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 M38: Turbulence: Theory/Modeling 
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Chair: Luca Biferale, University of Rome Tor Vergata Room: 304 
Tuesday, November 21, 2017 8:00AM  8:13AM 
M38.00001: Reynolds Stress Closure for Inertial Frames and Rotating Frames Charles Petty, Andre Benard In a rotating frameofreference, the Coriolis acceleration and the mean vorticity field have a profound impact on the redistribution of kinetic energy among the three components of the fluctuating velocity. Consequently, the normalized Reynolds (NR) stress is not objective. Furthermore, because the Reynolds stress is defined as an ensemble average of a product of fluctuating velocity vector fields, its eigenvalues must be nonnegative for all turbulent flows. These fundamental properties (realizability and nonobjectivity) of the NRstress cannot be compromised in computational fluid dynamic (CFD) simulations of turbulent flows in either inertial frames or in rotating frames. The recently developed universal realizable anisotropic prestress (URAPS) closure for the NRstress depends explicitly on the local mean velocity gradient and the Coriolis operator [1]. The URAPSclosure is a significant paradigm shift from turbulent closure models that assume that dyadicvalued operators associated with turbulent fluctuations are objective. [1] Koppula, K.S., A. Benard, and C. A. Petty, 2011, Turbulent Energy Redistribution in Spanwise Rotating Channel Flows, Ind. Eng. Chem. Res., 50 (15), 89058916. [Preview Abstract] 
(Author Not Attending)

M38.00002: Toward a generalized equation for the Reynolds stress: Turbulence momentum balance in noncanonical flows. T.W. Lee Recently, we developed a theoretical basis for determination of the Reynolds stress in canonical flows. Writing momentum balance for a control volume moving at the local mean velocity, along with a differential transform $\frac{\partial }{\partial x}=C_{1} U\frac{\partial }{\partial y}$, a turbulence momentum balance is discovered which includes the Reynolds stress as a function of root turbulence parameters: $\frac{\partial (u'v')}{\partial y}=C_{1} U\frac{\partial u'^{2}}{\partial y}+\nu_{m} \frac{\partial^{2}u_{rms} '}{\partial y^{2}}$. Then, the Reynolds stress can simply be computed by integrating in the ydirection using the righthand side (RHS). This is obviously a far simplification of complex modeling of the Reynolds stress, but contains the correct physics, as borne out by comparisons with experimental and DNS data in canonical flows in our earlier works (e.g. in APS 2016). The RHS contains only two parameters, U and u'. In this work, we seek extensions of this solution to noncanonical flows such as wakes, flow over a step, and mixing layers. Comparisons with experimental and DNS data will be presented. [Preview Abstract] 
Tuesday, November 21, 2017 8:26AM  8:39AM 
M38.00003: Multiple stages of decay in twodimensional turbulence Lei Fang, Nicholas Ouellette We report measurements of the free decay of turbulence in a quasitwodimensional laboratory flow. We observe three clearly distinguished stages of decay, each characterized by an exponential decrease of the kinetic energy with time, but with different decay constants. Using filtering techniques, we identify the physics that controls each stage of decay. The first, most rapid stage is not due to the merger of likesign vortices as has often been suggested but rather to the rapid relaxation of downscale spectral energy leakage. The second stage is a manifestation of dynamical inverse energy cascade processes, and lasts until the separation of scales becomes small. The final stage of decay appears to be dominated by the vertical stratification in our experiment. Our results clarify the dynamical processes at work in decaying twodimensional turbulence. [Preview Abstract] 
Tuesday, November 21, 2017 8:39AM  8:52AM 
M38.00004: How inertia and topology influence singleparticle irreversibility in turbulence Andrew Bragg, Josin Tom It has recently been suggested that the irreversibility of a single fluid particle in turbulence may be quantified by considering the evolution of its power, which has been shown to posses a negatively skewed Probability Density Function (PDF). This has been interpreted in terms of flightcrash events, wherein fluid particles tend to gain energy slowly and lose it fast. Furthermore, it has been argued that the dynamical origin of the negative skewness is the predominance of vortex stretching over compression in turbulence. Here, we consider the irreversibility of a single inertial particle in turbulence. We find that weak inertia can enhance the irreversibility through the way that inertia causes the particles to preferentially interact with the topology of the turbulent flow. When inertia is moderate to strong, the irreversibility is significantly reduced since the inertial particles have a damped response to the flightcrash events in the flow. By following the fluid power along inertial particle trajectories, we also probe whether vortex stretching really is the cause of the negative skewness of the fluid power, or whether the dynamical origin is in fact the selfamplification of the strain field. [Preview Abstract] 
