Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session GC: Turbulence Theory II: Computational Studies |
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Chair: Federico Toschi, Istituto per le Applicazioni del Calcolo Room: 002A |
Monday, November 24, 2008 8:00AM - 8:13AM |
GC.00001: Quantifying the locality of nonlinear interactions in turbulence Julian Domaradzki, Daniele Carati, Bogdan Teaca The locality functions introduced by Kraichnan give the fraction of the energy flux across a given cutoff wavenumber $k_c$ that is due to nonlinear interactions with wavenumbers $k$ smaller than the cutoff (the infrared locality function) or greater than the cutoff (the ultraviolet locality function). The theory predicts that in the limit of the infinite inertial range the locality functions scale as $(k/k_c)^n$, where n=4/3 and -4/3 for the infrared and the ultraviolet limit, respectively. We have computed the locality functions using several DNS databases. At lower Reynolds numbers, despite of only short inertial range, the data points for computed infrared function are still aligned with the 4/3 slope. However, they always lie above the asymptotic theoretical line, i.e., the nonlinear interactions are more infrared nonlocal than the asymptotic result. The data points for the ultraviolet function show more significant departure from the theoretical scaling and are always below the asymptotic line, i.e., the nonlinear interactions are less ultraviolet nonlocal than the asymptotic result. The analysis was repeated for data obtained in DNS that enforce the inertial range spectrum over an extended range of wavenumbers. The qualitative features of the locality functions remain unchanged but differences between computed values and the theory are reduced. [Preview Abstract] |
Monday, November 24, 2008 8:13AM - 8:26AM |
GC.00002: Short-term forecasts and scaling of intense events in turbulence Diego A. Donzis, K.R. Sreenivasan Turbulence at high Reynolds numbers is replete with strong fluctuations in vorticity, dissipation and other features of small-scale motion, which can be thousands times their respective mean values. The understanding of these extremes is important for intermittency theory and reacting flows, but also for other extreme events such as strong earthquakes. Using direct numerical simulations of isotropic turbulence at up to $R_\lambda\approx 400$ we explore the extent to which extreme events can be predicted dynamically through a precursor. We study the evolution equation of vorticity to show that advection dominates when vorticity peaks in a fixed frame of reference. The growth of squared-vorticity during large excursions follows a universal power-law with a single exponent when normalized by the proper timescale. This description is shown to be consistent with multifractal models. Large viscous contributions are identified as precursors for intense vorticity, forming a reasonable basis for forecasts on short timescales that can be estimated simply by a suitable combination of viscosity and large-scale velocity. Definitive forecasts are shown to be possible if this information is supplemented by the sign of different terms in the vorticity equation. Implications for other intermittent quantities are briefly mentioned. [Preview Abstract] |
Monday, November 24, 2008 8:26AM - 8:39AM |
GC.00003: ABSTRACT WITHDRAWN |
Monday, November 24, 2008 8:39AM - 8:52AM |
GC.00004: The effects of energy dissipation rate surrogates on the inertial-range intermittency and refined similarity hypothesis Saba Almalkie, Stephen de Bruyn Kops Due to limitations in making multi-point instantaneous measurements of a turbulent flow field at sufficiently high resolution to accurately compute the dissipation rate of turbulence kinetic energy, direct calculation of local and averaged dissipation rates are surrogated by using estimates based on more easily measured quantities. The underlying assumptions behind the surrogates and the accuracy of the surrogates for estimating the dissipation rate are investigated by using direct numerical simulations of flow fields including homogeneous isotropic turbulence, stratified turbulence, and plane channel flow. Three commonly used surrogates of local and locally averaged energy dissipation rates, {\it i.e.}, one-dimensional, spectral, and structure function-based estimates, are selected for this study. The statistical behaviors of these surrogates are analyzed and compared with those of the directly computed dissipation rates. The main emphasis is on inertial range intermittency, deviation from the refined similarity hypothesis, and scale sensitivity of the results. [Preview Abstract] |
Monday, November 24, 2008 8:52AM - 9:05AM |
GC.00005: Intermittency and scale dependent statistics in fully developed turbulence Katsunori Yoshimatsu, Naoya Okamoto, Kai Schneider, Yukio Kaneda, Marie Farge We compare high resolution DNS data of isotropic turbulence computed at resolution $2048^3$ with incompressible Gaussian random fields having the same energy spectrum and, either the same helicity distribution as the DNS data, or vanishing helicity. The flatness of velocity increases with scale for the turbulent but not the random fields. A new measure, the scale dependent relative helicity, quantifies the geometrical statistics of the flow at different scales and shows that only the turbulent flow is intermittent and helical. Scale dependent statistical analyses of Eulerian and Lagrangian accelerations show significant differences and hence confirm the inherently different dynamics of turbulent and random flows. [Preview Abstract] |
Monday, November 24, 2008 9:05AM - 9:18AM |
