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 EL: Free-Surface Flows III |
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Chair: William Schultz, University of Michigan Room: Hilton Chicago Astoria |
Sunday, November 20, 2005 4:10PM - 4:23PM |
EL.00001: Free Surface Waves in Equilibrium with a Vortex Kenneth Miller, Alan Elcrat Computations are given of finite amplitude solitary waves in equilibrium with a point vortex, with or without a submerged obstacle. The method of solution is collocation of Bernoulli's equation at a finite number of points on the free surface coupled with the equations for an equilibrium point vortex. The Kirchhoff-Routh theory for locating an equilibrium point vortex is implemented through numerical conformal mapping between the flow domain and an infinite strip. For a given obstacle, solutions are parametrized with respect to Froude number and vortex strength. For fixed Froude number, solutions can be computed up to a maximum amplitude solution with an angle of 120 degrees on the free surface. As amplitude increases the vortex strength increases to a maximum value, then decreases as the critical solution is approached. [Preview Abstract] |
Sunday, November 20, 2005 4:23PM - 4:36PM |
EL.00002: Surface modification of clutch plates to reduce disengaged drag torque Chinar R. Aphale, William W. Schultz, Steven L. Ceccio Viscous drag torque in disengaged clutches is a significant source of power loss in modern transportation. The main way to reduce this drag torque is to introduce air between the plates when disengaged without reducing the transmission fluid flow eventually needed for reengagement. Six different groove patterns are tested experimentally to determine which have the lowest drag characteristics. Our computations using Fluent showed that the contact angle made by oil with the stationary plate is critical in determining aeration initiation. Experiments coating the stationary plate with an oleophobic substance like Teflon, confirmed these simulations. We will show torque comparisons and visualization through a quartz disk acting as one of the clutch plates. [Preview Abstract] |
Sunday, November 20, 2005 4:36PM - 4:49PM |
EL.00003: Precipitative Growth Templated by a Fluid Jet David Stone, Braddon Lewellyn, James Baygents, Raymond Goldstein Tubular growth by chemical precipitation at the interface between two fluids, a jet and its surroundings, underlies the development of such important structures as chimneys at hydrothermal vents. This growth is associated with strong thermal and/or solute gradients localized at those interfaces, and these gradients, in turn, often produce radial compositional stratification of the resulting tube wall. A fundamental question underlying these processes is how the interplay between diffusion, advection, and precipitation determines the elongation rate of the tubes. Here we report experimental and theoretical results which reveal a regime in which there exists a new scaling law for tube growth. The model system studied consists of a jet of aqua ammonia injected into a ferrous sulfate solution, precipitating iron hydroxides with varying oxidation states at the jet boundary. Despite the complex chemistry and dynamics underlying the precipitation, the tube growth exhibits a strikingly simple scaling form with characteristic lengths and times increasing linearly with the mean velocity of the jet. These observations are shown to follow from a kinetic model of advection-dominated flows. [Preview Abstract] |
Sunday, November 20, 2005 4:49PM - 5:02PM |
EL.00004: Theoretical Analysis of Critical Marangoni Number for Oscillatory Flows with High Prandtl Number Fluids Driven by Surface Tension Shinichi Yoda, Satoshi Matsumoto, Atsuki Komiya Many experiments to determine the critical Marangoni number (\textit{Ma}$_{c})$ at the onset of oscillatory flows for high Prandtl number (\textit{Pr}) fluids have showed a dependence of a characteristic length. This fact contradicts the similarity principle in fluid physics. This paper investigates the reasons why the critical Marangoni number has shown such a dependency by considering the difference in temperature distribution on the free surface. higher \textit{Pr} fluids form a thermal boundary layer with a steep temperature gradient in the vicinity of both the hot and cold disks, although the middle of the free surface has no temperature gradients. The temperature distribution produced a velocity distribution on the free surface. This velocity distribution generates characteristic length dependence for the \textit{Ma}$_{c}$ in higher \textit{Pr} fluids. By considering the partial temperature distribution on the free surface, a basic model for the understanding of \textit{Ma} number for higher\textit{ Pr} fluids is proposed by introducing a dimensionless parameter, the effective \textit{Ma} number. Experimental results showed that this effective Marangoni number does not have the characteristic length dependence at the onset of oscillatory flows. This parameter is consistent with the similarity principle in Marangoni convection behavior. [Preview Abstract] |
Sunday, November 20, 2005 5:02PM - 5:15PM |
