Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L38: Turbulence Theory I |
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Chair: Michael Wilczek, Max Planck Institute Room: Georgia World Congress Center Ballroom 1/2 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L38.00001: Cancellation exponent in isotropic turbulence and MHD turbulence Xiaomeng Zhai, Pui-Kuen Yeung, Katepalli Raju Sreenivasan Small scale characteristics of turbulence, such as velocity gradients and vorticity, fluctuate in magnitude and oscillate in sign rapidly in space and time. At high Reynolds number, the oscillatory character can be characterized by a cancellation exponent, which measures the propensity of the quantity considered to cancel out when averaged over a region of space or interval of time. Past experimental work suggests that the exponents depend on the dimensionality considered. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence up to R_{λ} of 1300 on 8192^{3}grids. The 2D and 3D results for the cancellation exponent are the same, while the 1D data are smaller for transverse velocity gradients and vorticity. We show that the increased degree of spatial coherency, for example in elongated vortex structures along the magnetic field in MHD turbulence (Zhai & Yeung, PRF 2018), results in substantially smaller cancellation exponents in one dimension. Likewise, the presence of vortical filaments in isotropic turbulence leads to smaller cancellation exponents in 1D. Our results suggest that cancellation exponents in higher dimensions tend to be more reliable. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L38.00002: Role of pressure and viscous processes on velocity gradient dynamics Rishita Das, Sharath S Girimaji Non-local pressure and viscous processes profoundly influence velocity gradient (A_{ij} = ∂u_{i}/∂x_{j}) dynamics and small scale structures in turbulent flows. Development of simple closure models for the pressure and viscous processes have long been sought in literature. To facilitate model development, we propose to normalize intermittent A_{ij} by magnitude (A^{2 }= A_{ij}A_{ij}) leading to mathematically bounded normalized velocity gradient tensor (b_{ij} = A_{ij}/(A^{2})^{1/2}). The present study examines the role of pressure and viscous processes on b_{ij}-evolution described in terms of second (q) and third (r) invariants of b_{ij}. Direct Numerical Simulation (DNS) data is used to exhibit that q-r dynamics furnishes new physical insights and is more amenable to closure modeling. The dependence of the pressure and viscous processes on Taylor Reynolds number (Re_{λ}) is characterized. The nature of pressure processes are mildly sensitive to Re_{λ} at low Re_{λ}. However, the viscous processes show a strong dependence on Re_{λ}: the nature of viscous effects are significantly different before and after the onset of dissipation anomaly. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L38.00003: Effect of forcing and mean shear on velocity gradient dynamics in turbulent flows Divya Sri Praturi, Sharath S Girimaji Velocity gradient dynamics including anomalous scaling exponents and intermittency have been widely studied in literature using direct numerical simulations (DNS) of forced isotropic turbulence. In most cases, the forcing is Gaussian in nature and this differs from the manner in which turbulence is generated in naturally occurring flows. In order to isolate the effect of forcing on the findings, this study examines the velocity gradient dynamics in decaying isotropic turbulence and shear driven turbulence. Following the works of Yakhot and Donzis (Phys. Rev. Lett. 2017), we examine the Reynolds number dependence of various moments of dissipation and velocity gradients. The goal is to identify the Taylor Reynolds number at which noticeable deviations from a Gaussian character are observed. We seek to determine the anomalous scaling exponents of different moments. We also examine the dependence of small scale topology (Q-R diagram) on imposed shear and Taylor Reynolds number. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L38.00004: The filtering approach as a tool for analyzing turbulence Massimo Germano The filtering approach was originally proposed by Leonard (1974) as a possible theoretical framework for the Large Eddy Simulation of turbulent flows. Today this technique is more and more applied to the analysis of turbulent flows. It mainly consists of a filtered representation of the turbulent flow at different filtering resolutions, and compared to the traditional multiscale techniques, Fourier, wavelets, POD, is very simple and intuitive. One drawback of the filtering approach, and in general of any decomposition technique, is the extension to inhomogeneous flows, due to the non commutivity of the filtering operator with the statistical average. A simple way to overcome this difficulty is to apply the partial statistical filtering procedure introduced by Yoshizawa (1982) in order to separate statistically the large scales from the subgrid scales. The practical implementation of this filter in LES modeling is very expensive, but its actuality as a tool for analyzing turbulence has to be remarked. In the contribution the Leonard and the Yoshizawa filtering approaches are compared and the peculiar properties of the latter are discussed in detail. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L38.00005: Similarity in decaying isotropic turbulence: functional forms, constraints in single- and two-time evolution, and DNS results Clayton Byers, Jonathan F MacArt, Michael Mueller, Marcus Hultmark A similarity solution is proposed for two-space, two-time decaying isotropic turbulence. Constraint equations for the temporal evolution of the turbulence intensity and characteristic length scale are found and determine the decay exponent for the turbulence. These constraints and temporal evolution equations furthermore specify the evolution of the dissipation without any additional fitting parameters. A new non-dimensional time variable is found that characterizes self-similar behavior across logarithmic differences in time. The similarity solutions and constraints are applied to a Direct Numerical Simulation (DNS) of decaying isotropic turbulence at two grid resolutions (1024^{3 }and 1536^{3}) and different Reynolds numbers. The decay exponent is found to be determined solely from the evolution of the length scale and is dependent on the Reynolds number. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L38.00006: Turbulence theory by machine Javier Jimenez The question of whether especially significant sub-volumes of a turbulent flow can be `blindly' identified by automatic means, independently of a-priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined as influence on the future evolution of the flow, and the problem is cast as an unsupervised machine `game' in which the rules are the Navier--Stokes equations. It is shown that significance is an intermittent quantity in this flow, and that it is different from relevance. For example, high-energy regions are not necessarily more significant than low energy ones. In accordance with previous intuition, the most significant features are found to be vortices, while the least significant ones are dominated by strain. Subject to cost considerations, the method should be applicable to more general turbulent flows. