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 GJ: Convection and Buoyancy-Driven Flows I |
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Chair: Thomas Peacock, Massachusetts Institute of Technology Room: Salt Palace Convention Center 250 D |
Monday, November 19, 2007 10:30AM - 10:43AM |
GJ.00001: The Diffusion Fish Thomas Peacock, Roman Stocker, Eric Lauga, Chiang Mei Nature has evolved a prodigious variety of propulsion mechanisms. We have discovered a remarkable new one that requires no moving parts, instead coupling molecular diffusion and gravity to spontaneously propel asymmetric objects in stratified fluids. This can occur in lakes or marine environments, where temperature and salinity often create stable density gradients. The phenomenon is demonstrated using a triangular wedge, ``the diffusion fish,'' in salt-stratified water. [Preview Abstract] |
Monday, November 19, 2007 10:43AM - 10:56AM |
GJ.00002: Diffusion-Driven Layering Michael Allshouse, Tom Peacock Diffusion-driven flow arises in stratified fluids with inclined boundaries. We have discovered that when this phenomenon occurs on the surface of a concentration of neutrally-buoyant particles, the diffusion evolution of the system is significantly altered; providing a novel mechanism for generating thin density layers. We present a series of complementary analytical and experimental studies that clearly demonstrate the effect. [Preview Abstract] |
Monday, November 19, 2007 10:56AM - 11:09AM |
GJ.00003: Front dynamics and macroscopic diffusion in buoyant mixing in a tilted tube J.-P. Hulin, T. S\'eon, J. Znaien, D. Salin, B. Perrin, E.J. Hinch The buoyancy driven interpenetration of two fluids of different densities has been studied in a long tilted tube in the strong mixing regime for which the mean concentration profile along the tube length satisfies a macroscopic diffusion equation. Variations of the corresponding macroscopic diffusion coefficient $D$ and of the front velocity $V_f$ are studied as a function of the Atwood number $At$, the viscosity $\nu$, the tube diameter $d$ and the tilt angle $\theta$. Introducing the characteristic inertial velocity $V_t$ and the Reynolds number $Re_t$, the normalized front velocity $V_f/ V_t$ and dispersion coefficient $D/ (V_t d)$ are observed to scale respectively as $Re_t^{-3/4}$ and $Re_t^{-3/2}$ for $Re_t \alt 1000$. Also, $V_f$ increases linearly with $\tan \theta$ and the ratio $(D/V_f^2)$ remains of the order of ($35 \pm 10) d/V_t$ in a wide range of values of the tilt angle and of the other control parameters. This close relation observed between the variations of $D$ and $V_f^2$ will be discussed in terms of the characteristic time for transverse mixing across the flow channel. [Preview Abstract] |
Monday, November 19, 2007 11:09AM - 11:22AM |
GJ.00004: Intermittency in buoyancy-induced mixing in tilted tubes J. Znaien, J.-P. Hulin, F. Moisy, D. Salin, E.J. Hinch Intermittency is studied in buoyancy-induced mixing in tilted tubes of two fluids of different densities but the same viscosity ($\mu = 10^{-6}\,m^2\,s^{-1}$). Alternate phases of laminar counterflow and turbulent transverse mixing are observed. This is analysed by mapping the relative concentrations with a Laser Induced Fluorescence technique. At a given density contrast (characterised by an Atwood number $At=4\times 10^{-3}$), intermittency is observed at tilt angles from the vertical from $15$ to $75^o$, with a weakly varying period of the order of $30\pm10 s$. The different flow regimes are characterised by the transverse mean concentration profiles in the tube section: at low $\theta$ ($\le 45^{\circ}$), the profiles display a nearly constant gradient whose value is lower in the mixing phase than in the counterflow phase. At higher $\theta$, segregation occurs with regions of high concentration of the two original fluids near the upper and lower walls and a mixed zone in the central part whose width decreases with $\theta$. [Preview Abstract] |
Monday, November 19, 2007 11:22AM - 11:35AM |
GJ.00005: Mixing behind the head of a gravity current propagating over a free-slip boundary Alberto Scotti Three-dimensional numerical simulations of a gravity current propagating over a free-slip boundary show that behind the head two states are possible: a high-mixing state, characterized by the development of initially two-dimensional billows, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, in which the primary mode of instability is a mix of spanwise convective and centrifugal instabilities, and hence accessible only to three-dimensional simulations. The latter state appears at values of the Grashof number lower than the critical value $Gr_c$ for the formation of unsteady billows in two-dimensional flows, and persists above $Gr_c$ over the span of Grashof numbers considered. To access the high-mixing state, it is necessary to add a source of turbulence ahead of the foot of the current. At high values of the Grashof number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5\% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the head due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to convective instabilities that develop within the heavy fluid in the head, and suppress the formation of billows. [Preview Abstract] |
Monday, November 19, 2007 11:35AM - 11:48AM |
