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 GU: Convection and Buoyancy Driven Flows II |
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Chair: Charles Doering, University of Michigan Room: Hilton Chicago Marquette |
Monday, November 21, 2005 10:34AM - 10:47AM |
GU.00001: Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Benard convection G. Ahlers, E. Brown, D. Funfschilling, S. Grossmann, D. Lohse Non-Oberbeck-Boussinesq (NOB) effects on the heat flux in strongly turbulent Rayleigh-Benard convection in water are investigated both experimentally and theoretically. In the experiment, the heat current and the temperature at the horizontal mid-plane are measured for three samples of different heights, but constant aspect ratio. For the largest temperature differences the kinematic viscosity and the thermal expansion coefficient due to their temperature dependence vary by more than a factor of two between the top and bottom plates. The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus is no longer valid. Nevertheless, the Nusselt number Nu is only slightly smaller (at most 1.5\%) than in the next larger sample with the same Ra number, where the material constants are still basically height-independent. The Reynolds numbers in the OB and NOB case even agree within experimental precision (2\%). Theoretically, we account for the robustness of Nu and Re with respect to NOB corrections by extending the unifying theory for scaling in thermal convection to the NOB case. The NOB modifications at top and bottom boundary layer turn out to nearly compensate each other, so that the net NOB effects on Nusselt and Reynolds remain minor. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GU.00002: Flow bifurcations in a cubical cavity heated from below at Pr = 130 Dolors Puigjaner, Joan Herrero, Francesc Giralt, Carles Simo Bifurcation diagrams of steady convective flow patterns inside a cubical cavity heated from below and filled with silicone oil (Pr = 130) were determined for adiabatic and perfectly conducting lateral walls. The diagrams were obtained for Rayleigh numbers up to 1.5 10$^{5}$ by means of a parameter continuation procedure based on the Galerkin spectral method. A complete set of basis functions satisfying implicitly all boundary conditions and the continuity equation was used to expand the velocity and the temperature fields. Present results are in agreement with experimental PIV data and visualizations previously reported in the literature for both adiabatic and perfectly conducting lateral walls boundary conditions. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GU.00003: Sidewall effects in mushy-zone convection Steven Roper, Stephen Davis, Peter Voorhees The directional solidification of a two-component melt forming a dendritic mushy zone can lead to convective instabilities in the mush that lead to localized chimneys that in turn can lead to imperfections (freckles) in the solid. We extend present theories to include the presence of ampule sidewalls at which heat is lost. The result is a curved mush-liquid front, solutal/thermal boundary layers at the sides, and altered convective patterns and chimneys. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GU.00004: Ultrasonic Measurement of Thermal Convection in Liquid Gallium Layer Masataka Yoshida, Yuji Tasaka, Yasushi Takeda, Takatoshi Yanagisawa Thermal convection appearing in low Prandtl number fluid layer is investigated experimentally. A container, which has 50 mm height, 200 mm width and 50 mm depth, was filled with liquid gallium, which has Prandtl number 0.03. An instantaneous velocity profile in the fluid layer was measured using Ultrasonic Velocity Profiler (UVP), which can be used for opaque fluid such as liquid metal. The results represent a convective flow pattern, rolls arranging along the longer side of the container, and its temporal fluctuation. There are some situations, where 2, 3 or 4 convection rolls appear, on the visualized convective motion. A variation of the number of rolls is shown by spatio-temporal velocity map. Simultaneous measurement using two ultrasonic transducers represent phase delay on temporal fluctuation of the rolls on the axial direction of the roll. Temporal fluctuation of the temperature measured by thermistor at some points in the fluid layer is compared with that of the velocity profiles measured by UVP. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GU.00005: Bounds on vertical heat transport for infinite Prandtl number Rayleigh-B\'enard convection Charles R. Doering, Felix Otto, Maria G. Reznikoff For the infinite Pandtl number limit of the Boussineq equations, the enhancement of vertical heat transport in Rayleigh-B\'enard convection, the Nusselt number $Nu$, is bounded above in terms of the Rayleigh number $Ra$ according to $Nu \leq .644 \times Ra^{1/3} [\log Ra]^{1/3}$ as $Ra \rightarrow \infty$. This rigorous estimate follows from the utilization of a novel logarithmic profile in the background method for producing bounds on bulk transport together with new estimates for the bi-Laplacian in a weighted $L^2$ space. It is a quantitative improvement over the best currently available analytic result, and it comes within the mild logarithmic factor of the pure 1/3 scaling anticipated by both the classical marginally stable boundary layer argument and the most recent high-resolution numerical computations of the optimal bound on $Nu$ using the background method. [Preview Abstract] |
Monday, November 21, 2005 11:39AM - 11:52AM |
GU.00006: Stratification of a closed region containing two buoyancy sources Andrew Thompson, Paul Linden Many closed systems such as lakes, ocean basins, rooms etc. have inputs of buoyancy at different levels. We address the question of how the resulting stratification depends on the location of these sources. For example a lake is heated and cooled at the surface, while for a room cool air may be applied at the ceiling but the heat source may be a person standing on the floor. We present an experimental study of convection in a finite box in which we systematically vary the vertical location of two well-separated, constant buoyancy sources. We specifically consider the case of a dense source and a light source so that there is no net buoyancy flux into the tank. We study the development of the large-time stratification in the tank, which falls between one of two limits. When the location of the dense source is significantly higher than the light source, the fluid is well mixed and the system remains largely unstratified. When the location of the light source is significantly higher than the dense source, a two- layer stratification develops. We find that the circulation pattern is dominated by counter-flowing shear layers (Wong, Griffiths \& Hughes, 2001), whose number and strength are strongly influenced by the buoyancy source locations. The shear layers are the primary means of communication between the plumes and thus play a large role in the resulting stratification. We support our findings with a simple numerical model. [Preview Abstract] |
Monday, November 21, 2005 11:52AM - 12:05PM |
GU.00007: Stochastic simulations of buoyancy-reversal experiments Scott Wunsch Buoyancy reversal occurs when the mixing of two fluids, initially stably stratified, produces a mixture which is more dense than either pure fluid. The resulting instability generates turbulent mixing, and may play an important role in several geophysical flows. In this work, a simple scaling hypothesis for buoyancy reversal is presented and compared to experimental results. The scaling is used to extrapolate from laboratory-scale flows to natural systems. [Preview Abstract] |
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