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10:45   Boundary Free Turbulence 3 10:45 15 mins #327 Permanence of large eddies in variable-density homogeneous turbulence Olivier Soulard, Jérôme Griffond, Benoît-Jospeh Gréa, Giovanni Viciconte Abstract: In this work, we study the influence of density variations on the behavior of the very large scales of a homogeneous decaying turbulent flow. We show that a non-linear term involving pressure and density alters the way energy is transferred at large scales. As a result, the conditions under which large scales remain permanent is modified compared to a constant density flow. Implicit large eddy simulations are performed to verify these predictions. 11:00 15 mins #416 What is a "Length Scale" in Variable Density Turbulence? Dongxiao Zhao, Hussein Aluie Abstract: A "length scale" in a fluid flow does not exist as an independent entity but is associated with the specific flow variable being analyzed. While this might seem obvious, we often discuss the "inertial range" or the "viscous range" of length scales in turbulence as if they exist independently of a flow variable, which in incompressible turbulence is the velocity field. How should we analyze "length scales" in flows with significant density variations, such as across a shock or in multiphase flows? A choice can be made according to the so-called inviscid criterion. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at sufficiently large "length scales." Recently, Aluie 2013 proved that a Hesselberg-Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. We present numerical demonstrations of those results, where we also show that other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density (VD) turbulence. Our results imply that some of the widely used scale-decompositions in VD turbulence, such as those relying on (i) triadic interactions to analyze energy transfer (despite the nonlinearity being cubic in VD flows, and not quadratic as in incompressible turbulence) (ii) analyzing $\sqrt{\rho}u$, such as its spectrum, effectively treating kinetic energy as a quadratic quantity, can yield counter-intuitive or misleading results. This is due to persistently high viscous contamination at all scales and a lack of an inertial range using such decompositions. To measure the spectrum in VD flows, we use a new method which is consistent with the inviscid criterion. It relies on a straightforward filtering in physical space, guarantees energy conservation, and can extract spectra of non-quadratic quantities self-consistently, such as kinetic energy in VD flows, which the wavelet and Fourier spectra cannot. This work was supported by NASA grant 80NSSC18K0772 and the DOE Office of Fusion Energy Sciences grant DE-SC0014318. 11:15 15 mins #250 SCALE-SPACE TURBULENCE ENERGY DENSITY IN COMPRESSIBLE MIXING LAYER S Arun, A Sameen, Balaji Srinivasan, Sharath Girimaji Abstract: Energy density in the scale space is defined for compressible turbulent flows using two point statistics. The objective is to quantify the energy associated with different scales in inhomogeneous turbulent flows, where it is not possible to obtain an energy spectrum for wavenumber space. Energy density in scale space is defined as, similar to the incompressible case [2], E(x,r)=-∂/∂r (Q(x, r),) where Q(x, r) is the two point velocity correlation for compressible turbulent flows[1]. The energy contained in scales ranging from r to r + dr is given by E(x, r)dr. DNS of temporally evolving compressible mixing layer are performed using a finite volume gas kinetic scheme [3] and the data is examined using the scale energy density. We investigate the energy density at different transverse locations for different convective Mach numbers (M c = 0.5, 0.9, 1.2). In the present study we study the energy distribution in one dimensional scale space. Energy density in streamwise scales at different transverse locations for one of the cases (M c = 0.5) is shown in figure 1(a) and a similar pattern is observed for other Mach numbers. We observe that the energy density peak occurs at a scale comparable to the Taylor length scale and that more than two-thirds of the energy is contained in scales larger than the Taylor scale. An evolution equation for E(x, r) is derived for compressible turbulent flow. This budget equation helps to understand how various physical mechanisms, viz energy production and dissipation, varies across the scales. The budget at the centerline for M c = 0.5 shown in figure 1(b) clearly shows that production (P) happens in large scales, small scales are dissipative and energy transfer (π) is from larger scales to smaller scales. These results will be discussed in detail at the conference. 