EL.00005: Energy flow and energy dissipation in a free surface. Walter Goldburg, Mahesh Bandi, John Cressman Turbulent flows on a free surface are strongly compressible [1] and do not conserve energy in the absence of viscosity as bulk fluids do. Despite violation of assumptions essential to Kolmogorov's theory of 1941 (K41) [2, 3], surface flows show strong agreement with Kolmogorov scaling, though intermittency is larger there. Steady state turbulence is generated in a tank of water, and the spatially averaged energy flux is measured from the four-fifth's law at each instant of time. Likewise, the energy dissipation rate as measured from velocity gradients is also a random variable in this experiment. The energy flux - dissipation rate cross-correlation is measured to be correlated in incompressible bulk flows, but strongly anti-correlated on the surface. We argue that the reason for this discrepancy between surface and bulk flows is due to compressible effects present on the surface. \newline \newline [1] J. R. Cressman, J. Davoudi, W. I. Goldburg, and J. Schumacher, New Journal of Physics, 6, 53, 2004. \newline [2] U. Frisch. Turbulence: The legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, 1995. \newline [3] A. N. Kolmogorov, Doklady Akad. Nauk SSSR, 32, 16, 1941. [Preview Abstract] |
Sunday, November 20, 2005 5:15PM - 5:28PM |
EL.00006: Energy Dissipation in Small Scale Breaking Waves Kelli Hendrickson, Dick K.P. Yue Direct numerical simulations of small scale breaking waves under a fully couple air-water interface is obtained from the Navier-Stokes equation using a level-set method. An ensemble of non-breaking, and spilling and plunging breaking deep-water waves is generated through different breaking mechanisms, including the effect of wind. The dissipation rate of the breaking event, an unsteady and localized phenomenon, is characterized for both spilling and plunging breaking waves. Total energy lost due to the breaking event is found to be strongly correlated with the amount of energy in the wave prior to breaking. Qualitative comparison to large-scale breaking waves experiment is also found. The results of this work provide a foundation for the development of wave breaking dissipation models for use in computational ship hydrodynamics and ocean wave modeling. [Preview Abstract] |
Sunday, November 20, 2005 5:28PM - 5:41PM |
EL.00007: Free surface waves above turbulence Ralph Savelsberg, GertJan van Heijst, Willem van de Water Surprisingly little is known about the statistical nature of the shape of a free surface above turbulence. We study this in a free surface water channel in which turbulence is generated with an active grid. It produces turbulence with a Taylor-based Reynolds number Re$_\lambda$ of $\mathcal O$(300) and allows us to control the isotropy of the turbulence. Naively one would expect surface wrinkles to be primarily associated with low pressure in the cores of vortices attached to the surface. Although simultaneous measurements of the surface shape and the sub-surface velocity field show that part of the surface shape is indeed correlated with large sub-surface structures, spectra of the surface shape in time and space show that much of the surface actually consists of gravity-capillary waves. These waves are radiated from turbulent structures and travel in all directions across the surface. As a consequence the anisotropy of the surface shape is directly connected to the anisotropy of the sub-surface turbulence. [Preview Abstract] |
Sunday, November 20, 2005 5:41PM - 5:54PM |
EL.00008: The Thermal Structure of a Near Surface Developing Turbulent Jet on Clean and Contaminated Free-surfaces K. Peter Judd, Geoffrey B. Smith, Robert A. Handler The thermal structure of a near surface turbulent submerged round liquid jet on clean and contaminated free-surfaces was investigated experimentally for several Reynolds numbers and depth to nozzle diameter ratios (h/d). The objective of this investigation is to shed light on the interaction and morphology of near surface turbulent structures by examining their resulting thermal signatures. A gravity feed supplied the jet water, whose ambient temperature is slightly above that of the test facility. Thus the warmer fluid serves as a passive marker. Using high spatial and temporal resolution infrared imagery, thermal maps of the surface were generated. The detector, an IR CCD camera, was sensitive to radiation in the 3-5 micron wavelength band with temperature sensitivity of 0.02 K. As the Reynolds number was increased from 1000 to 4800, clear structural changes in the thermal field were apparent at the turbulent/non-turbulent interface and in the core region. In addition, the subsurface flow was simultaneously interrogated using DPIV. Surface thermal structures are discussed in light of the resulting hydrodynamic characteristics of the flow field and level of surface contamination. [Preview Abstract] |
Sunday, November 20, 2005 5:54PM - 6:07PM |
