Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session LN: Turbulence Theory III* |
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Chair: Guo-wei He, Chinese Academy of Sciences Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 9 |
Tuesday, November 21, 2006 8:00AM - 8:13AM |
LN.00001: 3D Particle Tracking in Turbulent Flows using Real-time Image Compression Daniel Blum, King-Yeung Chan, Emmalee Riegler, Rachel Brown, Greg A. Voth We measure 3D trajectories of particles advected in a turbulent flow between two oscillating grids in order to extract multi-particle Lagrangian trajectories. Images of the particles are captured using high speed cameras (1024 x 1280 pixels at 500Hz and faster at lower spatial resolution) arranged stereoscopically. The video stream is then processed by novel real-time compression hardware. The filtering circuit in the compression hardware outputs the position and brightness data of pixels above a brightness threshold. The compression factor dynamically varies from 100 to 1000 depending on the number of bright pixels. The resulting data rate is low enough that it can be recorded directly to hard drive, which allows data acquisition times that were previously limited to 10 seconds to be extended to several days. We report preliminary measurements characterizing the nearly homogeneous turbulence in a 1m x 1m x 1.5m flow between oscillating grids. [Preview Abstract] |
Tuesday, November 21, 2006 8:13AM - 8:26AM |
LN.00002: Experimental study of multi-particle statistics and structures in turbulence Haitao Xu, Nicholas Ouellette, Kelken Chang, Eberhard Bodenschatz We report our recent optical Lagrangian Particle Tracking (LPT) experiments in a laboratory von-Karman water flow with Taylor microscale Reynolds numbers up to 815. The LPT technique provides direct Lagrangian measurements of passive tracer particles in the flow, from which multi-particle statistics, both Lagrangian and Eulerian, can be obtained. In this talk, we present results of multi-point geometrical statistics following Lagrangian trajectories. We also investigate the structure of turbulence through Eulerian multi-point correlation functions. This work is supported by NSF and Max Planck Society (MPG). [Preview Abstract] |
Tuesday, November 21, 2006 8:26AM - 8:39AM |
LN.00003: Experiments and models of inertial particles in high Reynolds number turbulence. S. Ayyalasomayajula, A. Gylfason, Z. Warhaft, L. Collins, E. Bodenschatz We present measurements of the probability density function (pdf) of inertial particles in high Reynolds number wind tunnel, turbulent flow. The particles are water droplets, sprayed into the tunnel at the grid, and the Lagrangian trajectories are determined by high speed camera moving with the mean flow. The Stokes number is varied from 0.1 to 0.5 and the Taylor Reynolds number is 250. Inertial particles are expected to have trajectories differing from fluid (inertia-less) particles in the same flow. For example they may be ejected from regions of high vorticity and accumulate in regions of high strain. Here we show that the tails of the pdf become narrower than that of a fluid particle as the St increases. By means of a simple simulation consisting of a potential array of vortices we mimic the measurements of the pdf. On the other hand, subjecting the inertial particles to a fluid velocity obtained from a stochastic model of the Lagrangian fluid velocity (B.L . Sawford, Phys. Fluids 3 (6), 1577 (1991)) yields no change in the normalized pdf. The implications of these results are discussed in terms of selective sampling of inertial particles compared to those of fluid particles. The work is supported by the US National Science Foundation. [Preview Abstract] |
Tuesday, November 21, 2006 8:39AM - 8:52AM |
LN.00004: Heavy particles clustering in the dissipative and inertial range of turbulence Alessandra S. Lanotte, Jeremie Bec, Luca Biferale, Massimo Cencini, Stefano Musacchio, Federico Toschi The statistics of heavy particles and of fluid tracers transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations, at varying the Reynolds and the Stokes numbers, i.e. the fluid turbulence and the particle inertia, respectively. At those scales where the fluid velocity is smooth, we show that particles clusterise on a fractal set whose dimension depends on the Stokes number only. As spatial inhomogeneities extend up to the the largest scales of the system, we contrast the mass statistics of heavy particles with that of tracers at scales belonging to the inertial range, also. We show that distribution of the coarse-grained mass has power-law tails; in addition, we show that, when varying the inertia, mass distributions collapse one onto the other, if the correct rescaling is applied. [Preview Abstract] |
