Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G25: Turbulence: Theory I 
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Chair: Charles Meneveau, Johns Hopkins University Room: 2005 
Monday, November 24, 2014 8:00AM  8:13AM 
G25.00001: The nature of turbulence at high Mach numbers Sharath Girimaji We begin by listing the features of a \textit{real} turbulence flow field and identifying the quintessential characteristics. We contrast these with the main features of wavelike motion. We examine the competition between \textit{wavelike} and \textit{real} turbulence characteristics in two elementary flow cases: (i) direct numerical simulation (DNS) of a decaying flow field that is initially anisotropic and purely dilatational; and (ii) DNS and linear analysis of a homogeneously sheared velocity field which is initially entirely solenoidal. The first case examines the nonlinear aspects while the latter study addresses linear processes as well. Returntoisotropy, potentialtodilatational energy partition and broadbandedness of the energy spectra are examined. Important, but not necessarily conclusive, arguments are presented. [Preview Abstract] 
Monday, November 24, 2014 8:13AM  8:26AM 
G25.00002: On the direct and inverse energy transfer in 2dimensional and 3dimensional turbulent flows and in turbulent models Ganapati Sahoo, Luca Biferale, Massimo De Pietro In this seminar, I will discuss a few important open problems in ``Fully Developed Turbulence'' concerning its most idealized realization, i.e. the case of statistically homogeneous and isotropic flows. I will discuss the importance of inviscid conserved quantities in relation to the most striking statistical properties shown by all turbulent flows: the growth of smallscales, strongly nonGaussian fluctuations, including the presence of anomalous scaling laws. By using unconventional numerical methodology, based on a Galerkin decimation of helical Fourier modes [13], I will argue that some phenomena characterizing homogeneous and isotropic flows might be important also for a much larger spectrum of applications, including flows with geophysical and astrophysical relevance as for the case of rotating turbulence and/or conducting fluids. Results about both real 3D decimated NavierStokes equations and dynamical models of it will be presented. \\[4pt] [1] L. Biferale, S. Musacchio and F. Toschi, Phys. Rev. Lett. 108 164501(2012).\\[0pt] [2] L. Biferale, E.S. Titi, J. Stat. Phys. 151, 1089(2013).\\[0pt] [3] L. Biferale, S. Musacchio and F. Toschi, J. Fluid Mech. 730, 309(2013). [Preview Abstract] 
Monday, November 24, 2014 8:26AM  8:39AM 
G25.00003: Turbulence under Fractal Fourier Decimation Luca Biferale, Alessandra Lanotte, Shiva Malapaka, Federico Toschi We present a systematic investigation of 3D turbulent flows evolved on a highly decimated set of Fourier modes. In particular, we investigate the change in smallscales intermittency when the flow is constrained to excite only a fractal set of modes but keeping the symmetries of the original 3D NavierStokes equations. [Preview Abstract] 
Monday, November 24, 2014 8:39AM  8:52AM 
G25.00004: Depletion of nonlinearity in twodimensional turbulence Andrey Pushkarev, Wouter Bos, Robert Rubinstein The strength of the nonlinearity is measured in decaying twodimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a twostep process. First a fast relaxation is observed on a timescale comparable to the time of formation of vortical structures, as also observed in 3 dimensions [1], then at long times the nonlinearity relaxes further during the phase when the eddies merge to form the final dynamic state of decay. Both processes seem roughly independent of the value of the Reynolds number. \\[4pt] [1] Bos, W. J. T., \& Rubinstein, R. (2013). On the strength of the nonlinearity in isotropic turbulence. Journal of Fluid Mechanics, 733, 158170. [Preview Abstract] 
Monday, November 24, 2014 8:52AM  9:05AM 
G25.00005: Angular statistics of fluid particle trajectories in turbulence Wouter Bos, Benjamin Kadoch, Kai Schneider The angle between subsequent particle displacement increments is evaluated as a function of the time lag, following a recent proposition by Burov et al. [1]. First, the link between the investigated angle and the curvature of the trajectories is explained. Subsequently we compare the Lagrangian trajectories in twodimensional periodic and wallbounded turbulent flows. We show that at long times the probability density function of the angles carries the signature of the confining domain if finite size effects are present. At short times, the PDF of the cosine of the angle is given by a power law with a well defined exponent, reminiscent of the close to Gaussian character of the velocity field. \\[4pt] [1] Burov, S., Tabei, S. A., Huynh, T., Murrell, M. P., Philipson, L. H., Rice, S. A. \& Dinner, A. R. (2013). Distribution of directional change as a signature of complex dynamics. Proc. Natl. Acad. Sci., 110(49), 1968919694. [Preview Abstract] 
