Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JJ: Convection and Buoyancy-Driven Flows II |
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Chair: Guenter Ahlers, University of California, Santa Barbara Room: Salt Palace Convention Center 250 D |
Monday, November 19, 2007 3:35PM - 3:48PM |
JJ.00001: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 3:48PM - 4:01PM |
JJ.00002: Scaling of the local convective heat flux in turbulent Rayleigh-B{\'e}nard convection Penger Tong, Xiao-Dong Shang, Ke-Qing Xia Local convective heat flux $J(r)$ in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in a cylindrical cell filled with water. The measured $J(r)$ at different locations in the convection cell is found to scale with the Rayleigh number Ra as $J( r) \sim Ra^{\beta}$. The scaling exponent $\beta$ at the cell center far away from the cell boundaries is found to be $\beta\simeq 0.5$, in agreement with the Kraichnan scaling for the ultimate state of thermal convection. Near the sidewall and lower conducting plate, we find $\beta\simeq 0.24$. The experiment thus provides new insights into the mechanism of heat transport in turbulent convection. \newline \newline *Work supported by the Research Grants Council of Hong Kong SAR. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JJ.00003: Patterns in rotating Rayleigh-Benard convection at high rotation rates Patricia Mutyaba, Terri Kimmel, Janet Scheel We present the results from numerical investigations of rotating Rayleigh-Benard convection for relatively large rotation rates, well above the Kuppers-Lortz instability. Unexpected square patterns were found experimentally by Bajaj, et al., in this parameter regime. These square patterns have not yet been understood theoretically. Sanchez-Alvarez, et al., have found square patterns in numerical simulations for similar parameters when only the Coriolis force is included. We present detailed numerical studies of rotating Rayleigh-Benard convection for the same parameters as the experiments. To better understand the square patterns, we compare the effects of the Coriolis force as well as the centrifugal force. We also investigate the influence of the travelling wave on the patterns. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JJ.00004: Bifurcations of free thermal vibrational convection in cylindrical fluid layer in micro-gravity numerical and analytical research Albert Sharifulin The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to the vibrations. With this aim the theoretical investigation for infinite plane and cylindrical fluid layers are performed. We investigated simple case of the fluid response-thermal vibrational convection in a cylindrical fluid layer with rigid conducting boundaries. It is found that steady modes of thermal vibrational convection are subjected to various bifurcations. Bifurcations cause sharp changes in heat transfer. The Lorenz model is generalized (GLM) and used to conduct the analysis of bifurcations caused by the changing of the cavity shape and vibrational Rayleigh number. The shape of steady-state surface in 3D space of the streamfunction of mean flow, vibrational Rayleigh number and the cavity curvature is found. The numerical 2D solution is performed for plane and cylindrical fluid layers. The results of the analysis based on the GLM model are compared with the data obtained by direct numerical simulation. The bifurcation curve with extremum is found. Thus, bifurcations of complex shape could be observed. Comparisons with space experiments and its discussions are presented. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JJ.00005: Five-mode model of thermal vibrational convection in a cold water near its density maximum Vadim Sharifulin, Dmitri Lyubimov Thermal vibrational convection in a fluid with temperature inversion of density, e.g. the cold water near its density maximum is studied. High frequency vibration case is considered. Equations for average and pulsation components of the velocity and temperature field are derived by averaging method. Linear stability of a conductive state of cold water in a horizontal layer with rigid conductive boundaries subjected to the vertical vibrations is analyzed. The Lorenz-like five-mode dynamical system is constructed for the investigation of non-linear behavior of the fluid. The diagram of the existence of different regimes (conductive state, single-layer and double-layer steady flows, chaotic regimes) in the parameter space is obtained. It is found that, similar to the case of usual fluid with linear temperature dependence of density, absolute stabilization is observed under strong enough vibrations, moreover, the closer the point of temperature inversion of the density to the layer midplane the lower vibration intensity is needed to achieve the absolute stabilization. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JJ.00006: Experimental investigation of the transition to spatiotemporally chaotic convection with a system-size control parameter. Dan Spiegel We employ soft-boundary electroconvection experiments with a system size that is controlled by modest laser heating to examine how the onset of spatiotemporal chaos (STC) depends on the size of the system. The experiment was motivated by recent computer simulations showing that Ginzburg-Landau STC is composed of definite interacting building blocks whose presence and size can be measured when the system size is only large enough to contain two or three building blocks. When we Fourier transform along the time axis of our spacetime diagrams for different system sizes, it becomes clear that temporal periodicity, averaged over spatial positions, is strongly quenched as the system size increases. The loss of temporal periodicity can be monitored quantitatively by measuring the fourth moment (kurtosis) of the temporal power spectra. From the kurtosis measurements one may then extract a natural chaotic length scale for the STC. We employ this length scale to attempt to determine the physical characteristics of the fundamental STC building blocks. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JJ.00007: Isothermal buoyancy instabilities due to an A+B $\rightarrow$ S reaction in a Hele-Shaw cell P. Trevelyan, Y. De Decker, A. De Wit We investigate theoretically the conditions necessary to trigger buoyancy-driven convection in a Hele-Shaw cell when two solutions containing separate reactants A and B are brought in contact. The initial density stratification is statically stable. We show that a simple isothermal A+B $\rightarrow$ S chemical reaction can induce nonmonotonic density profiles in the course of time which then lead to buoyancy-driven convective instability. As the base state is time dependent, we perform linear stability analysis of the problem using a quasi-steady state approximation to predict which regions of the parameter space spanned by diffusion coefficient ratios and Rayleigh numbers will have unstable reaction fronts. Full non-linear simulations are used to verify the predictions. A useful guide to the instability is provided by approximating the density profile by its large time analytical asymptotic limit. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JJ.00008: Convective chimney formation in a mushy layer: experiments, simulations and theory Richard Katz, Grae Worster Laboratory experiments on directional solidification of aqueous ammonium chloride in a Hele-Shaw cell produce a convectively unstable, partially crystalline mushy layer. Within this layer, reactive flow of buoyant fluid creates chimneys of zero solid fraction. We have investigated the development of chimneys with new, time-dependent, computational simulations of directional solidification. These simulations employ the Enthalpy method coupled with Darcy's law to describe the thermodynamics and fluid mechanics of the system. A comparison between simulations and experimental results raises questions about the mode of instability that leads to chimney formation: do chimneys originate from disturbances at the mush-liquid interface and grow downwards or are they the product of an instability within the mushy layer? Is there a clear distinction between these two modes? To address this question we consider a hydrodynamic stability analysis of the system, substituting the Darcy-Brinkman equation for Darcy's law. This allows for a flexible choice of permeability functions. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JJ.00009: Convective instabilities of ternary mixtures in thermogravitational columns Abdelfattah Zebib Convective instabilities in side heated infinite vertical slots containing a single fluid are stationary, shear driven when the Prandtl number $Pr<12.5$ while they are oscillatory, buoyancy dominated with $Pr>12.5$ due to the diminished influence of the thermal diffusivity with increasing $Pr$. Here we examine the influence of the concentration field generated by thermodiffusion in a ternary mixture of otherwise uniform concentration on this phenomenon. We first derive expressions and calculate the basic steady one-dimensional flow taking into account the vertical concentration gradients caused by thermodiffusion. Linear stability of this basic state is performed and the critical Rayleigh number, wavenumber, frequency, and vertical concentration gradients are determined as function of the two separation ratios, ratio of thermal expansivities, four Lewis numbers, and $Pr$. The results are in agreement with the base flow of the ternary mixture considered by Leahy-Dios et al., J. Chem. Phys. (2005). Stability results are in agreement with those from a simplified model in the long wave approximation as well as when restricted to binary mixtures. Stability restrictions on the operation of the thermogravitational column will be discussed. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JJ.00010: New spatio-temporal instability scenarios in non-Boussinesq mixed convection Sergey A. Suslov Mixed convection flows in a tall vertical channel with differentially heated walls subject to large cross-channel temperature gradients are shown to exhibit enormous variety of instability scenarios which have two physically distinct origins: the shear and the buoyancy of the flow. In order to visualize the most typical spatio-temporal patterns and complement previous analytical stability studies the Fourier integrals representing linearised disturbances arising from an initially localised source are evaluated numerically. The disturbance fields are obtained for strongly non-Boussinesq high-temperature convection of air. They are contrasted to their counterparts in the Boussinesq limits of small temperature gradients. A drastic difference in disturbance evolution scenarios is found. In particular, it is shown that non-Boussinesq natural convection is convectively unstable while mixed convection flows can be absolutely unstable. These scenarios are opposite to the ones detected in the classical Boussinesq convection in the same geometry. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JJ.00011: An experimental study of kicked thermal turbulence Ke-Qing Xia, Xiaoli Jin We present an experimental study of turbulent thermal convection when the input energy that drives the turbulent flow is in the form of periodical pulses. It is found that in this ``kicked'' thermal turbulence the heat transfer efficiency is enhanced compared to the case of constant energy input. It is further found that the shape the input pulse has a strong effect on heat transport enhancement, spiky pulses produce larger enhancement of the Nusselt number Nu than tubby pulses of the same energy and that for sinusoidally modulated heating input no Nu enhancement is found. For appropriate ranges of the kicking strength $A $and kicking frequency $f$, the Rayleigh number \textit{Ra}($t)$ is found to reach a saturation level that scales as the product of (\textit{Af}), thus confirming the mean-field theory for kicked turbulence proposed by Lohse. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JJ.00012: Experimental study of instability patterns in a non- uniformly heated Rayleigh-B\'{e}nard-Poiseuille cell Emeric Grandjean, Navid Borhani, Peter A. Monkewitz The effect of non-uniform heating on the convective roll patterns in a Rayleigh-B\'{e}nard-Poiseuille system of large transverse aspect ratio has been studied experimentally. The influence of the lateral walls has been further reduced by keeping a strip adjacent to each side wall well below critical, thus providing a ``sponge region'' for the roll patterns. The study consisted of three parts: Firstly, the transition between the convective and the absolute instability of the transverse rolls was determined with uniform heating of the channel bottom. Secondly, the impulse response of the uniformly heated system was determined by applying a spatially localized thermal pulse to a uniform sub-critical base flow. Thirdly, the effect of spatially non-uniform, but temporally steady heating upon the roll dynamics was studied. These experimental results will be compared to the theoretically expected response of the system [JFM, \textbf{502}, 175 (2004)]. [Preview Abstract] |
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