Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session HB: Turbulence: Fundamentals II |
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Chair: Robert Rubinstein, NASA Langley Research Center Room: 101B |
Monday, November 23, 2009 10:30AM - 10:43AM |
HB.00001: Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence Yue Yang, D.I. Pullin, Ivan Bermejo-Moreno The recently developed multi-scale methodology (see J. Fluid Mech. 603, 101-135, 2008) is applied to study the non-local geometry of finite-sized Lagrangian structures in forced isotropic turbulence. A particle backward-tracking method was first applied to obtain the Lagrangian scalar field $\phi$ governed by the pure advection equation. The temporal evolution of Lagrangian structures was obtained by extracting iso-surfaces of $\phi$ with resolution $1024^3$. The multi-scale geometric analysis was then applied on the evolution of $\phi$ to extract structures at different length scales and to characterize their non-local geometry in a ``visualization space" of reduced geometrical parameters. We observe an evolutionary breakdown of Lagrangian blobs that first distort and then stretch into sheets. Compared with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence, Lagrangian structures tend to exhibit more prevalent sheet-like shapes at inertial-range and small scales. Furthermore, after a finite time, the evolutionary geometry of Lagrangian structures appears to be insensitive to the form of the initially smooth Lagrangian scalar field. [Preview Abstract] |
Monday, November 23, 2009 10:43AM - 10:56AM |
HB.00002: Bridging from Eulerian to Lagrangian statistics in turbulent flows Oliver Kamps, Rudolf Friedrich, Holger Homann, Rainer Grauer The problem of relating Lagrangian and Eulerian statistics is a long standing problem in basic and applied turbulence research. Motivated by the investigation of Lagrangian statistics in the inverse cascade regime of 2D turbulence and in fully developed 3D Turbulence we adress the question of relating Lagrangian and Eulerian velocity increment statistics. It turns out that a formal connection between both frames of reference can be established via transition probabilities, which can be estimated from numerical simulations. We also focus on the validity of Corrsin's independence hypothesis in the context of 2D and 3D flows which is of general interest for turbulent transport and mixing processes. [Preview Abstract] |
Monday, November 23, 2009 10:56AM - 11:09AM |
HB.00003: Eulerian statistics from Lagrangian dynamics Federico Toschi, Luca Biferale, Enrico Calzavarini, Andrea Scagliarini Some statistical properties of fluid dynamics turbulence are very difficult to study usually because of the extremely low signal to noise ratio. Here we show how the Lagrangian approach can help unravelling elusive statistics of Eulerian turbulence. Studying the collective dynamics of bunches of light particles we are able to measure the time of life of Eulerian vortex filaments (arXiv:0908.0205). By means of Lagrangian tracers we are able to measure the full multi-scale and multi-time correlation functions in 3D turbulence. [Preview Abstract] |
Monday, November 23, 2009 11:09AM - 11:22AM |
HB.00004: Lagrangian intermittency and time--correlations in two--dimensional turbulence Kai Schneider, Wouter Bos, Benjamin Kadoch, Salah Neffaa The statistical properties of Lagrangian particle transport are investigated in dissipative drift-wave turbulence considering the Hasegawa-Wakatani model. This model allows to study the change in dynamics for different turbulent flow regimes by varying the adiabaticity parameter c. The hydrodynamic limit is obtained for c = 0, while the geostrophic limit is recovered for c $\gg$ 1. For c of order unity the quasi-adiabatic regime, relevant for fusion plasmas in Tokamaks, is obtained. By means of direct numerical simulation we consider four values for c and show that the Lagrangian dynamics is only intermittent in the hydrodynamic regime, while the other regimes are not. This is illustrated by considering the probability density function (PDF) of velocity increments, autocorrelation functions of velocity and acceleration and structure functions. In both, quasi-adiabatic and quasi-geostrophic regimes the PDFs of acceleration exhibit exponential tails. This behaviour is due to the pressure term in the acceleration and not a signature of intermittency. Furthermore the long time correlation of the modulus of acceleration is found for all regimes which hence does not imply intermittency either. [Preview Abstract] |
Monday, November 23, 2009 11:22AM - 11:35AM |
HB.00005: Modulated Turbulence Hakki Ergun Cekli, Willem van de Water Many turbulent flows are subject to periodic modulation, examples are the pulsatile flow of blood through arteries and geophysical flows driven by periodic tides. When the modulation is slow, the turbulence will adjust adiabatically, but when the modulation period comes close to an internal time scale of the flow, the turbulence may resonate with the driving. The possibility of a resonance is intriguing as one may object that turbulence does not have a single dominant timescale, but a continuum of strongly fluctuating times. In our experiment we periodically modulate a turbulent windtunnel flow with an active grid. An active grid is a regular grid of axes with attached vanes which are rotated by servo motors. By controlling the time-dependent angle of all axes precisely, the grid cycles through a sequence of transparency patterns. Thus we modulate turbulence in space, characterized by these patterns, and time, characterized by the modulation frequency. We consider 3 distinct spatial modes, all share the same transparency sequence. We find a large resonant enhancement of the mean turbulent dissipation rate at a modulation frequency which equals the large-eddy turnover rate. Thus, we find the best frequency to inject energy in a turbulent flow. The resonant enhancement depends on the spatial mode of the grid, but all spatial modes share the same behavior of the response. Modulation only affects the large-scale spatial structure of turbulence, leaving the small-scale motion unaltered. [Preview Abstract] |
Monday, November 23, 2009 11:35AM - 11:48AM |