11:30 15 mins #418 MEASURING THE FULL VELOCITY GRADIENT AND DISSIPATION RATE TENSOR IN HOMOGENEOUS TURBULENCE USING SHAKE-THE-BOX AND FLOWFIT Andreas Schroeder, Daniel Schanz, Sebastian Gesemann, Florian Huhn, Daniel Garaboa Paz, Vicente Pérez-Muñuzuri, Eberhard Bodenschatz Abstract: We present measurements of the full velocity gradient and dissipation rate tensor based on dense fields of fluid particle trajectories in homogeneous turbulence at Re~270 and ~350 in a von Kármán flow between two counter-rotating propellers. Applying the Shake-The-Box (STB) particle tracking algorithm [1], we are able to instantaneously track up to ~100.000 particles in a measurement volume of 50 x 50 x 15 mm³. The mean inter-particle distance is lower than 7 Kolmogorov lengths. The data assimilation scheme FlowFit [2] with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity, acceleration and jolt statistics, as well as the Eulerian counterparts on velocity and pressure gradients with respective Q-R-diagrams, compute the energy dissipation rate directly by using local velocity gradient information gained by FlowFit at midpoints of particle tetrahedra in close proximity of a few Kolmogorov lengths and compare it to known indirect approaches. 11:45 15 mins #560 Unifying local and global descriptions of turbulent entrainment Maarten van Reeuwijk, Christos Vassilicos, John Craske Abstract: In this contribution, we provide a definition of turbulent entrainment which can be applied both to the local and global viewpoints. We derive integral equations that describe turbulent free shear flows developing in space, time or both. The description clarifies the connection between the local and global descriptions of turbulent entrainment, and provides a seamless connection between the implicit description of TNTI required for the former and the explicit description usually adopted for the latter. The description is applied to several canonical flows, including the axisymmetric jet, the planar wake and the temporal jet. 12:00 15 mins #343 Effect of high-order finite difference discretization of the nonlinear term on turbulence statistics Naoya Okamoto, Tsuguo Matsuzaki, Mitsuo Yokokawa, Yukio Kaneda Abstract: Direct numerical simulation (DNS) of the Navier-Stokes (NS) equations using a Fourier spectral (SP) method is a powerful tool for turbulence research. For example, a recent massively parallel DNS of three-dimensional incompressible homogeneous turbulence achieved the Taylor microscale Reynolds number R_\lambda=2300 with the number of grid points N=12288^3. However, most of the elapsed time of the DNS was spent on global communication, since fast Fourier transform was used many times to compute the alias-free nonlinear term in the NS equations. The peak performance of the DNS was only about 2% on the K-computer, although this was highly efficient for the SP method. With the upcoming exascale era, considering less communicative methods than the SP method would be worthwhile. In this study, as a first step, we examine how the finite difference discretization of the nonlinear term affects the statistics of three-dimensional homogeneous isotropic turbulence using the numerical methodology we have developed. For more detail abstract, please see the uploaded pdf file. 12:15 15 mins #457 Filter-width dependence of the dynamics of homogeneous variable density turbulence Juan Saenz, Denis Aslangil, Daniel Livescu Abstract: We investigate variable density effects on subgrid-scale (SGS) dynamics, in the context of large Eddy Simulations (LES), in homogeneous variable density turbulence (HVDT) with Atwood (At) numbers between 0 and 1. In flows with large At, differential acceleration and differential diffusion lead to important variable density (VD) effects. These effects include e.g. 1) asymmetry of the mixing layer in Rayleigh-Taylor and two fluid Kelvin-Helmholtz instabilities, where the half layer position shifts to the light fluid, and the density, mean velocity and mass flux profiles within the mixing layer are asymmetrical; 2) different turbulence characteristics in the light and heavy fluid regions, with more intense turbulence and faster mixing near the pure fluid regions [6, 7, 10, 9, 1]. Modeling of turbulence in the presence of VD effects poses unique challenges, beyond those encountered in incompressible single-fluid systems. Velocity is no longer divergence-free and pressure-strain correlation becomes nontrivial. Additional variables appear due to