Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session H2: Convection and Buoyancy-Driven Flows V: Exchange Flows |
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Chair: Ross Griffiths, Australian National University Room: 23A |
Monday, November 19, 2012 10:30AM - 10:43AM |
H2.00001: Internal Waves Generated by Mixed Region Collapse in the Ocean Amber Holdsworth, Bruce Sutherland Tropical cyclones are known to mix the relatively warm near-surface fluid with the cooler underlying fluid creating a well-mixed region of uniform density. The well-mixed region collapses into the stably stratified ambient and forms an intrusive gravity current. This motion is a mechanism for the generation of downward propagating internal waves. We will present a series of laboratory experiments used to examine the axisymmetric collapse of a well-mixed region in a uniformly stratified and rotating fluid. A square tank was filled with uniformly stratified fluid and a hollow cylinder of radius $R_c\sim 5$\,cm and depth $H_m$ between $5$ and $15$\,cm was\, suspended at the center of the tank. Synthetic Schlieren was used to determine wave characteristics such as the frequency $\omega$ and radial wavenumber $k_r$. We found that internal wave frequencies were set by the buoyancy frequency $\omega \approx 0.75N$, the radial wavenumber scaled with $R_c$ so that $k_rR_c \approx 3.5$ and the vertical displacement amplitude increases with $H_m$. To explore a wider range of parameters the experimental data was used to calibrate a numerical model of the axisymmetric collapse. We examined the effects of changing the aspect ratio of the lock $R_c$/$H_m$ and the Rossby number $Ro$. [Preview Abstract] |
Monday, November 19, 2012 10:43AM - 10:56AM |
H2.00002: On the spreading and instability of gravity current fronts of arbitrary shape N. Zgheib, T. Bonometti, S. Balachandar Experiments, simulations and theoretical analysis were carried out to study the influence of geometry on the spreading of gravity currents. The horizontal spreading of three different intial planforms of initial release were investigated: an extended ellipse, a cross, and a circle. The experiments used a pulley system for a swift nearly instantaneous release. The case of the axisymmetric cylinder compared favorably with earlier simulations. We ran experiments for multiple aspect ratios for all three configurations. Perhaps the most intriguing of the three cases is the ``ellipse,'' which within a short period of release flipped the major and minor axes. This behavior cannot be captured by current theoretical methods (such as the Box Model). These cases have also been investigated using shallow water and direct numerical simulations. Also, in this study, we investigate the possibility of a Rayleigh-Taylor (RT) instability of the radially moving, but decelerating front. We present a simple theoretical framework based on the inviscid Shallow Water Equations. The theoretical results are supplemented and compared to highly resolved three-dimensional simulations with the Boussinesq approximation. [Preview Abstract] |
Monday, November 19, 2012 10:56AM - 11:09AM |
H2.00003: Filling box stratification fed by a gravity current Charlie Hogg, Herbert Huppert, Jorg Imberger Fluids in confined basins can be stratified by the filling box mechanism. The source of dense fluid in geophysical applications, such as a cold river entering a warmer lake, can be a gravity current running over a shallow slope. Filling box models are often, however, based on the dynamics of vertically falling, unconfined, plumes which entrain fluid by a different mechanism to gravity currents on shallow slopes. Laboratory tank experiments of a filling box fed by a gravity current running over a shallow slope were carried out using a dye attenuation technique to investigate the development of the stratification of the ambient. These results demonstrate the differences in the stratification generated by a gravity current compared to that generated by a plume and demonstrate the nature of entrainment into gravity currents on shallow slopes. [Preview Abstract] |
Monday, November 19, 2012 11:09AM - 11:22AM |
H2.00004: The hydraulics of exchange flow between adjacent confined building zones Saleh Nabi, Morris Flynn Buoyancy-driven flow between two finite zones containing fluid of slightly different density is investigated. The two zones are connected through a common opening that spans the channel width so that a two layer exchange flow develops once it is removed. In the zone that initially contained dense fluid, a buoyant plume of light fluid mixes with the dense fluid leading, over time, to the development of a nontrivial ambient density stratification. Meanwhile, dense fluid flows as a gravity current into the zone that initially contained light fluid. This gravity current reflects from the end wall and propagates back toward the opening in the form of an internal bore. When the bore reaches the opening, the dynamics of the exchange flow (and consequently the source conditions of the buoyant plume) are substantially altered. Such dynamics are modeled by combining elements of gravity current, internal bore, plume and exchange flow theory; model predictions, such as that the density jump across the first front steadily decreases once the exchange flow becomes transient, are corroborated by salt-bath laboratory experiments. Substantially different predictions arise when either or both of the adjacent zones are assumed to be well-mixed so that no vertical gradient of density is allowed. [Preview Abstract] |
Monday, November 19, 2012 11:22AM - 11:35AM |
H2.00005: Buoyancy driven turbulent flows over irregular rough surfaces Raghib Chowdhury, Eric Ruiz, Kiran Bhaganagar Density currents over irregular rough surfaces generated in lock-exchange mechanism have been simulated using direct numerical simulations. The surface roughness has been introduced using immersed boundary method. The governing Navier-stokes equations are solved in the vertical velocity-vertical vorticity formulation. The roughness has been characterized using statistical parameters. A preliminary analysis has been performed to understand the effect of surface roughness height on the evolution of the density currents generated in lock-exchange mechanism. The results have revealed density currents over rough wall travel at a lower speed compared to those over smooth wall. The front velocity and mixing have been characterized in terms of roughness parameters. [Preview Abstract] |
