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 FL: Convection and Buoyancy Driven Flows I |
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Chair: Abdelfattah Zebib, Rutgers University Room: Hilton Chicago Astoria |
Monday, November 21, 2005 8:00AM - 8:13AM |
FL.00001: Steady-state propagation of gravity currents into a linearly stratified ambient: a generalization of Benjamin's results Marius Ungarish The classical results of Benjamin (J. Fluid. Mech. vol. 31, 1968) concerning the propagation of a steady gravity current into a homogeneous ambient fluid, are generalized to the case of a stratified ambient fluid. The current of thickness $h$ and density $\rho_c$ propagates, with speed $U$, at the bottom of a long horizontal channel of height $H$, into the unperturbed ambient fluid whose density increases linearly from $\rho_o$ to $\rho_b$. The reduced gravity is $g' = (\rho_c/ \rho_o -1)g$ and the governing parameters are $a = h/H$ and $S = (\rho_b-\rho_o)/(\rho_c-\rho_o)$, with $0 [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FL.00002: Convection in Binary Mixures with Negative Soret Effect Valentina Shevtsova, Denis Melnikov, Jean-Claude Legros Double diffusive convection in a cubic cell filled with a binary mixture of water and isopropanol is numerically analyzed. The system is heated from above while the Soret coefficient, i.e. thermodiffusion, is negative. Negative Soret effect corresponds to component separation in binary mixtures with the denser component migrating to the hot wall. In the case of heating from above density stratification is stable in a pure liquid. However in the case of a binary mixture with negative Soret effect unstable density stratification is established in the system. Due to negative Soret effect the heavier liquid is accumulated on the top of the lighter one. At some moment this unstable stratification leads to the appearing of motion in the liquid volume. 3D numerical simulations of the non-linear time-dependent Navier-Stokes, heat and mass transfer equations were performed. The parameters of the system correspond to a realistic binary mixture enabling comparison of theoretical predictions with planned experimental studies; Schmidt and Prandtl numbers are Sc=1620, Pr=10.85. The development of fluid motion in space and time is analyzed to identify the underlying physical mechanisms leading to instability. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FL.00003: Double diffusive instabilities of chemical fronts A. Zebib, J. D'Hernoncourt, A. De Wit Gravitational Hele-Shaw fingering of an autocatalytic reaction diffusion interface is investigated theoretically. Dimensional analysis based on reaction diffusion length, time, and velocity scales reveal the dependence on the Lewis number $Le$, and thermal and concentration Rayleigh numbers $R_T$ and $R_c$. Linear stability analysis of a planar upward propagating (against the gravitational acceleration) interface results in an eigenvalue problem for each wavenumber $k$ which we solve using a Chebyshev pseudospectral method. A novel light over heavy instability of an endothermic reaction was found when $Le>1$. It is shown that this instability is equivalent to that of a downward propagating exothermic wave. Nonlinear second-order Crank-Nicolson, finite volume simulations are in agreement with linear theory and also show the docile nature of the interface breakup. A displaced particle argument confirms that this unexpected instability is local, that it is subdued by a region of local stability, and elucidates its dependence on the underlying reaction diffusion mechanism. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FL.00004: Traveling circular waves in rotating convection A. Rubio, J.M. Lopez, F. Marques Boussinesq convection in a rotating circular cylinder is investigated numerically. For low Raleigh numbers, a steady wall mode is established which develops into a steady cellular target pattern (circular waves) on increasing the Raleigh number (analogous to the onset of Taylor cells from endwall vortices as the Reynolds number is increased). Beyond a critical Raleigh number, the circular waves begin to drift radially inward. Centrifugal buoyancy (nonzero Froude number) effects play an important role in this flow. