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 AR: Turbulence Theory I |
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Chair: Shiyi Chen, Johns Hopkins University Room: Hilton Chicago Stevens 3 |
Sunday, November 20, 2005 8:00AM - 8:13AM |
AR.00001: The second turbulence and the first galaxies Gibson Carl The first turbulence was the strongly exothermic turbulent combustion that produced the big bang (1). Strong force freeze-out by quark-gluon-viscous forces damped the turbulence and inflated space (2). The second turbulence occurred in the plasma epoch, triggered by the expansion of space and gravitational fragmentation of the H-He plasma into proto-supercluster-voids. Proto-galaxies formed in chains just before the transition to gas, reflecting viscous straining along vortex lines, where maximum positive rate-of-strain plus the positive straining of the expanding universe stretched and separated proto-galaxies caused by gravity and maximum negative rate-of-strain compression opposing universe expansion. The dim most distant galaxies revealed by the Hubble Space Telescope (figure) are in chains of clumps (3) with $\sim $1500 times more dark matter (planets) than luminous matter (stars). See figure at http://www-acs.ucsd.edu/$\sim$ir118 \newline \newline 1. Gibson, C. H., ``The First Turbulent Combustion,'' Combustion Science and Technology, 177: 1049--1071, 2005 \newline 2. Gibson, C. H., ``The first turbulence and the first fossil turbulence.'' Flow Turbulence and Combustion, 72, 161--179, 2004 \newline 3. Elmegreen, D. M. et al., ``Chain galaxies {\ldots} '', ApJ 603:75, 2004 [Preview Abstract] |
Sunday, November 20, 2005 8:13AM - 8:26AM |
AR.00002: Multi-scale distribution of energy transfer in two-dimensional turbulence Michael Twardos, Michael Rivera, Robert Ecke The scale-by-scale distribution of energy transfer is experimentally investigated in the inverse energy cascade range of two-dimensional turbulence. These experiments analyze data taken from a electromagnetically forced stratified fluid layer using a multi-scale method derived from the filtering approach for measuring scale-to-scale energy transfer. We find that the majority of energy transfered to scales above a given length scale comes from length scales that are significantly ({\em i.e.} a factor of eight) smaller. Further analysis of terms arrising from an expansion of the multiscale equation allow for some speculation as to the energy transfer mechanisms at work in the inverse cascade of two-dimensional turbulence. [Preview Abstract] |
Sunday, November 20, 2005 8:26AM - 8:39AM |
AR.00003: Spatial transport vs. spectral transfer in NS turbulence Jacques Lewalle Aside from source/production and dissipation terms, the spatial representation of the equations for momentum (Navier-Stokes), vorticity, kinetic energy, etc., includes the divergence of fluxes, which are interpreted as (spatial) transport. Viscous diffusion, for example, is a momentum transport term; however for energy it combines transport and dissipation. A similar pattern holds for the nonlinear terms. In the Fourier representation, the viscous term becomes dissipative only, whereas the non-linear terms are reinterpreted as (spectral) transfer terms. Here, we focus on the {\bf wavelet} representation, in which both transport and transfer terms can be identified. The unique analytical properties of the Mexican hat wavelet yield manageable exact equations, which show that all transfer terms are also transport terms, but the converse is not true; and that the interpretation of terms as transport, transfer and/or other (production / dissipation / non-local exchanges) is not unique. A physical basis for the selection of the various options will be discussed, in the broad context of intermittent cascades and modeling. [Preview Abstract] |
Sunday, November 20, 2005 8:39AM - 8:52AM |
AR.00004: Statistics of energy transfer in the inertial subrange --Data analysis of high-resolution DNS of incompressible turbulence in a periodic box Takashi Ishihara, Yukio Kaneda Statistics of energy transfer in the physical and wave vector space are studied by using a series of high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box. The number of grid points in the DNS and the Taylor micro-scale Reynolds number $R_\lambda$ are up to $4096^3 $ and $1130$, respectively. We used two kinds of filtering ($S$) a spectral cutoff filter and ($G$) a Gaussian filter to define the grid scale (GS) and sub-grid scale (SGS) components. The DNS data suggest (i) the pdf's of energy transfer from GS to SGS components in ($G$) are more asymmetric in a systematic manner about the most probable value than those in ($S$), (ii) spectral eddy viscosity in ($G$) is almost constant ($\approx 0.35\big<\epsilon\big>^{1/3}k_c^{-4/3}$) for the wavenumber $k<0.8k_c$ provided that the cutoff wavenumber $k_c$ is in the inertial subrange, where $\big<\epsilon\big>$ is the mean rate of energy dissipation per unit mass, and (iii) the volume ratio of the backscatter region in ($G$) scales well with $k_c\eta$ irrespectively of $R_\lambda$ and is about $8\%$ in the inertial subrange, where $\eta$ is the Kolmogorov dissipation length. [Preview Abstract] |