Monday, November 19, 2012 11:35AM - 11:48AM |
H2.00006: Direct numerical simulations of gravity currents on a slope with sedimentation and resuspension H.J. Anjum, J.N. McElwaine, C.P. Caulfield We report on direct numerical simulations of gravity currents on a slope with sedimentation and resuspension in two-dimensions. We use a hindered sedimentation model where the sedimentation flux is $u_s\phi(1-\alpha \phi)$, where $u_s$ is the dilute limit sedimentation velocity, and $\phi$ is a (nondimensional) particle concentration. We consider in detail the two limiting cases of $\alpha=0$ and $\alpha=1$. On the boundaries we apply a zero flux boundary condition, which models resuspension. This means physically that any particles that are deposited are immediately re-entrained. On the upper surface entrainment of the ambient fluid can be balanced by sedimentation and since no buoyancy is lost through the bottom surface nearly steady currents are possible, although buoyancy is gradually lost through the tail. We compare our simulations with an analytic model based on equations for the total buoyancy, $B=\int\phi_V\,dV$ and the down-slope centre of mass $X=1/B\int x\phi_V\,dV$. These require a closure relation based on the Froude number which we define using the vertical centre of mass $H=1/B\int y\phi_V\,dV$ similarly to Anjum et al. (2012). We show that with this definition the Froude number is constant for most of the flow's evolution. [Preview Abstract] |
Monday, November 19, 2012 11:48AM - 12:01PM |
H2.00007: Steady rotating density currents on a slope Woosok Moon, Georgy Manucharyan, Florian Sevellec, Andrew Wells, Jin-Qiang Zhong, John Wettlaufer We consider the dynamics of steady turbulent entraining density currents on a conical sloping surface in a rotating fluid. A theoretical plume model is developed to describe both axisymmetric flow and single stream currents of finite angular extent. An analytical solution is derived for flow dominated by the initial buoyancy flux, which serves as an attractor for solutions with alternative initial conditions where the initial fluxes of mass and momentum are non-negligible. The solutions indicate that the downslope propagation of the current halts at a critical level where there is purely azimuthal flow in geostrophic balance, and the boundary layer approximation breaks down. A set of laboratory experiments are consistent with the dynamics predicted by the model, with flow approaching a critical level. Interpretation in terms of the theory yields an entrainment coefficient proportional to the inverse of the rotation rate ($E\propto 1/\Omega$, where $E$ is the entrainment and $\Omega$ the rotation rate). Our theoretical model provides a framework for designing and interpreting laboratory studies of turbulent entrainment in rotating dense flows on slopes. [Preview Abstract] |
Monday, November 19, 2012 12:01PM - 12:14PM |
H2.00008: Flushing of passive contaminants through ship ballast tanks Zhixin Qi, Ian Eames, Alistair Greig Ballast water is taken up in ports and carried by ships to maintain balance, trim, and structural integrity. Since the volume of ballast water taken up is significant, it is likely that aquatic species are taken into the tank and transported to another ecosystem. To prevent damage to ecosystems, the International Maritime Organization's Ballast Water Management Convention requires that ballast water tanks must be pumped through with at least three volumes, less is permissible if it can be demonstrated that at least a 95\% of initial water is exchanged. The purpose of this talk is to examine how the exchange process depends on the geometrical complexity of the ballast tank and the density contrast between the initial ballast water and the water used for flushing. These physical processes are studied using a new mathematical model to describe flushing of contaminants from a ballast tank based on models of transport in multiroom buildings. A series of laboratory tests were undertaken using an acrylic model of a 2 to 20 compartmented ballast tank to examine the flushing of a dye from each compartment. The agreement between the theoretical and experimental results is good. These results are finally discussed in the context of international regulations for flushing ballast tanks. [Preview Abstract] |
Monday, November 19, 2012 12:14PM - 12:27PM |
H2.00009: The Competition Between a Localised and Distributed Source of Buoyancy Jamie Partridge, Paul Linden We propose a new mathematical model to study the competition between localised and distributed sources of buoyancy within a naturally ventilated filling box. The main controlling parameters in this configuration are the buoyancy fluxes of the distributed and local source, specifically their ratio $\Psi$. The steady state dynamics of the flow are heavily dependent on this parameter. For large $\Psi$, where the distributed source dominates, we find the space becomes well mixed as expected if driven by an distributed source alone. Conversely, for small $\Psi$ we find the space reaches a stable two layer stratification. This is analogous to the classical case of a purely local source but here the lower layer is buoyant compared to the ambient, due to the constant flux of buoyancy emanating from the distributed source. The ventilation flow rate, buoyancy of the layers and also the location of the interface height, which separates the two layer stratification, are obtainable from the model. To validate the theoretical model, small scale laboratory experiments were carried out. Water was used as the working medium with buoyancy being driven directly by temperature differences. Theoretical results were compared with experimental data and overall good agreement was found. [Preview Abstract] |
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