Tuesday, November 21, 2017 8:52AM  9:05AM 
M38.00005: Time irreversibility of fully developed turbulence: multifractal statistics of Lagrangian power Guido Boffetta, Luca Biferale, Massimo Cencini, Massimo De Pietro The irreversible energy cascade of fully developed turbulence is a prototype for systems far from equilibrium. Recently, time irreversibility in turbulence has been discovered at the level of single Lagrangian trajectory, whose rate of kinetic energy change  the Lagrangian power  displays an asymmetric distribution with a powerlaw dependence on the Reynolds number. In this contribution the statistics of Lagrangian power, obtained from extensive direct numerical simulations at different Reynolds numbers, is shown to be well described by the Multifractal model of turbulence. The predictions of the multifractal model are also compared with the results from a shell model of turbulence, which allows to reach very high Reynolds numbers. Surprisingly in this case the even moments of power, insensitive to time asymmetry, are well described by the model, while the odd moments display different scaling exponents. The relevance of our finding for modeling Lagrangian turbulence are discussed. [Preview Abstract] 
Tuesday, November 21, 2017 9:05AM  9:18AM 
M38.00006: Negative probability of random multiplier in turbulence Xuan Bai, Weidong Su The random multiplicative process (RMP), which has been proposed for over 50 years, is a convenient phenomenological ansatz of turbulence cascade. In the RMP, the fluctuation in a large scale is statistically mapped to the one in a small scale by the linear action of an independent random multiplier (RM). Simple as it is, the RMP is powerful enough since all of the known scaling laws can be included in this model. So far as we know, however, a direct extraction for the probability density function (PDF) of RM has been absent yet. The reason is the deconvolution during the process is illposed. Nevertheless, with the progress in the studies of inverse problems, the situation can be changed. By using some new regularization techniques, for the first time we recover the PDFs of the RMs in some turbulent flows. All the consistent results from various methods point to an amazing observationthe PDFs can attain negative values in some intervals; and this can also be justified by some properties of infinitely divisible distributions. Despite the conceptual unconventionality, the present study illustrates the implications of negative probability in turbulence in several aspects, with emphasis on its role in describing the interaction between fluctuations at different scales. [Preview Abstract] 
Tuesday, November 21, 2017 9:18AM  9:31AM 
M38.00007: Multiscale analysis of polymerdiluted turbulent flow using a new elastic dumbbell model with incorporation of variable nonaffinity. Kiyosi Horiuti, Shotaro Sayama We consider turbulent flows diluted with the polymers. The polymer chains are modeled as elastic dumbbells and represented by Brownian dynamics. The motion of solvent fluid is pursued by DNS. Affinity in the motion of the beadspring configuration with the fluid surrounding the dumbbells is commonly assumed, but it results in emergence of Elastoinertial turbulence (EIT) regime. When the polymers are highly stretched, molecular motions may not precisely correspond to the macroscopic deformation (de Gennes 1986). We develop a new dumbbell model in which the affine constraint is removed and nonaffinity is introduced by allowing slippage of the dumbbells against the solvent. This is done by adopting the lowerconvective derivative in addition to the upperconvective derivative in the governing equation for the motion of the dumbbells. We conduct its assessment in the forced homogeneous isotropic turbulence. It is shown that the dumbbells obtained from the case with complete affinity are rotated and converted to the alignment of the dumbbells in the complete nonaffine case, and vice versa. This alteration of configurations is repeated quasiperiodically with the intervals comparable to the relaxation time. The largest stretching of the dumbbells and elastic energy production are achieved in the complete nonaffine dumbbells. Occurrence of EIT is eliminated and de Gennes hypothesis is justified. [Preview Abstract] 