Sunday, November 20, 2005 8:52AM - 9:05AM |
AR.00005: Cascade time-scales for energy and helicity in isotropic homogeneous turbulence Susan Kurien, Mark Taylor, Takeshi Matsumoto Energy and helicity are the two conserved quantities of the inviscid Navier-Stokes equations. Energy has been thought to dominate the dynamics in the inertial range of scales with helicity being carried along more or less passively. We show how an estimate for the time-scale for helicity transfer in wavenumber space implies a richer structure for turbulence dynamics in which helicity can play a significant role. In particular we show that our analysis admits a $k^{-4/3}$ scaling of the energy and helicity spectra, which is slightly shallower than the $k^{-5/3}$ scaling prediction of Kolmogorov (1941). Furthermore, a new helicity-dependent dissipation scale is revealed; this scale becomes much larger than the Kolmogorov dissipation scale as the Reynolds number becomes very large. We will present numerical simulations data which lend some support to our analytical predictions. [Preview Abstract] |
Sunday, November 20, 2005 9:05AM - 9:18AM |
AR.00006: Inertial Range Similarity in Isotropic Turbulence Mogens Melander, Bruce Fabijonas We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. We show how scaling invariance of one function, together with power laws for the structure functions, can account for the phenomenon of anomalous scaling. Our similarity theory yields expressions for scaling exponents, coefficients, PDF, and cumulants. Also, a turbulence length scale with no Reynolds number dependence emerges. The theory is a sharper version of our 2004 presentation: a better similarity hypothesis, fewer assumptions, and excellent agreement with shell model data. [Preview Abstract] |
Sunday, November 20, 2005 9:18AM - 9:31AM |
AR.00007: Scale-by-scale approach to isotropy in homogeneous turbulent flows Jamison Szwalek, Werner Dahm Kolmogorov's local isotropy hypothesis suggests that the increasingly smaller lengths scales in turbulent flows become increasingly independent of the large scales, and at small enough scales the turbulence attains a universal isotropic state. However, within the last 25 years, several researchers have presented evidence for the persistence of anisotropy at scales for which the assumption of local isotropy would be expected to hold. We thus report results from an investigation into the approach to the isotropy on a scale-by-scale basis. We quantify the level of anisotropy at each length scale by analyzing DNS data for homogeneous uniformly-sheared turbulence for several different mean shear rates. Vorticity and strain rate orientations are examined for each wavenumber to provide insight into the physical mechanisms involved in the approach to isotropy. [Preview Abstract] |
Sunday, November 20, 2005 9:31AM - 9:44AM |
AR.00008: Lagrangian velocity structure functions in high reynolds number turbulence Haitao Xu, Nicholas Ouellette, Michael Bourgoin, Eberhard Bodenschatz We report measurements of the Lagrangian velocity structure functions, up to order 10, in a high Reynolds number (up to a Taylor microscale Reynolds number $R_ \lambda$ = 815) turbulence experiment, in which the motion of passive tracer particles was followed optically in three dimensions using multiple high speed cameras. We measure the scaling exponents of the Lagrangian structure functions using the extended self-similarity hypothesis, and compare our experimental data with previous measurements and DNS data. This work is supported by the NSF and the Max Planck Society. [Preview Abstract] |
Sunday, November 20, 2005 9:44AM - 9:57AM |