the coupling between the fluids and the driving mechanism. For example, in the context of the Reynolds-averaged Navier-Stokes (RANS) framework, [3] (BHR) showed that the turbulent mass flux, or turbulent density-velocity correlation (ai), is important for the production mechanism of Reynolds stresses (Rij). In turn, the production of turbulent mass flux is modulated by the density-specific volume covariance (b). To capture these effects, additional transport equations are needed for a consistent second order closure compared to flows with zero or small density variations [10, 9]. More advanced modeling efforts include extensions to Fokker-Planck equation methods [2] and spectral closures [8]. The latter approach alleviates the need for phenomenological length-scale transport equations and can account for complex initial conditions spectra. However, extensions to inhomogeneous flows are difficult. On the other hand, VD effects on SGS dynamics are not well understood. Recently, by examining compressible, decaying VD turbulence, [4] showed that VD SGS effects are important for the dynamics of thermally inhomogeneous flows. Nevertheless, for such flows it is difficult to distinguish between density variations due to i) acoustic, ii) thermal, or iii) compositional effects. To isolate the VD effects due to compositional variation, which have been studied only scarcely compared to the other two effects, we focus on homogeneous VD turbulence (HVDT), where two incompressible miscible fluids with different densities in a triply-periodic volume move under constant gravitational acceleration [5, 6, 1]. Buoyancy-generated motions ensue from a quiescent state, producing a transition to turbulent flow. Initially, the ratio of production (P) to dissipation (ε) of turbulent kinetic energy (K) is large (P/ε ≫ 1) and decays with time as the fluids mix. As a result, TKE first has a growth stage, reaches a maximum when P/ε = 1, then decays [1]. We carry out a filtering analysis of spatial fields from recent high resolution direct numerical simulations of HVDT [1], in which we investigate the dynamics of statistical quantities that are used to model VD turbulence, and explore the effects of filter size on these dynamics. With the goal of informing the development of SGS closures for LES and for hybrid RANS/LES modeling, we investigate the dynamics of K, Rij, ai, b, and ε at several filter widths, and compare them to the behavior of the corresponding RANS statistics. The results are contrasted during the turbulence growth and decay stages. In particular, the presence of concentrated turbulence regions associated with the pure light fluid during the growth stage significantly affects the backscatter properties. While significantly reduced during the decay stage, subtle differences compared to regular turbulence decay can still be identified. References [1] D. Aslangil, D. Livescu, and A. Banerjee. Atwood and Reynolds numbers effects on the evolution of buoyancy-driven homogeneous variable- density turbulence, (Under review). Los Alamos National Laboratory, Technical Report LA-UR-18-29157. [2] J. Bakosi and J. R. Ristorcelli. A Fokker-Planck approach to a moment closure for mixing in variable-density turbulence, (Under Review). Los Alamos National Laboratory, Technical Report LA-UR-18-23839. [3] D. Besnard, F. H. Harlow, R. M. Rauenzahn, and C. Zemach. Turbulent transport equations for variable density turbulence and their relationship to two-field models. Los Alamos National Laboratory, Technical Report LA-12303-MS. [4] S. GS and G. V. Candler. Subgrid-scale effects in compressible variable-density decaying turbulence. J. Fluid Mech., 846:428–459, 2018. [5] D. Livescu and J. R. Ristorcelli. Buoyancy-driven variable-density turbulence. J. Fluid Mech., 591:43–71, 2007. [6] D. Livescu and J. R. Ristorcelli. Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech., 605:145–180, 2008. [7] D. Livescu, J. R. Ristorcelli, R. A. Gore, S. H. Dean, W. H. Cabot, and A. W. Cook. High-Reynolds number Rayleigh–Taylor turbulence. J. Turbul., 10:N13, 2009. [8] N. Pal, S. Kurien, T. Clark, D. Aslangil, and D. Livescu. Two-point spectral model for variable-density homogeneous turbulence. Phys. Rev. Fluids, 3:124608, 2018. [9] J. D. Schwarzkopf, D. Livescu, J. R. Baltzer, R. A. Gore, and J. R. Ristorcelli. A two-length scale turbulence model for single-phase multi-fluid mixing. Flow Turbul. Combust., 96(1):1–43, 2016. [10] J. D. Schwarzkopf, D. Livescu, R. A. Gore, R. M. Rauenzahn, and J. R. Ristorcelli. Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids. J. Turbul., 12:N49, 2011.