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L38.00007: Using persistent accelerations to determine one-particle statistics in turbulence Lukas Bentkamp, Cristian C Lalescu, Michael Wilczek Lagrangian particles frequently encounter extreme acceleration events in fully developed turbulence. Intense small-scale structures such as vorticity filaments can give rise to acceleration events exceeding the typical root-mean-squared fluctuations by orders of magnitude. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared Lagrangian acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from direct numerical simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. Based on this observation, which provides a new perspective on the Lagrangian refined similarity hypothesis, we develop a theory of Lagrangian single-particle statistics covering the acceleration, velocity increments as well as single-particle dispersion. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L38.00008: The large scale structure of decaying stratified Saffman turbulence Yukio Kaneda, Katsunori Yoshimatsu We consider freely decaying turbulence of incompressible fluid evolving in the presence of imposed stratification in which the energy spectrum E(k) ~ k^2 at small wavenumber k. Turbulence with this kind of spectrum is called here Saffman turbulence. The turbulence field can be represented in terms of three eigenmodes of a linear operator including the buoyancy effect, say zeta_1 (voritical mode), zeta_2 and zeta_3 (wave modes). Within the linearized approximation ignoring the nonlinear coupling between the modes, the velocity correlation spectrum <|u_i(p)|^2> (no summation over i) in general oscillates in time due to the presence of buoyancy force, while the spectra Z_a(p)=<|zeta_a(p)|^2> (a=1,2,3) do not oscillate, where p is the wave vector. A simple analysis under certain assumptions shows that there are an infinite number of invariants associated with each of the spectra Z_1, Z_2 and Z_3 at small |p|. The invariants may depend on the direction of the wave vector p. Theoretical conjectures based on the analysis are examined by comparison with direct numerical simulation data. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L38.00009: An Improved Sparse Direct Interaction Perturbation Closure for Scalar Mixing David Petty, Carlos Pantano New equations that govern the scalar power spectrum of constant-density homogeneous isotropic turbulence have been derived by applying the Sparse Direct-Interaction Perturbation (SDIP) technique. Traditional SDIP treats integrable singularities, which appear at zero time separation, as invariant to arbitrary time separation. This results in a two-time scalar correlation, and response function, that does not incorporate turbulence stirring effects. The proposed higher-order closure relaxes this simplification and allows a more complex coupling between the Lagrangian map and the scalar fields. Fourier analysis of the newly derived equations is required to identify how the traditional solution is modified, and how a previously neglected component evolves to become materially significant. The condition of statistical isotropy simplifies this analysis substantially. The resulting equations demonstrate that a delicate cancellation of singularities must occur for the integrals to converge. The theoretically predicted Obukhov-Corrsin constant from the present closure is in better agreement with experimentally obtained values when compared to the traditional SDIP approach. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L38.00010: The statistical properties of turbulence in presence of smart small-scale forcing Michele Buzzicotti, Luca Biferale, Federico Toschi Fluid dynamics turbulence is characterized by intermittent fluctuations distributed over a wide range of space- and time-scales. In the limit of infinite Reynolds numbers, the number of dynamical degrees of freedom tends towards infinity. Are all these degrees of freedom equally relevant for the dynamics? By means of high-resolution and high-statistics numerical simulations, we compare the statistical properties of homogenous and isotropic turbulence to those of the Navier-Stokes equation where, thanks to a non-linear viscosity, small-scale vortex filaments are strongly depleted. This non-linear forcing can be seen as a small-scale forcing, selectively acting on high-vorticity regions. Our results indicate that the presence of this “smart” small-scale forcing can strongly reduce the intermittency. Additionally, by comparing our results with those from an “a-posteriori” filtered analysis, we show that the influence of the small-scale forcing has an important influence on the dynamical evolution of turbulence. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in the dynamics of fluid dynamics turbulence as well as on the statistics vs. coherent structure duality. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L38.00011: Using deep learning for prediction of turbulent flow statistics at high Reynolds numbers Mathis Bode, Michael Gauding, Jens Henrik Göbbert, Heinz Pitsch The turbulent motion of fluid flows is a complex, strongly non-linear, multi-scale phenomenon, which poses some of the most difficult and fundamental problems in classical physics. Turbulent flows are characterized by random spatio-temporal fluctuations over a wide range of scales. The general challenge of turbulence research is to predict the statistics of these fluctuating velocity and scalar fields. A precise and computationally affordable prediction of these statistical properties of turbulence would be of practical importance for a wide field of applications ranging from geophysics to combustion science. Deep learning (DL) has been improved substantially in recent years and has proven to contribute to the solution of many problems in a large variety of fields. In this work, DL is used to predict statistics of turbulent flows at high Reynolds numbers. Despite the stochastic nature of turbulence, DL can be used to trace certain coherent structures and statistical symmetries exhibiting turbulence. By applying DL to highly-resolved homogeneous isotropic turbulence data, different DL strategies such as network architecture and loss functions are discussed with respect to their suitability for predicting statistics of scalar fields and the scalar dissipation rate. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L38.00012: A spatiotemporal theory of turbulence in terms of exact coherent structures Matthew N Gudorf, Predrag Cvitanovic The recurrent flows observed in moderate Reynolds number turbulence are shaped by close passes to unstable invariant solutions of Navier-Stokes equations. While in recent years many such solutions been computed, so far all have been confined to small computational domains. |
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