AR.00009: Analysis of Intermittency of Turbulence by Lagrangian Renormalized Perturbation Method Yukio Kaneda, Kazuto Ueno We applied a Lagrangian renormalized perturbation (RPT) method to analyze the intermittency of the enstrophy and the energy dissipation rate in incompressible turbulence. A simple dimensional argument using the mean energy dissipation rate and wave number $k$ shows that both of the spectra of the squares of these fields scale as $\propto k^{5/3}$ in the inertial subrange. On the other hand, recent direct numerical simulations with the Taylor micro-scale Reynolds number up to about 1200 suggest that they scale as $\propto k^{a}$ in the range, with the exponent $a$ about $-2/3$ instead 5/3, while the spectrum of the square of the Laplacian of the pressure scales as $\propto k^a$ with $a \sim 1.8$, in fairly good agreement with the normal scaling $a=5/3$. All of the enstrophy, the energy dissipation rate and the Laplacian of the pressure are second order in the first space derivative of the velocity. The difference between the spectra comes only from the difference in their componental or tensorial dependence on the velocity derivatives. It is therefore unlikely that any theory discarding the tensorial dependence would explain the difference. The lowest order terms in the RPT expansions agree with the quasi-normal approximation and give the normal scaling $\propto k^{5/3}$ for these spectra. However, a class of higher order terms is shown to give intermittency corrections to the spectra of the squares of the enstrophy and the energy dissipation rate, which involve the dissipation length scale. [Preview Abstract] |
Sunday, November 20, 2005 9:57AM - 10:10AM |
AR.00010: Unified Multifractal Description of Eulerian and Lagrangian Velocity Increments in Turbulence L. Chevillard, A. Arneodo, B. Castaing, E. L\'ev\^eque, J.-F. Pinton, S.G. Roux In fully developed turbulence, most of the experimental, numerical and theoretical works have focused on the statistics of the Eulerian longitudinal velocity increments. It is now well established that the structure functions behave as power laws in the inertial range with a non linear exponent. This anomalous scaling is referred to the so-called intermittency phenomenon: the probability density function (PDF) of velocity is close to Gaussian, while the PDF of velocity gradients exhibits fat tails. Very recently, two experimental groups have succeeded in following particle tracers in turbulent flows realizing a Lagrangian description of the fluid. Lagrangian velocity shares many properties with its Eulerian counterpart but is found much more intermittent. We show that the multifractal approach, combined with a proper probabilistic formulation, reproduces the velocity increments PDFs, in both Eulerian and Lagrangian frameworks, for both the inertial and dissipative ranges of scales, using a single parameter function ${\mathcal D}(h)$ and a universal constant. This approach is shown to account quite well of the skewness of the longitudinal velocity increments PDF. [Preview Abstract] |
Sunday, November 20, 2005 10:10AM - 10:23AM |
AR.00011: Lagrangian Velocity Statistics in High Reynolds Number Turbulence Nicholas Ouellette, Haitao Xu, Mickael Bourgoin, Eberhard Bodenschatz We report measurements of the second order Lagrangian velocity structure functions and the Lagrangian velocity spectrum in a high Reynolds number (up to a Taylor microscale Reynolds number of $R_\lambda = 815$) turbulence experiment. The motion of tracer particles is followed optically and in three dimensions using multiple high speed cameras. Values of the Lagrangian structure function scaling constant $C_0 $, which is of central importance to stochastic turbulence models as well as to understanding particle pair dispersion and scalar mixing, are obtained both from the structure functions and from the spectra, and these two measurements are shown to agree. Additionally, the Reynolds number dependence of $C_0$ is investigated, and is found to be in agreement with an existing model. This work is supported by the NSF and the Max Planck Society. [Preview Abstract] |
Sunday, November 20, 2005 10:23AM - 10:36AM |
AR.00012: Numerical scaling analysis of the small-scale structure of turbulence Panagiotis Stinis, Alexandre Chorin We show how to use numerical methods within the framework of successive scaling to analyse the microstructure of turbulence, in particular to find inertial range exponents and structure functions. The methods are first calibrated on the Burgers problem and are then applied to the 3D Euler equations. Known properties of low order structure functions appear with a relatively small computational outlay; however, more sensitive properties cannot yet be resolved with this approach well enough to settle ongoing controversies. [Preview Abstract] |
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