Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session E28: Turbulence: Theory & Experiment IIExperimental Turbulence
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Chair: Diego Donzis, Texas A&M University Room: 207 |
Sunday, November 19, 2017 4:55PM - 5:08PM |
E28.00001: Intermittency in small-scale turbulence: a velocity gradient approach Charles Meneveau, Perry Johnson Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation $\mathbf{A}^2$ term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. [Preview Abstract] |
Sunday, November 19, 2017 5:08PM - 5:21PM |
E28.00002: Geometry and Scaling Laws of Excursion and Iso-sets of Enstrophy and Dissipation in Isotropic Turbulence Jose Hugo Elsas, Alexander Szalay, Charles Meneveau We examine the spatial structure of sets with varying small-scale activity levels. These sets are defined using indicator functions on excursion and iso-value sets, and their geometric scaling properties are analyzed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation, and velocity gradient invariants $Q$ and $R$ and their joint spatial distibutions, using data from a DNS of isotropic turbulence at ${\rm Re}_\lambda \approx 430$. Such power-law scaling in the inertial range is found in the radial correlation functions. Thus a geometric characterization in terms of these sets' correlation dimension is possible. Strong dependence on the threshold is found, consistent with multifractal behavior. Nevertheless the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on the multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow. We show that sets defined by joint conditions on strain and enstrophy, and on $Q$ and $R$, also display power law scaling behavior. [Preview Abstract] |
Sunday, November 19, 2017 5:21PM - 5:34PM |
E28.00003: Characterization and prediction of extreme events in turbulence Enrico Fonda, Kartik P. Iyer, Katepalli R. Sreenivasan Extreme events in Nature such as tornadoes, large floods and strong earthquakes are rare but can have devastating consequences. The predictability of these events is very limited at present. Extreme events in turbulence are the very large events in small scales that are intermittent in character. We examine events in energy dissipation rate and enstrophy which are several tens to hundreds to thousands of times the mean value. To this end we use our DNS database of homogeneous and isotropic turbulence with Taylor Reynolds numbers spanning a decade, computed with different small scale resolutions and different box sizes, and study the predictability of these events using machine learning. We start with an aggressive data augmentation to virtually increase the number of these rare events by two orders of magnitude and train a deep convolutional neural network to predict their occurrence in an independent data set. The goal of the work is to explore whether extreme events can be predicted with greater assurance than can be done by conventional methods (e.g., D.A. Donzis & K.R. Sreenivasan, J. Fluid Mech. 647, 13-26, 2010). [Preview Abstract] |
Sunday, November 19, 2017 5:34PM - 5:47PM |
E28.00004: Quantify the complexity of turbulence Xingtian Tao, Huixuan Wu Many researchers have used Reynolds stress, power spectrum and Shannon entropy to characterize a turbulent flow, but few of them have measured the complexity of turbulence. Yet as this study shows, conventional turbulence statistics and Shannon entropy have limits when quantifying the flow complexity. Thus, it is necessary to introduce new complexity measures--- such as topology complexity and excess information---to describe turbulence. Our test flow is a classic turbulent cylinder wake at Reynolds number 8100. Along the stream-wise direction, the flow becomes more isotropic and the magnitudes of normal Reynolds stresses decrease monotonically. These seem to indicate the flow dynamics becomes simpler downstream. However, the Shannon entropy keeps increasing along the flow direction and the dynamics seems to be more complex, because the large-scale vortices cascade to small eddies, the flow is less correlated and more unpredictable. In fact, these two contradictory observations partially describe the complexity of a turbulent wake. Our measurements (up to 40 diameters downstream the cylinder) show that the flow's degree-of-complexity actually increases firstly and then becomes a constant (or drops slightly) along the stream-wise direction. [Preview Abstract] |
Sunday, November 19, 2017 5:47PM - 6:00PM |
E28.00005: Dissipation scales in Navier-Stokes turbulence using highly resolved Direct Numerical Simulations (DNS) Sualeh Khurshid, Diego Donzis, Katepalli Sreenivasan Recent work has shown that turbulent dissipation acquires strong fluctuations and other properties that maintain, even at low enough Reynolds numbers ($Re$), the same relationship with the inertial range, as if $Re$ is very high. In this work we further investigate these conclusions by using highly resolved DNS at a range of $Re$. We highlight the difficulties associated with investigating sub-Kolmogorov scales accurately from numerical as well as statistical standpoints. Results on the time evolution of dissipative modes are presented. The connection of this observation to large-scale and inertial-range dynamics is presented, pointing to potential shortcomings in determining coefficients of the presumed exponential roll off of energy spectrum. Further consequences of these findings are discussed. [Preview Abstract] |
Sunday, November 19, 2017 6:00PM - 6:13PM |
E28.00006: The number of Eulerian points required to describe a turbulent field Florine Paraz, Mahesh Bandi Whereas Kolmogorov's turbulence theory concerns an instantaneous field average, an Eulerian temporal velocity ($v$) measurement with Taylor's hypothesis suffices to obtain the famous -5/3 Kolmogorov spectrum. Yet, an Eulerian point cannot instantaneously encode the full field information. We ask, what is the minimum number of spatially discrete, temporal Eulerian point measurements needed to describe a turbulent field? Since both the Eulerian point and field spectra yield the same -5/3 exponent, we focus on higher order spectra ($v^m, m>1$) to analyse the scaling differences between the point and the field. The spectral scaling of $v^m$ as a function of the number of sampled spatial points then provides the convergence rate towards the asymptotic field average. We put this idea to experimental test in both two (2D) and three (3D) dimensional turbulence. Kolmogorov theory together with Random Sweeping arguments sets the scaling expectations for interpretation of the 3D turbulence data. However, we currently have no explanation for our 2D turbulence results. [Preview Abstract] |
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