GC.00006: The turbulence dissipation constant is proportional to the number of large-scale stagnation points and is therefore not universal John Christos Vassilicos, Susumu Goto Bos et al (PoF 19, 045101, 2007) showed how the turbulence dissipation constant $C_{\epsilon}$ can differ between stationary and decaying homogeneous isotropic turbulence (HIT) and Mazellier \& Vassilicos (PoF 20, 015101, 2008) showed how this constant is in fact proportional to the third power of the number of large-scale zero-crossings of a 1D velocity component signal sampled from a 3D HIT. Their result implies and quantifies the non-universality of $C_{\epsilon}$ and was obtained by application of the Rice theorem and the 2/3 scaling-range scaling of the number density of zero crossings (Davila \& Vassilicos PRL 91, 144501, 2003). We generalise the Rice theorem to stagnation points and use it in conjunction with the exponent 2 scaling-range scaling of the number density of stagnation points (Davila \& Vassilicos 2003) to show that $C_{\epsilon}$ is proportional to the number of large-scale stagnation points in HIT. We run DNS of HIT with different low wavenumber energy spectra and show that different values of $C_{\epsilon}$ result from these different simulations, and that these different values are well accounted for by the differences in stagnation point structure of the different HIT flows. Our formula linking $C_{\epsilon}$ to this stagnation point structure allows to collapse all data into a single $Re_{\lambda}$-dependence curve and explains, quantitatively, the non-universality of $C_{\epsilon}$. [Preview Abstract] |
Monday, November 24, 2008 9:18AM - 9:31AM |
GC.00007: Unconfined isotropic turbulence in time-decay Gaetano Sardina, Paolo Gualtieri, Carlo Massimo Casciola Homogeneous isotropic turbulence in time decay has been a paradigm in turbulence. Since the first experiments it appeared that scaling laws characterize the time decay. It was found that the turbulent kinetic energy introduced in the system with various forcing techniques decreases in time as a power law with exponent $n$. From experiments it appeared that the values of $n$ are sensitive to the forcing and to the geometry of the apparatus. There are been a number of attempts to understand this dispersion of data, under the assumption that the value of $n$ should be universal. We introduce a new numerical methodology to follow the time decay of homogeneous isotropic turbulence free from confinement effects. In these conditions we find that a universal scaling exponent emerges, $n=1$, consistent with previous predictions based on suitable closure assumptions. It follows that the Taylor-Reynolds number is constant in time and the process of decay essentially amounts to an increase of scales according to $L=L_0 t^{1/2}$. Resort to standard simulation techniques in bounded domains allows to understand the confinement effects which alters the scaling exponent of the decay, giving rise to the scatter in the experimental data. [Preview Abstract] |
Monday, November 24, 2008 9:31AM - 9:44AM |
GC.00008: Markovian properties of the turbulent acceleration Oliver Kamps, Holger Homann, Rudolf Friedrich, Rainer Grauer In recent years it has been shown that by exploiting the Markovian properties of the velocity increments it is possible to extremely reduce the information necessary to describe the Eulerian velocity statistics. This approach, motivated by the theory of stochastic processes, is even more natural to the Lagrangian view of turbulence. Nevertheless a systematic analysis of the Markovian properties of Lagrangian observables is still missing. In this talk we focus on the acceleration of Lagrangian tracer particles which is a central quantity in fundamental and applied turbulence research. Based on data from numerical simulations of the Navier-Stokes equation we investigate two and three time joint probability distributions of acceleration time series in order to estimate the time scale where the process becomes Markovian. Additionally we use this information to reconstruct the intermittent cascade of Lagrangian velocity increments. [Preview Abstract] |
Monday, November 24, 2008 9:44AM - 9:57AM |
GC.00009: Temporal correlations along particles' trajectories in turbulent flows Federico Toschi, Roberto Benzi, Luca Biferale, Enrico Calzavarini, Detlef Lohse, Andrea Scagliarini Inertial particles advected by turbulent flows are characterized by preferential concentration in space and non trivial temporal correlations, as a response to fluctuations of the advecting turbulent velocity field. An important open problem deals with the possibility to statistically relate fluid to particles' properties. We analyze a numerical database from Direct Numerical Simulations of fluid tracers and of heavy/light inertial particles at medium and high-resolutions ($Re_{\lambda} \simeq 180$ and $\simeq 380$). We present results on the temporal autocorrelation of fluid velocity gradients along particles trajectories, also in the form of a Lagrangian version of the Refined Kolmogorov Similarity Hypothesis (LRKSH) for neutral, heavy and light particles. We use multiparticle correlations to extract information on the statistical properties of the advecting turbulent flow. [Preview Abstract] |
Monday, November 24, 2008 9:57AM - 10:10AM |
GC.00010: Turbulence energy cascade associated with hierarchical energy spectrum Kiyosi Horiuti, Kensaku Saito The role of the hierarchical energy spectrum which was extracted in forced homogeneous isotropic turbulence (Horiuti \textit{et al.} 2008) in the generation of the energy cascade is studied. It is shown using the DNS data that the temporal variations of the spectrum are divided into the two phases. Analysis of the energy transfer function in the Fourier space reveals that a large energy input occurs at the scale corresponding to the integral length in Phase 1, and the stretched spiral vortex which induces the $-7/3$ spectrum is created associated with this energy input. Creation of this input is attributable to the backward cascade of the energy in the high wavenumber range to the low wavenumber range in addition to the effect of forcing. The energy contained in the low-wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. The spiral vortex in Phase 1 is converted into another mode of configuration which gives the $-5/3$ spectrum in Phase 2 and this mode becomes predominant. Moderately large dissipation events primarily occurs in Phase 2, but the dissipation field is more intermittent in Phase 1 than in Phase 2. The extreme events in dissipation and enstrophy fields overlap in space in Phase 1. These events occur along the vortex sheets of the spiral vortex which are strained and stretched by the vortex tube in its core. [Preview Abstract] |
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