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FL.00005: The effects of stochastic gravity modulation on fluid mixing V.K. Siddavaram, G.M. Homsy We study the effects of zero-mean stochastic gravity modulation on the mixing characteristics of two miscible fluids initially separated by a thin diffusion layer. Both correlated and uncorrelated gravity modulation are considered and the 2D time-dependent Boussinesq equations are solved numerically. The flow is characterized by a Grashof number, $Gr=\frac{\Delta\rho}{\bar{\rho}}g\frac{l^{ 3}_{\nu}}{\nu^{2 }}$, based on the viscous length scale, $l_{\nu}=\sqrt{\nu/\omega}$, where $\omega$ is a frequency defined through the power spectrum; the Schmidt number, $Sc$; and geometric aspect ratios. We vary $Gr$, holding the other parameters constant, and study the evolution of the interface. For both correlated and uncorrelated jitter, the ensemble averages of realizations exhibit dispersive spreading of the interface at a rate which is amplified by $Gr$, and which is larger for correlated jitter. Individual realizations exhibit the formation of folds, which are more pronounced in the case of correlated jitter. Many of the phenomena occurring for deterministic jitter also occur in the stochastic case, but at a lower equivalent $Gr$. Accordingly, the rate of mixing for stochastic jitter is higher than that for deterministic harmonic jitter. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FL.00006: Influence of Richardson number on the ejection of a miscible contaminant from a rectangular cavity by an incoming fully turbulent overflow George Constantinescu, KyoungSik Chang, Seung-O Park The 3D flow past a rectangular shallow cavity is investigated using LES. The flow upstream the cavity is fully turbulent. The unsteady purging mechanism corresponding to ejection of a neutrally buoyant (Richardson number, Ri=0.0) and of a dense miscible contaminant (Ri=0.2) introduced instantaneously inside the cavity is studied. In the non-buoyant case it is shown that along with the engulfment of high concentration fluid by the large scale vortices in the separated shear layer, the coherent structures convected from the near wall region of the channel upstream the cavity can play an important role in accelerating the extraction of contaminant from cavity. In the buoyant case, after the initial stages of the mixing, a sharp density interface is observed whose oscillations are playing a major role in the entrainment process. The main phenomenon is the presence of an internal wave of relatively high amplitude which interacts with a strong recirculation eddy inside the cavity situated near the trailing edge corner. Through this interaction the denser contaminant is extracted from the region beneath the internal wave where it is concentrated. The process is similar even after the density interface starts interacting with the cavity bottom. The period of the internal wave oscillations is found to increase in time. Global diffusion coefficients are estimated for the different mass exchange regimes observed in the simulations. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FL.00007: Two-Dimensional Viscous Exchange Flows Gary P. Matson, Andrew J. Hogg We consider two fluids that are confined in a horizontal, two dimensional channel of fixed height and are initially separated by a thin, vertical lock. The lock gate is instantaneously removed and due to the density difference between the two fluids, the denser fluid slumps under the less dense fluid. We analyse this motion theoretically and experimentally. On the assumption of lubrication theory, a similarity solution is constructed for the height profile of the interface and the two points at which the interface contacts the upper and lower boundary are found numerically. We show that the rate of advance of one fluid into the other is proportional to $\sqrt{\Delta\rho gd^3 t / \mu}$, where $\Delta\rho$ is the density difference between the two fluids, $g$ is gravity, $d$ is the height of the channel, $\mu$ is the viscosity of one of the fluids and $t$ is the time since release. The constant of proportionality is found to depend only on the ratio of the fluid viscosities, $r$. Asymptotic methods are used to study the regimes $r\to 0$ and $r\to\infty$ with results agreeing remarkably well with the numerical solutions. Experimental results within the regime $r \sim 1$ also compare favourably with theoretical predictions. [Preview Abstract] |