Tuesday, November 21, 2017 9:31AM  9:44AM 
M38.00008: Effects of polymers on the spatial structure of turbulent flows Michael Sinhuber, Joseph G. Ballouz, Nicholas T. Ouellette It is well known that the addition of minor amounts of polymers to a turbulent water flow can significantly change its properties. One of the most prominent effects is the observed drastic reduction of drag in wallbounded flows that is utilized in many engineering applications. Much of the research on polymers in turbulence has focused on their influence on the turbulent energy cascade and their interaction with the energy transfer processes. Much less investigated are their effects on the spatial structure of turbulent flows. In a classical vonKárman swirling flow setup, we used Lagrangian particle tracking to obtain threedimensional particle trajectories, velocities, and accelerations and find that polymers have a significant effect on Lagrangian measures of the turbulence structure such as radial distribution functions and the curvature of particle trajectories. We find that not only do the statistical distributions change, but also that polymers appear to affect the spatial statistics well beyond the size of the polymers themselves. [Preview Abstract] 
Tuesday, November 21, 2017 9:44AM  9:57AM 
M38.00009: Reynolds number scaling of straining motions in turbulence. Gerrit Elsinga, T. Ishihara, M.V. Goudar, C.B. da Silva, J.C.R. Hunt Strain is an important fluid motion in turbulence as it is associated with the kinetic energy dissipation rate, vorticity stretching, and the dispersion of passive scalars. The present study investigates the scaling of the turbulent straining motions by evaluating the flow in the eigenframe of the local strainrate tensor. The analysis is based on DNS of homogeneous isotropic turbulence covering a Reynolds number range \textit{Re}$_{\lambda }$~$=$~34.6  1131. The resulting flow pattern reveals a shear layer containing tubelike vortices and a dissipation sheet, which both scale on the Kolmogorov length scale, $\eta $. The vorticity stretching motions scale on the Taylor length scale, while the flow outside the shear layer scales on the integral length scale. These scaling results are consistent with those in wallbounded flow, which suggests a quantitative universality between the different flows. The overall coherence length of the vorticity is 120$\eta $ in all directions, which is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Transitions in flow structure are identified at \textit{Re}$_{\lambda }$~$\approx $~45 and 250. Below these respective Reynolds numbers, the smallscale motions and the vorticity stretching motions appear underdeveloped. [Preview Abstract] 
Tuesday, November 21, 2017 9:57AM  10:10AM 
M38.00010: Orientation patterns of nonspherical particles in turbulence Bernhard Mehlig, Lihao Zhao, Kristian Gustavsson, Rui Ni, Stefan Kramel, Greg Voth, Helge I. Andersson Turbulent strains tend to align nonspherical particles advected by turbulence. When two such particles spend extended time near each other, they might reasonably be expected to converge toward the same orientation. We show here that this intuition fails in general. Orientations of nearby particles can be very different in turbulence because the distribution of relative orientations of nearby particles has powerlaw tails. We measure the moments of this distribution in experiments and numerical simulations, and explain their anomalous scaling as a function of centreofmass distance by analysing a statistical model. Our analysis builds on a description of the relative motion in a phase space that includes not only the usual spatial coordinates, but also the angular degrees of freedom. In this phase space the dynamics evolves to a fractal attractor. We explain how its geometry determines the anomalous scaling exponents. Our results provide a foundation for understanding collisions of nonspherical particles in turbulence, since relative orientations are critical in modeling collision rates and outcomes.. This talk is based on L. Zhao, K. Gustavsson, R. Ni, S. Kramel, G. A. Voth, H. I. Andersson, and B. Mehlig, arxiv:1707.06037 [Preview Abstract] 
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