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 GA: Turbulence Theory I |
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Chair: Siva Thangam, Stevens Institute of Technology Room: Long Beach Convention Center 101A |
Monday, November 22, 2010 8:00AM - 8:13AM |
GA.00001: Public-database enabled analysis of Lagrangian dynamics of isotropic turbulence near the Vieillefosse tail Huidan Yu, Charles Meneveau We study the Lagrangian time evolution of velocity gradient dynamics near the Vieillefosse tail. The data are obtained from fluid particle tracking through the $1024^4$ space-time DNS of forced isotropic turbulence at $Re_{\lambda}=433$, using a web-based public database (http://turbulence.pha.jhu.edu). Examination of individual time-series of velocity gradient invariants $R$ and $Q$ show that they are punctuated by strong peaks of negative $Q$ and positive $R$. Most of these occur very close to the Viellefosse tail along $Q = - (3/2^{2/3}) R^{2/3}$. It is found there that the magnitude of pressure Hessian has positive Lagrangian time-derivative, meaning that it increases in order to resist the rapid growth. We also observe a ``phase delay'' of the pressure Hessian signals compared to those of $R$ and $Q$, indicative of an ``overshoot'' of the controlling mechanism. We also examine the trajectories in the recently proposed 3-D extension of the $R-Q$ plane (see L\"{u}thi B, Holzner M, Tsinober A. 2009, J. Fluid Mech. {\bf 641}, 497-507). Finally, Lagrangian models of the velocity gradient tensor are examined in the same light to identify similarities and differences with the observed dynamics. Such comparisons supply informative guidance to model improvements. [Preview Abstract] |
Monday, November 22, 2010 8:13AM - 8:26AM |
GA.00002: Signatures of non-universal large scales in conditional structure functions from eight different turbulent flows Greg Voth, Daniel Blum, Eberhard Bodenschatz, Mathieu Gilbert, Haitao Xu, Laurent Mydlarski, Armann Gylfason, P.K. Yeung We present a systematic comparison of conditional structure functions in eight turbulent flows. The flows studied include DNS of a periodic box, passive grid wind tunnel, active grid wind tunnel (in both synchronous and random driving modes), counter-rotating disks, oscillating grids, and the Lagrangian exploration module (in both constant and random driving modes). We compare longitudinal Eulerian second order structure functions conditioned on the instantaneous large scale velocity in order to assess ways in which the large scales affect the small scales in a wide variety of turbulent flows. Structure functions are shown to have larger values when the large scale velocity is large in all flows except the passive grid wind tunnel and DNS indicating that dependence on the large scales is typical in turbulent flows. The effects of the large scale velocity on the structure functions can be quite dramatic, with the structure function varying by up to a factor of 2 when the large scale velocity changes by 2 standard deviations. In general, the conditional dependence of the structure functions on the large scale velocity is similar at all scales which indicates large scale effects are scale independent. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GA.00003: Conditional statistics near strong thin shear layers in DNS of isotropic turbulence at high Reynolds number Takashi Ishihara, Julian C.R. Hunt, Yukio Kaneda Data analysis of high resolution direct numerical simulations (DNS) of isotropic turbulence with the Taylor scale Reynolds number up to 1131 shows that there are thin shear layers consisting of a cluster of strong vortex tubes. The widths of the layers are approximately 5\textit{$\lambda $}, where \textit{$\lambda $} is the Taylor micro length scale. According to the analysis of one of the layers, coarse grained vorticity in the layer aligns roughly in one direction, large velocity jump of order of magnitude as large as almost the root-mean-square of the fluctuating velocity occurs across the layer, and energy dissipation averaged over the layer is larger than ten times the average over the whole flow. The mean and the standard deviation of the energy transfer $T(k$,$x)$ from scales larger than 1/$k$ to scales smaller than 1/$k$, at position x in the layer are larger than those outside the layer, but the probability distribution function of $T$ in the layer under an appropriate normalization is similar to that outside the layer. The fact that the correlation of velocity fluctuation falls sharply at one of the boundary of the layer suggests that the boundary acts as a barrier of turbulent fluctuations. The space fillingness of such shear layers will be also discussed in the talk. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GA.00004: Decay of fractal-generated homogeneous turbulence Pedro Valente, Christos Vassilicos We present new hot wire anemometry measurements of decaying homogeneous, quasi-isotropic turbulence generated by low-blockage space-filling fractal square grids using different anemometry systems and hot-wires of decreasing diameter for increased spatial resolution. We find good agreement with previous works by Seoud {\&} Vassilicos (2007) and Mazellier {\&} Vassilicos (2010) but also extend the length of the assessed decay region. It is shown that the measured 1D spectra can be reasonably collapsed using a single length-scale (George 1992, George {\&} Wang 2009) over the entire decay region even though the Reynolds number is high enough for conventional decaying turbulence to display 1D spectra with two-scale (inner and outer) Kolmogorov scaling. The weak anisotropy of the flow can be accounted for by computing the 3D spectrum function from two component velocity signals leading to further improved single-scale non-Kolmogorov collapse. Detailed checks on homogeneity and isotropy are presented as well as measurements with a regular grid indicating that the single-length scale locking is neither an artifice of, hardly present, inhomogeneity nor an effect of confinement from the wind-tunnel walls. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GA.00005: Asymptotic analysis of homogeneous isotropic decaying turbulence with unknown initial conditions Philip Schaefer, Markus Gampert, Jens Henrik Goebbert, Michael Gauding, Peters Norbert In decaying grid turbulence there is a transition from the initial state immediately behind the grid to the state of fully developed turbulence downstream which is believed to become self-similar and is characterized by a power law decay of the turbulent kinetic energy with a decay exponent $n$. The value of this exponent however depends on the initial distribution of the velocity moments. In the non-dimensionalized form of the von K\'arm\'an-Howarth equation a decay exponent dependant term occurs whose coefficient will be called $\delta$. We exploit the fact that $\delta$ vanishes for $n=2$ to formulate a singular perturbation problem, where another small number in the equation, namely 1/4, is assumed to be of the same order as of magnitude as $\delta$. In the limit of infinitely large Reynolds numbers, we obtain an outer layer as well as an inner layer of the thickness of the order ${\cal O}(\delta^{\frac{3}{2}})$, where the Kolmogorov scaling is valid. To leading order, we obtain in the outer layer an algebraic balance between the two-point correlation and the third order structure function. [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GA.00006: Scaling of the two-point velocity difference along scalar gradient trajectories Markus Gampert, Philip Schaefer, Jens Henrik Goebbert, Norbert Peters To analyze the geometrical properties of scalar turbulent fields, the concept of dissipation elements has been proposed by Peters and Wang (J. Fluid Mech. 2006, 2008). Starting from every grid point, trajectories can be traced in directions of ascending and descending gradient until a local extreme point is reached. Based on these trajectories, a dissipation element is defined as the region containing all grid points, whose trajectories share the same pair of extreme points. To parameterize dissipation elements, the linear length between and the scalar difference at the extreme points have been chosen. While the conditional scalar difference follows Kolmogorov scaling, Wang (Phys. Rev. E, 2009) showed that the velocity difference between maximum and minimum follows a linear scaling proportional to $\tau/\lambda$, where $\tau$ is the integral time scale and $\lambda$ the Taylor microscale. In this context, the intention of the present paper is the comparison and analysis of the scaling of the conditional velocity difference in the viscous and the inertial range. Therefore, Direct Numerical Simulations (DNS) of different turbulent flows at various Reynolds numbers $R_ {\lambda}=70-300$ are studied and discussed. It is concluded that the scaling is valid in all the above mentioned flows and thus posses a universal character. [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GA.00007: DNS and Rapid Distortion Theory investigations of Mach number effects on velocity- pressure field interactions in strongly sheared flows Gaurav Kumar, Sharath Girimaji, Rebecca Bertsch Computations based on the Rapid Distortion Theory of homogeneously sheared compressible flow show three distinct types of velocity and thermodynamic field interactions depending upon the gradient Mach number. The difference arises due to the changing role of pressure at sub-sonic, sonic and hypersonic gradient Mach numbers. To understand and further examine the varying role of pressure, we perform direct numerical simulations (DNS) of compressible homogeneous shear flow using Gas Kinetic Method (GKM). We investigate linear and non-linear effects of (a) gradient Mach number (b) perturbation Mach number and (c) initial thermodynamic fluctuations on velocity-thermodynamics interactions. This study is expected to contribute toward the development of improved transition and turbulence closure models in highly compressible shear flows. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GA.00008: Effects of Mach number and compressibility on vorticity and strain-rate turbulence dynamics Sawan Suman, Sharath Girimaji We study the effects of Mach number and compressibility on strain-rate and vorticity dynamics in decaying isotropic turbulence employing direct numerical simulations. Since local Mach number and dilatation are two direct indicators of compressibility of a fluid element, we use these quantities as conditioning parameters to examine the various aspects of turbulence dynamics. Several interesting observations along with the underlying physics pertaining to the inertial (vortex stretching and self-straining) and pressure (pressure Hessian and baroclinic) terms in the budget of strain-rate and vorticity dynamics will be presented in the talk. The contrasting nature of these physical effects in expanding vs. contracting and supersonic vs. subsonic fluid elements will be highlighted. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GA.00009: Compressible Turbulence: Cascade, Locality, and Scaling Hussein Aluie While Kolmogorov's 1941 phenomenology forms the cornerstone for our understanding of incompressible turbulence, no analogous results exist for compressible flows. We present a rigorous framework to analyzing highly compressible turbulence. We show how the sole requirement that viscous effects on the dynamics of large-scale flow be negligible naturally leads to a density weighted coarse-graining of the velocity field, also known as Favre averaging. We prove that there exists a range of scales over which viscous and large-scale forcing contributions are negligible in the kinetic energy budget. An important part of our work proves that the non-linear transfer of kinetic energy to small scales is in the form of a local cascade process. Using scale-locality, we show that the \emph{average} pressure-dilatation only acts at large-scales and that the mean kinetic and internal energy budgets statistically decouple beyond a ``conversion'' scale-range. We rigorously prove that over the ensuing inertial range, scaling exponents of velocity structure functions $\langle|\delta{\bf u}|^{p}\rangle^{1/p}\sim \ell^{\sigma_p}$ are constrained by $1/3 \ge\sigma_p$ for all $p\ge3$. By assuming self-similarity, we show semi-rigorously that $\sigma_p=1/3$ for $p>0$ which implies a Kolmogorov spectrum $E^{u}(k)\sim k^{-5/3}$ for the velocity field. [Preview Abstract] |
Monday, November 22, 2010 9:57AM - 10:10AM |
GA.00010: Life at high Reynolds number Prasad Perlekar, Roberto Benzi, David Nelson, Federico Toschi We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field: mimicking a surface flow. We show that the interplay between turbulent dynamics and population growth leads to quasi-localization and a remarkable reduction in the carrying capacity. The statistical properties of the population density are investigated and quantified via multifractal analysis. We investigate numerically the limit of negligibly small growth rates and delocalization of population ridges triggered by uniform advection. We also study the role of compressibility on the quasi-localization. [Preview Abstract] |
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