GJ.00006: Thermally Modulated Flow in a Channel Matt Fotia, Jerzy M. Floryan We consider pressure driven flow in a two-dimensional channel that is subject to spatially distributed heating with the gravity field acting across the channel. The fluid is assumed to be of the Boussinesq type. In the absence of pressure gradient the convective flow field consists of rolls whose spatial distribution is determined by the form of the heating. Addition of pressure gradient forces motion of the fluid in the axial direction. At sufficiently small values of the Reynolds number the flow field consists of large separation zones maintained by the buoyancy force and a fluid stream meandering between these zones. At higher values of the Reynolds number the separation zones are swept away with the stream filling in the interior of the channel. It is shown that for certain combinations of the Reynolds and Rayleigh numbers the changes in the flow pattern lead to the reduction of axial pressure gradient required to maintain mass flow rate that is the same as in a channel without the heating. Issues related to the stability of such flow are also addressed, with specific attention focused on the formation of streamwise vortices [Preview Abstract] |
Monday, November 19, 2007 11:48AM - 12:01PM |
GJ.00007: A new exact solution of the Boussinesq equations S.J.S. Morris We give a solution of the coupled nonlinear equations describing horizontal flow in a layer of viscous but thermally non--conducting fluid with uniform internal heating. The shear stress and heat flux both vanish at the top and bottom of the layer; the flow is driven purely by the small--amplitude long--wave baroclinicity due to internal heating, and heat generated internally is removed by the purely horizontal flow. This solution models flow near the centre of a long convection cell, like that occurring beneath the Pacific plate. (There, heat generated internally is transported horizontally over the cell length, then removed at the cell end by mixing of hot matter with the cold plume, i.e. the subducted slab. Our solution models only the first of those processes.) Though it is estimated that 50--80\% of earth's heat loss is generated internally within the mantle, our conceptual picture of mantle flow is based on simplified boundary layer models for bottom heated convection, in which the temperature is adiabatic outside thin boundary layers, and the flow is driven purely by the excess mass of cold plumes. By contrast, our solution does not contain a cold plume and predicts that the small--amplitude long--wave density field due to internal heating can, by itself, generate velocities close to those observed. Simplified mantle flow models that assume the motion to be driven purely by density differences across slabs may be ignoring an essential part of the forcing. \newline Morris, S. J. S., {\it Geophys. Res. Lett.}, {\bf 34}, doi:10.1029/2007GL030059 [Preview Abstract] |
Monday, November 19, 2007 12:01PM - 12:14PM |
GJ.00008: Spatially localized states in Marangoni convection in binary mixtures Edgar Knobloch, Pauline Assemat, Alain Bergeon Two-dimensional Marangoni convection in binary mixtures is studied in periodic domains with large spatial period in the horizontal. For negative Soret coefficients convection may set in via growing oscillations which evolve into standing waves. With increasing amplitude these waves undergo a transition to traveling waves, and then to more complex waveforms. Out of this state emerge stable stationary spatially localized structures embedded in a background of small amplitude standing waves. The resulting states are related to time-independent spatially localized states obtained by numerical continuation, and the role of the background waves in sustaining the states is elucidated. Direct numerical simulation in time is used to explore the dynamics both inside and outside of the associated pinning region. [Preview Abstract] |
Monday, November 19, 2007 12:14PM - 12:27PM |
GJ.00009: Laminar thermochemical plumes in viscous fluids Ichiro Kumagai, Anne Davaille, Kei Kurita Experimental studies on a laminar starting plume generated from a thermal boundary layer which is stratified in composition were carried out using simultaneous visualization of temperature and composition fields. The plume morphology and amount of dense material carried upwards depend on the initial buoyancy ratio B, the ratio of the stabilizing chemical buoyancy to the destabilizing thermal buoyancy. For small B, the destabilizing thermal density anomaly is sufficiently strong to counterbalance the stabilizing compositional density anomaly, and the whole thermal boundary layer becomes unstable, generating starting plume morphology close to the purely thermal case. For large B, the thermal density anomaly cannot counterbalance the compositional anomaly and convection develops above the compositional interface. For intermediate B, the interplay between the thermal and compositional effects generates complicated morphologies. As the thermo-chemical plume material rises, it cools down and looses its buoyancy. Therefore the compositionally denser blob rises only up to the level of neutral buoyancy, where it stops, then sink back down. The secondary thermally buoyant plumes are generated from the hot sinking blob and thin tendrils of the dense material are entrained by the convective motion. [Preview Abstract] |
Monday, November 19, 2007 12:27PM - 12:40PM |
GJ.00010: The melting and dissolving of icebergs Andrew Wells, M. Grae Worster The rate of ablation of polar icebergs depends on both the temperature and salinity of the ocean. If the ablation rate is controlled by the supply of heat to the interface, we say that the ice is \emph{melting}. Alternatively, the supply of salt may control the ablation rate, in which case the ice \emph{dissolves} into the salty ocean. We study the transition between melting and dissolving of a vertical ice surface under the influence of buoyancy-driven convection. We use an asymptotic analysis of laminar flow, deriving the detailed structure of the boundary layer in each case. We also consider the impact of turbulent convection on this transition. Melting gives faster ablation rates and larger vertical mass fluxes than are obtained for dissolving. This raises the possibility that a small increase in ocean temperature could be responsible for a rapid acceleration in iceberg disintegration by causing a transition from dissolving to melting. [Preview Abstract] |
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