Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session LA: Turbulent Mixing III |
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Chair: Douglas H. Kelley, Yale University Room: Long Beach Convention Center 101A |
Monday, November 22, 2010 3:35PM - 3:48PM |
LA.00001: Regularization mechanism of Rayleigh-Taylor turbulent mixing Snezhana I. Abarzhi Turbulent mixing induced by Rayleigh-Taylor instability plays an important role in a variety of natural and artificial phenomena spanning astrophysical and low to high energy density regimes. We apply group theory to analyze symmetries, invariants, scaling and spectra of turbulent mixing induced by the Rayleigh-Taylor instability. The properties of this statistically unsteady, anisotropic, and inhomogeneous turbulent process are found to depart from the canonical Kolmogorov scenario. Time- and scale-invariance of the rate of momentum loss leads to non-dissipative momentum transfer between the scales, to 1/2 and 3/2 power-law scale dependencies of the velocity and Reynolds number respectively, and to spectra distinct from Kolmogorov. Turbulent mixing exhibits more order compared to isotropic turbulence and its viscous and dissipation scales are set by the flow acceleration. To trigger relaminarization of RT mixing, few mechanisms are proposed, including highly coherent initial conditions and flow acceleration by high favorable pressure gradient. [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LA.00002: Vortex interactions and mixing in large Atwood number two-dimensional turbulence Laurent Joly, Jean Noel Reinaud, Jerome Fontane We perform direct numerical simulations of the relaxation of variable-density two-dimensional turbulence. An initial collection of vortices is evolved in time together with an initially bimodal density field corresponding to an Atwood number $A=2/3$. The initial vortex collection counts a thousand Gaussian vortices and spans a radius decade. The vortex Reynolds number of the smaller ones $\Gamma/\nu =300$ and we consider a unit Schmidt number. The misaligned density-gradient and fluid acceleration trigger baroclinic sources and sinks of vorticity on density fronts. The adaptive spatial resolution increase up to $6144^2$ at peak enstrophy production time. We analyze the bias on both the evolution of the vortex population (number and radii) and the mixing progress, against a passive scalar reference simulation started from the same initial fields. Vortex carrying high-density fluid are mass-depleted or break-up into filamentary debris rapidly removed by mass diffusion. Meanwhile, intense vortices merge and trap almost unmixed low-density fluid. The resulting density field is negatively skewed and the mass exchange between vortices and the interlacing medium is shown to be the result of vortex interactions of different types among which asymmetric binary interactions are playing a central role in the mass-segregation by vorticity. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LA.00003: Transport, dispersion and mixing in quasi-two-dimensional steady jets J.R. Landel, C.P. Caulfield, Andrew W. Woods The study of turbulent jets in relatively enclosed geometries is relevant to many chemical engineering processes. Predicting the concentration of chemical reactants in time and space requires a good understanding of the jet dynamics. We consider experimentally and theoretically the behaviour of liquid jets in a quasi-Hele-Shaw cell, where the jets are constrained in a narrow gap whose width is two orders of magnitude smaller than the other two flow dimensions. Classical theoretical models for plane jets are in excellent agreement with time-averaged experimental results obtained using both dyed jets and PIV techniques. Detailed examination of instantaneous structures of the flow reveals a high-speed sinuous core at the centre of the jet and large vortical structures on each side, which we analyse quantitatively using a variety of techniques. These structures have a large impact on the mixing and dispersion properties of the jet. We use a virtual-particle-tracking technique to assess and understand this effect. Comparisons between the instantaneous and the time-averaged velocity field show the importance of the inherently time-dependent vortical structures in the mixing and stretching of the fluid, substantially modifying the mixing and (vertical) dispersion within the jet. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LA.00004: Shape Dynamics of Lagrangian Clusters in Two-dimensional Flow Alexandre de Chaumont Quitry, Douglas Kelley, Sophia Merrifield, Nicholas Ouellette In an effort to understand the dispersion of passive scalars in two-dimensional flows, we investigate the shape evolution of three-particle clusters. We compute the trajectories of virtual Lagrangian points in an electromagnetically driven experimental flow. While our working flow is not turbulent, we observe the same stationary isotropic limit previously observed in turbulent flows. Further, we find that at different scales the triangles adopt preferred statistical shape distributions insensitive to their initial configuration. Our results thus emphasize the role of scale-dependent Lagrangian flow structures in the mixing process. This work is supported by the National Science Foundation. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LA.00005: Influence of flow topology on Lagrangian statistics in forced 2-D turbulence Benjamin Kadoch, Diego del-Castillo-Negrete, Wouter Bos, Kai Schneider Conditional Lagrangian statistics of forced two-dimensional turbulence in unbounded and bounded domains are studied by means of direct numerical simulation. The instantaneous flow domain is decomposed into either vorticity or strain dominated regions and a quiescent background region using the Okubo-Weiss criterion. The probability distribution function (PDF) of the residence time of the particles exhibits an exponential behavior in the background, while in the vorticity and strain dominated regions self-similar algebraic tails are found. For Lagrangian acceleration it is shown that both the vorticity and strain region are responsible for the heavy tails. Finally, the conditional PDFs of the curvature are found to be independent of the different flow domains yielding algebraic tails with slope close to -2, characteristic for an inverse chi-square distribution. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LA.00006: Experimental Study of Mixing dynamics in Stratified Jet Duo Xu, Jun Chen Stratification due to density difference or temperature difference modifies flow structures significantly. In order to characterize the mixing process in stratified flows, momentum and scalar flux terms are to be analyzed. In this study, Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) are applied to simultaneously measure velocity and density fields generated by a horizontal stratified turbulent jet. The effects of stable stratification and unstable stratification are examined. Flow dynamics at two characteristic Richardson numbers is analyzed to by examining the development of flow statistics. The dataset is also applied to test different mixing models. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LA.00007: Variational Theory of Hyperbolic Lagrangian Coherent Structures George Haller We describe a mathematical theory that clarifies the relationship between Lagrangian Coherent Structures (LCS) in unsteady fluid flows and invariants of the Cauchy-Green strain tensor field. Motivated by physical observations of tracer patterns, we define hyperbolic LCS as material surfaces that extremize an appropriate finite-time normal repulsion or attraction measure. Solving this variational problem leads to computable sufficient and necessary criteria for LCS. We also discuss constrained LCS problems, as well as the robustness of LCS under numerical errors and data imperfection. In several examples, we show how these results resolve earlier inconsistencies in the theory of LCS. [Preview Abstract] |
Monday, November 22, 2010 5:06PM - 5:19PM |
LA.00008: Separating stretching from folding in fluid mixing Douglas H. Kelley, Nicholas T. Ouellette Efficient large-scale mixing depends on stretching and folding~--- together they expand the periphery of material volumes, allowing diffusion to mix at small scales. Yet stretching and folding are difficult to decouple in real flows with complex spatiotemporal structure. We distinguish the two processes mathematically and study them separately in a laboratory flow. Our experimental apparatus is a quasi-two-dimensional electromagnetically driven stratified solution with lateral dimensions 90~cm x 90~cm. Optically tracking $\sim$30 000 particles per frame with a high-speed camera, we reconstruct the velocity field and express fluid deformations as the unique sum of an affine component (primarily stretching) and a non-affine component (primarily folding). At short times stretching dominates, but once fluid elements have elongated, folding becomes suddenly stronger and dominates thereafter. The relative strength of the two processes also varies strongly in space. This work is supported by the National Science Foundation. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LA.00009: Experimental evidence of a phase transition in a closed turbulent flow Fran\c{c}ois Daviaud, Pierre-Philippe Cortet, Arnaud Chiffaudel, B\'{e}reng\`{e}re Dubrulle Using stereoscopic particle image velocimetry, we experimentally study the susceptibility to symmetry breaking of a closed turbulent von K\'{a}rm\'{a}n swirling flow from $Re = 150$ to $Re \simeq 10^{6}$. The susceptibility of the mean flow is shown to increase from $1$ to $45$ as transition to turbulence proceeds from the laminar flow to the highly turbulent flow. We report a divergence of this susceptibility at an intermediate Reynolds number $Re = Re_\chi \simeq 90\,000$ which gives experimental evidence that such a highly space and time fluctuating system can undergo a ``phase transition''. This transition is furthermore associated with a peak in the amplitude of fluctuations of the instantaneous flow symmetry corresponding to intermittencies between metastable states. These states break spontaneously the symmetry of the forcing while the very long time-averaged mean flow respects the forcing symmetry. [Preview Abstract] |
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