Monday, November 24, 2014 9:05AM  9:18AM 
G25.00006: Backwards TwoParticle Dispersion in a Turbulent Flow Theodore Drivas We derive an exact equation governing twoparticle backwards meansquared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe consequences of our formula for short time and arrive at approximate expressions for the mean squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically calculate an exact $t^3$ contribution to the squared separation and additionally compute the average dispersion using direct numerical simulation (DNS) results of incompressible homogeneous isotropic turbulence. We find that this exactly calculable term accounts for almost all of the observed behavior. We argue that this contribution also appears to describe the asymptotic Richardsonlike behavior for deterministic paths and present DNS results to support this claim. [Preview Abstract] 

G25.00007: ABSTRACT WITHDRAWN 
Monday, November 24, 2014 9:31AM  9:44AM 
G25.00008: Local behavior of streamlines in turbulent flows Jonas Boschung, Fabian Hennig, Norbert Peters Although streamlines have often been used mainly to visualize flow fields, they have been studied in recent years to some extent in the search for a better, more intuitive description and decomposition of the flow field. Streamlines seem a good candidate, as they are tangential to the velocity field and thus are prescribed by its structure. Similarly to the $Q$$R$classification of flow topologies, it is possible to classify the behavior of streamlines in an absolute sense by the unit vector gradient tensor and its first and second invariant $H$ and $K$. The invariants are found to have a physical interpretation, inasmuch as they are a measure for the local net convergence or divergence of the streamlines and its rate of change, respectively. The joint pdf of $H$ and $K$ is evaluated for different Reynoldsnumbers from 119 to 330. It is found that streamlines expand rapidly while shrinking gently. As the local flow behavior is determined by the invariants, several quantities are conditioned on $H$ and $K$ in order to relate them to the structure of the flow. [Preview Abstract] 
Monday, November 24, 2014 9:44AM  9:57AM 
G25.00009: Symmetryplane models of 3D Euler fluid equations: Analytical solutions and finitetime blowup using infinitesimal Liesymmetry methods Miguel D. Bustamante We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a oneparameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finitetime blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a wellknown exact solution of 3D Euler equations [Gibbon et al., Physica D 132:497 (1999)]. We discuss practical applications. [Preview Abstract] 
Monday, November 24, 2014 9:57AM  10:10AM 
G25.00010: Joint Statistics of Finite Time Lyapunov Exponents in Isotropic Turbulence Perry Johnson, Charles Meneveau Recently, the notion of Lagrangian Coherent Structures (LCS) has gained attention as a tool for qualitative visualization of flow features. LCS visualize repelling and attracting manifolds marked by local ridges in the field of maximal and minimal finitetime Lyapunov exponents (FTLE), respectively. To provide a quantitative characterization of FTLEs, the statistical theory of large deviations can be used based on the socalled Cram\'er function. To obtain the Cram\'er function from data, we use both the method based on measuring moments and measuring histograms (with finitesize correction). We generalize the formalism to characterize the joint distributions of the two independent FTLEs in 3D. The ``joint Cram\'er function of turbulence'' is measured from the Johns Hopkins Turbulence Databases (JHTDB) isotropic simulation at $Re_\lambda = $ 433 and results are compared with those computed using only the symmetric part of the velocity gradient tensor, as well as with those of instantaneous strainrate eigenvalues. We also extend the largedeviation theory to study the statistics of the ratio of FTLEs. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude and the most likely ratio of FTLEs changes from 4:1:5 to 8:3:11, highlighting the role of rotation in decorrelating the fluid deformations along particle paths. [Preview Abstract] 
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