EL.00009: Stereo DPIV investigation of a free surface mixing layer Bradley Dooley, Morteza Gharib An experimental study has been conducted to examine a turbulent plane mixing layer intersecting a free surface at low \textit{Fr}. The local \textit{Re} was $\sim $10,000. Stereoscopic Digital Particle Image Velocimetry was used to obtain instantaneous three-component velocity fields within planar slices of the spatially developing mixing layer. Guided by previous studies revealing near-surface counter-rotating vortices in the mean flow, specific depths were chosen at a single downstream station for investigation. 3,000 consecutive image pairs were recorded at each location, allowing spectral analysis. Power spectra of all three components are shown; the isotropy seen to be present at depth is seen to disappear near the surface as surface-normal fluctuations are reduced. A slow transverse oscillation is deduced in the vicinity of the mean streamwise vortices. Not present at all at significant depth, the motions at this frequency are also observed to markedly decrease as the surface is approached. Comparisons are made with other observed meanderings in free surface flows, and the origin of the present oscillation will be discussed. This work is supported by the U.S. Office of Naval Research ({\#}N00014-98-1-0017). [Preview Abstract] |
Sunday, November 20, 2005 6:07PM - 6:20PM |
EL.00010: Air-flow separation over unsteady breaking wind waves Gaurav Saxena, Shubhra Misra, Fabrice Veron In air-sea interaction processes, when considering wind stress over small-scale breaking waves, there are few direct quantitative experimental investigations into the role of air-flow separation on the interfacial momentum flux. Reul \textit{et. al}, (1999), found multiple coherent patches of vorticity downwind of the crest that were strongly influenced by the geometric characteristics of the breaker. However, their breakers were generated by dispersive focusing techniques and, therefore, independent of the wind stress. We present experimental results obtained with particle image velocimetry (PIV) where moderate to strong winds directly generate unsteady small-scale breaking waves, a scenario commonly found in the open ocean. Particular attention has been devoted to capturing the spatio-temporal evolution of the air-water interface. Specifically, texture segmentation algorithms typically used for face recognition (Grey Level Co-occurrence Matrix (GLCM) and the Cross-Diagonal Texture Matrix (CDTM)) have been combined to yield robust and accurate estimates of the instantaneous breaker geometry. [Preview Abstract] |
Sunday, November 20, 2005 6:20PM - 6:33PM |
EL.00011: High Speed PIV of Breaking Waves on Both Sides of the Air-Water Interface A.H. Techet, A.K. McDonald High speed particle image velocimetry (PIV) is performed on plunging and spilling breakers to capture physics on both the air and water side of the free surface. Wave breaking on the surface of the ocean results in significant transfer of mass, momentum, heat and energy across the air-sea interface. In order to further understand the physics associated with wave breaking and to generate accurate models, experiments and simulations that consider the physics in both the air and water are necessary. Here, high speed PIV (500 $fps$) is used to capture the flow field in both the air and water. Reynolds numbers of the waves are on the order of $Re = 9x10^4$ to $2x10^6$, where $Re = \frac{\rho \sqrt{g \lambda^3}}{\mu}$, $\rho$ is fluid density, $\mu$ is fluid dynamic viscosity, $g$ is gravity, and $\lambda$ is the characteristic wavelength of the breaking wave upstream of the breaking event. Isopropyl alcohol (IPA) was mixed with the distilled water in the tank to reduce suface tension an thus achieve plunging breakers in the small tank on this scale. Experiments can be compared qualitatively with numerical simulations by Hendrickson (2004). This talk will present data from the experiments and discuss the experimental issues relating to measurements on the air-side of the air-sea interface. {\it References} {\bf Hendrickson KL} (2004) Navier-Stokes Simulations of Steep Breaking Water Waves with a Coupled Air- Water Interface. {\it PhD Thesis} Massachusetts Institute of Technology. [Preview Abstract] |
Sunday, November 20, 2005 6:33PM - 6:46PM |
EL.00012: Bore propagation in 1-D and 2-D using a Lattice Boltzmann approach Jannette Frandsen The objective of this research is to investigate the performance of a discretized form of the Lattice Boltzmann (LB) equations to model free-surface water in shallow water. The solutions are based on free-surface flows in square tanks which are excited in harmonic horizontal motions. The available equilibrium distribution functions for shallow water waves are utilized. The discretized solution on uniform grids implements an elastic-collision scheme assuming slip boundaries at the tank walls and bed. Typically at water depths h/b greater than 0.09 (h is the still water depth and b is the width of the tank), the water slosh back and forth. Herein the focus is on horizontally dominating free-surface waves as opposed to sloshing motions, i.e. h/b less than 0.09, since the governing equations are based on shallow water wave theory. The forcing amplitude is varied corresponding to tank aspect ratios h/b = 0.05. At this shallow water depth, it is known that traveling waves or bores will form depending on the forcing amplitude and frequency. The LB experiments reported on are limited to weak bores. The LB free surface results agree well with a Riemann solver and experimental data. The 1-D predictions suffice for the test cases studied. [Preview Abstract] |
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