straining flow and a long-wavelength model is constructed for the flow pattern and tendril profile. Analytical work on asymptotic solutions and their stability leads to conditions on the form of acceptable solutions. We find that to anchor a long-lived tendril, the interface must take the shape of a power-law cusp near the base of the tendril. Even without surface tension, such a cusp shape cannot be produced by only a weak deflection of the interface. [1] Jellinek and Manga, Rev. Geophys., 42, No. 3, RG3002 (2004). [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NU.00007: Turbulent structure beneath water surface during natural convection Kamran Siddiqui, Syed Junaid Bukhari Natural convection is an important phenomenon observed in a coupled air-water system during which the water surface undergoes evaporative cooling. A better knowledge of the flow structure is important in order to improve our understanding of the physical mechanisms that control the air-water heat exchange during this process. We report on a series of laboratory experiments conducted to investigate the near-surface flow structure beneath water surface during natural convection. The measurements were made at different magnitudes of the air-water heat flux. The results have shown that the flow field undergoes different flow interactions locally, which forms complex flow structure. Results have also shown that the turbulent velocity profiles are self-similar and that the scaling parameters developed for the natural convection above a heated wall are also applicable to the natural convection below an evaporative water surface. The interaction of the turbulent motions with the buoyancy forces will also be discussed. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NU.00008: WITHDRAWN: Similarity solution of free convection in a stratified porous medium with internal heat generation Ali Kalantarian, Morteza Khodabakhsh In this paper, free convection from inclined permeable wall embedded in a stratified porous medium is investigated. To achieve similarity solution, the internal heat generation is a linear function of X. It is assumed that the heated wall has constant temperature and permeability along the wall is variable. Because of the application in oil reservoir, Darcy's law as momentum equation has been used. To apply similarity solution, only large wall inclination angle have been considered. Effects of mass flux, permeability function, and inclination angle on thermal and velocity boundary layer thickness and heat transfer at the wall are investigated. Also, results are compared with the case without heat generation. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NU.00009: Counterpropagation and amplitude modulation of rolls in a broken-symmetry electroconvection experiment Dan Spiegel, Elliot Johnson, Skyler Saucedo We report a liquid-crystal electroconvection pattern-formation experiment along a narrow strip in which the translational symmetry is broken with a laser-induced thermal gradient. In contrast with other broken-symmetry patterns that display a uniform drift, we observe rolls that counterpropagate into a sink point and a strong temporally periodic amplitude modulation near this point. The time dependence of the amplitude at a fixed position is periodic but not sinusoidal. On the basis of experimental spacetime contours and wavenumber profiles, along with a measurement of the change in the roll-drift frequency with applied voltage at a fixed control parameter, we propose a simple qualitative model based on (1) the enhancement of thermal transport due to advection, and (2) a hyperbolic-tangent solution to the Ginzburg-Landau equation that is relevant near the Eckhaus boundary. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NU.00010: Stability Analysis of a natural circulation flow loop under supercritical condition Rachna Jain, Michael Corradini The stability of natural circulation flow loop geometry is under investigation in a specific thermo-dynamic region that encompasses the supercritical temperatures and pressures. This flow configuration is pertinent to the design of passive safety systems in some innovative reactor designs proposed for future generations of water-cooled nuclear reactors. Earlier studies employing both transient and linear stability approach considered supercritical natural circulation flow loop systems having a semi-closed boundary condition which required only the continuity in the pressure of the system around the loop. This is only true for loops that are connected to a large reservoir which theoretically can absorb any fluctuations in the flow velocity or temperatures and thus keep the inlet conditions fixed. A more realistic approach considered in the present study where a periodic boundary condition is imposed for such systems and requires continuity in the pressure, temperature and velocity as an essential boundary condition. With a highly non-linear equation of state specific to supercritical fluid and periodic boundary condition, the stability of this flow system is mathematically challenging to analyze. [Preview Abstract] |
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