Monday, November 21, 2005 9:31AM - 9:44AM |
FL.00008: Viscosity stratification and the aspect ratio of convection rolls S.J.S. Morris To clarify a mechanism by which earth's low--viscosity layer may increase the wavelength of mantle convection cells, we analyse the clockwise isothermal cellular motion driven by a uniform shear stress of magnitude $\tau$ applied at each end of a rectangle of height $2D$ and length $L$. The viscosity $\mu$ is a given piecewise-constant function of depth; within a low--viscosity channel of thickness $d$ located at the top of the layer, $\mu=m\mu_1$; elsewhere, within the `core', $\mu=\mu_1$. We show that in the double limit $d/D\to 0$, $m\to 0$, this two--layer flow is equivalent to one in single layer of viscosity $\mu_1$ with a new boundary condition at its top representing the interaction of the channel and core flows. Let $ x=x_*/L, $ $ y=y_*/D $ and $ \psi= \mu_1\psi_*/ \tau D^2. $ Then the stream function $\psi$ for the core motion satisfies the b.v.p. $ \psi_{yyyy}+2\alpha^2\psi_{xxyy} + \alpha^4\psi_{xxxx}=0; $ at $ |x|=1 $ , $\psi=0$, $ \alpha ^2\psi_{xx}=-1;$ at $ y=0 $, $\psi=0=\psi_{yy}; $ at $ y=1, $ $ \psi_{yy}- \alpha^2\psi_{xx}=0 $, and $ \psi_{yyy} +3\alpha^2\psi_{yxx} = 3\varepsilon\psi. $ Here $ \alpha=D/L $ and $ \varepsilon=mD^3/d^3. $ We find that for $\varepsilon\to 0$, the motion has two horizontal scales, namely $D$ and $L_1= D/\varepsilon^{1/2}\gg D$. If the rectangle length $L\sim L_1$, fluid sinks at one end and rises at the other; those end flows occur on the scale $D$, and are connected by a long--wave flow on the scale $L_1$. The cellular motion is closed within the low--viscosity layer. We have extended this method to treat convection rolls in a fluid of infinite Prandtl number. Our predicted heat flows agree well with those found in numerical simulations by Lenardic, Richards \& Busse {\it et al} (2005) ({\it J. Geophys. Res.}, to appear). [Preview Abstract] |
Monday, November 21, 2005 9:44AM - 9:57AM |
FL.00009: Cyclic Packing and Unpacking of Spheres by Thermal Convection Bin Liu, Jun Zhang We explore the dynamics of a multi-body interaction that is coupled to the large-scale circulation of a Rayleigh-Benard convection. This system is a collection of freely-moving spheres that sediment at the bottom of the convection cell. Once aggregated, they perturb collectively the convection in the bulk by reducing the local heat flux. As a consequence, the mean wind of circulation will reverse direction, driving the spheres to new positions. As this process continues, it causes the collection of spheres to move back and forth between the two ends of the convection cell along its long side. This system can be seen as a prototype of a self-organized, self-excited oscillating machine, which operates with regularity. The reversal time-scale represents the stochastic characteristic of the repetitive tunneling between the two degenerate ``ground states,'' which correspond to two modes of large-scale circulation. [Preview Abstract] |
Monday, November 21, 2005 9:57AM - 10:10AM |
FL.00010: Transition in Internally Heated Convection Yuji Tasaka, Yohichi Kudo, Yasushi Takeda, Takatoshi Yanagisawa Natural convection induced by internal heat generation in a shallow fluid layer was investigated experimentally. Internal heat generation was realized by passing electric current through ionic liquid. Kalliroscope flakes and thermo-chromic liquid crystal were utilized to clarify a transition of the convection with respect to the Rayleigh number, $R_{\mathrm{I}}$. Visualized flow pattern at higher Rayleigh number show two types of deformed cell shape, double cell structure, which has a small cell in a large cell, and spoke like cell structure, where descending flow neat the center of a cell spread like a spoke. Visualized temperature field was converted to temperature field in order to investigate the transition quantitatively. Variation of horizontal temperature fluctuation with respect to $R_{\mathrm{I}}$ may show critical Rayleigh number for the transition. [Preview Abstract] |
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