Tuesday, November 21, 2006 8:52AM - 9:05AM |
LN.00005: Evidence for Small Scale Grid-Induced Anisotropy Jamison L. Szwalek, Werner J.A. Dahm In the last 25 years, several studies have presented evidence for the persistence of anisotropy at scales for which the assumption of local isotropy would be expected to hold. We report results of an investigation into the approach to isotropy on a scale-by-scale basis from analysis of DNS data. We quantify the level of anisotropy at each length scale by investigating both its magnitude and directional preference in Fourier space. Results show clear evidence of strong anisotropy introduced at the grid scale by the directional characteristics of the differencing scheme. This grid induced anisotropy is found to propagate to intermediate scales, leaving no scale region unaffected by the numerical method. The present results demonstrate the limits of DNS data based on traditional differencing schemes for studies of small-scale anisotropy. [Preview Abstract] |
Tuesday, November 21, 2006 9:05AM - 9:18AM |
LN.00006: A New Method for Estimating Intrinsic Reynolds Numbers Stephan Barth, Anne Laupichler, Christoph Renner, Joachim Peinke We present a method to estimate the Reynolds number of a turbulent flow without any knowledge of exact external boundary conditions. Considering the turbulent cascade as a Markovian process the evaluation of the transition probability density of velocity increments on different scales $\tau$ can be described by a Fokker-Planck equation which is completely defined by a drift and a diffusion coefficient. The scale dependence of these coefficients is given by simple polynomials, the parameters of which are a function of Reynolds number. In particular the slope of the constant part of the diffusion term, representing the Gaussian contribution to the general multiplicative noise is suitable to estimate the Reynolds number. This method has already been successfully applied to flows of freejets as well as cylinder and grid wake flows. [Preview Abstract] |
Tuesday, November 21, 2006 9:18AM - 9:31AM |
LN.00007: Framework for filtering/averaging Boltzmann equation for turbulence description Sharath Girimaji Boltzmann equation enjoys a wider range of applicability than Navier-Stokes eqaution for describing flow transport phenomena. However, averaging or filtering the Boltzmann equation for turbulence description and closure model development has proven to be quite challenging. To reconcile the physics of filtered Boltzmann equation with that of filtered Navier-Stokes, we demonstrate that a crucial transformation of variables must be effected. The physical effects of the fluctuating velocity field on the evolution of the one-point velocity distribution function is clearly elucidated. This will pave the way for unifying the turbulence description of Navier-Stokes and Boltzmann equations and developing flow solvers valid over a wide range of Knudsen numbers. [Preview Abstract] |
Tuesday, November 21, 2006 9:31AM - 9:44AM |
LN.00008: An Inviscid Hamiltonian Shock Regularization Technique for Burgers Equation Greg Norgard, Kamran Mohseni While considered an oversimplified model of 1-D fluid dynamics, Burgers equation,$u_t+uu_x=\nu u_{xx}$, shares many of the same properties as Euler and Navier-Stokes equations, namely shocks and turbulence. Both shocks and turbulence can be considered a result of transfer of energy to high frequency wave modes. The $u u_x$ term in Burgers equation is responsible for generating high wave mode as time progresses. In viscous Burgers the accumulation of these high frequency modes is limited by the viscous term. This research proposes limiting the generation of higher wave modes by replacing the convective velocity with a low-pass filtered velocity $\bar{u}$, eliminating the need for a dissipative term, resulting in the equation,$u_t+\bar{u}u_x=0.$ This results in an inviscid regularization of Burgers equation that has a fully Hamiltonian structure. A specific case using the Helmholtz filter, $u=(I-\alpha^2 \partial_x^2) \bar{u},$ is examined in detail, with energy decay as well as other characteristics compared favorably with viscous Burgers. [Preview Abstract] |