HB.00006: Velocity kinematic relations in a turbulent flow past a grid Alex Liberzon, Roi Gurka, Gregory Kopp, Partha Sarathi, Arkady Tsinober We present velocity kinematic relations, involving average and difference of the longitudinal velocity component of the two points at distance $r$: $u_{+} = u(x+r) + u(x)$ and $u_{-} = u(x+r)-u(x)$, obtained using PIV measurements in a turbulent flow of water past a grid. The present study follows recent numerical and experimental studies, that demonstrated analytical and empirical evidence of the relations, their validity and it emphasizes the physical meaning of the relations. The relations that contain both the large ($u_{+}$) and small ($u_{-}$) scale quantities emphasize the non-local aspects of turbulent flows. For example, the pure kinematic relation of Hosokawa in conjunction with the the Kolmogorov 4/5 law leading to the $\langle u_{+}^2 u_{-} \rangle = \langle \epsilon \rangle r/30 $ shows that the that the large and small scale quantities are correlated contrary to what is suggested by the commonly used sweeping decorrelation hypothesis. Some relations are purely kinematic and some are dynamic, i.e. involving $\langle \varepsilon \rangle$, like the Kolmogorov 4/5 law. The most important aspect is that pure kinematic relations that emphasize the non-local effects, become dynamically significant. Furthermore, we suggest that many of these relations could be used for validation of experimental results. [Preview Abstract] |
Monday, November 23, 2009 11:48AM - 12:01PM |
HB.00007: A Kinetic Description of Turbulent Velocity and Vorticity Distributions Michael Wilczek, Anton Daitche, Rudolf Friedrich The single-point statistics of velocity and vorticity in fully developed homogeneous and isotropic turbulence displays very distinct features. While the former is known to exhibit nearly Gaussian behavior, the latter develops strong non-Gaussian tails, mirroring the differing spatial structure of both fields. We analyze these statistics within the framework of the Lundgren-Monin-Novikov hierarchy, which allows to derive kinetic equations for the evolution of the probability functions from first principles. The unclosed terms are estimated with the help direct numerical simulations. The results provide insight into the connection between basic dynamical flow structures such as vortex tubes and non-Gaussian statistics and characterize the influence of the different field topologies on the single-point statistics. [Preview Abstract] |
Monday, November 23, 2009 12:01PM - 12:14PM |
HB.00008: The ``Pullin scheme'' for non-stationary turbulence Robert Rubinstein The Pullin scheme obtains a solution of the Euler equations from a particle kinetic Boltzmann solution by relaxing the distribution function to a Maxwellian at each time step. We investigate the analog for turbulence closures, using the classical Heisenberg model applied to non-stationary turbulence due to either periodic or linearly increasing forcing as an illustration. Relaxing the spectrum to a local Kolmogorov steady-state spectrum at each time step enforces the Tennekes-Lumley balance between vortex stretching and enstrophy destruction and thereby causes the solution to reproduce the behavior of simple finite dimensional models. We explore the connection between incomplete relaxation and models intermediate in complexity between the full closure and the simplest finite dimensional models. [Preview Abstract] |
Monday, November 23, 2009 12:14PM - 12:27PM |
HB.00009: Small-scale intermittency estimations in isotropic homogeneous and anisotropic stably stratified turbulence Saba Almalkie, Stephen de Bruyn Kops Small-scale intermittency in isotropic homogeneous and anisotropic stably stratified turbulence is examined using high-resolution direct numerical simulations. Statistics of the locally averaged energy dissipation and the scaling exponents of its moments are used as quantitative indicators of intermittency. For the isotropic homogeneous cases, the results are in good agreement with theory and experiments over a range of Reynolds numbers. For the stratified cases, the results help to explain the turbulent bursts observed in stratified flows at low Froude number. Additionally, intermittency estimations based on the single component of the strain rate tensor, a commonly used surrogate, are considered. The differences between the statistical characteristics of the locally averaged surrogate and those of the energy dissipation rate result in overestimating intermittency even in isotropic turbulence. The characteristics of the surrogate in the stratified turbulence are also investigated and the higher level of variability in intermittency estimations in geophysical flows is discussed. [Preview Abstract] |
Monday, November 23, 2009 12:27PM - 12:40PM |
HB.00010: Pressure fluctuations and small-scale intermittency in DNS at high resolution P.K. Yeung, D.A. Donzis, K.R. Sreenivasan Pressure fluctuations in turbulence are closely related to local flow structure as well as (through the gradients) to the statistics of acceleration which is highly intermittent. We present results from direct numerical simulations of forced isotropic turbulence with $4096^3$ grid points, and Taylor-scale Reynolds numbers ($R_\lambda$) up to about 1000. For sufficiently high Reynolds number a $k^{-7/3}$ inertial range develops in the pressure spectrum, consistent with experiments. Our present interest is to understand the nature of local flow conditions that correspond to the negative skewmess for the pressure PDF. In particular, conditional statistics show that low pressure is associated with more kinetic energy, larger enstrophy as well as dissipation, i.e. events of strong intermittency which also make accurate sampling of the negative tails of the pressure PDF difficult. By contrast, high pressure is associated with conditions of near-stagnation with strong strain rate but little vorticity. We also observe that the conditionally-averaged dissipation given the pressure also shows much stronger Reynolds number dependence than conditional enstrophy. This is consistent with recent work concerning comparisons between PDFs of dissipation and enstrophy. [Preview Abstract] |
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