Tuesday, November 21, 2006 9:44AM - 9:57AM |
LN.00009: Magnetic Field Effects on the Turbulent Critical Energy using BCS Theory J.A. Johnson, III, E.D. Mezonlin, C.T. Raynor When the BCS theory is applied using the G-L equations to turbulence, and the value of the critical turbulent energy U$_{c, }$is derived directly from the force constraint (and intermolecular constants), the role of the electron can be replaced by the constituent atoms (or ions) and an explicit role for an external magnetic field can be determined. The existence of a lambda-like behavior in turbulent transport coefficients confirming that there may be a second order (continuous) phase transition as systems evolve from a non-turbulent to a turbulent state specifically allows for the isolation of the critical turbulent energy and speculation on the possibilities of direct manipulation of transport behaviors in a variety of plasma turbulent systems. [Preview Abstract] |
Tuesday, November 21, 2006 9:57AM - 10:10AM |
LN.00010: Turbulence and the formation of galaxies Carl H. Gibson Gravitational structure formation in the universe began by fragmentation of the primordial plasma at points of minimum density and maximum rate-of-strain when the largest Schwarz gravitational instability scale matched the scale of causal connection $ct$, where $c$ is the speed of light and $t$ is the time since the big bang. Observations and theory suggest this occurred soon after transition to weak turbulence at about $t=10^{12}$ s, forming proto-supercluster-voids and proto-superclusters of plasma mass $10^{45}$ kg along turbulent vortex lines (http://lanl.gov/astro-ph/0606073). The most massive fluid component (probably neutrinos) filled the voids by diffusion and did not form non-baryonic (cold) dark matter condensates, contrary to the standard model. As the universe expanded and cooled the fragmentation mass decreased to that of galaxies $10^{42}$ kg. Hubble space telescope images show the earliest galaxies have a linear morphology reflecting vortex lines of the primordial plasma turbulence. The viscosity decreased by $10^{13}$ at time $t=10^{13}$ s when the plasma turned to gas, permitting fragmentation at planetary $10^{24}$ kg and proto-globular-star-cluster (PGC) $10^{36}$ kg masses to form the baryonic dark matter. Only about 3$\%$ of these frozen H-He planets have formed stars. The frozen PGCs diffused to form $10^{22}$ m halos surrounding $4 \times 10^{19}$ m luminous fossils of the original proto-galaxies and the turbulence that set this scale. [Preview Abstract] |
Tuesday, November 21, 2006 10:10AM - 10:23AM |
LN.00011: Finite-time Properties of the Navier-Stokes Equations Under Lebesque Space Disturbances Kumar Bobba A complete understanding of the stability characteristics of the Navier-Stokes equations involve understanding both the transient response and the steady state response. The steady state (or infinite-time) response of the Navier-Stokes equations is characterized by the point spectrum and has been well studied. In this work, we study the transient (or finite-time) response of the unsteady Navier-Stokes equations linearized about plane Couette base flow under spatial and temporal varying disturbance forcing. The forcing and response are assumed to belong to infinite-dimensional Lebesque function spaces, $L_2$ and $L_{\infty}$. An analytical characterization is given for the induced norms that characterize the response. It is shown that the $L_2$ induced norm is tightly bounded by the $H_{\infty}$ norm of the transfer function operator and the $L_{\infty}$ induced norm is upper bounded by the $L_1$ norm of the impulse response operator. The structure of the worst case disturbances and their amplification rates are computed using spectral methods---with Fourier modes in homogeneous direction and Chebyshev collocation in non-homogeneous direction. The relevance of the present results to the channel flow laminar-turbulent transition experiments will be discussed. [Preview Abstract] |
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