Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C15: Turbulence: Mixing 
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Chair: Nathanael Machicoane, University of Washington Room: 310 
Sunday, November 24, 2019 8:00AM  8:13AM 
C15.00001: Scalar power spectra and turbulent length scales in highSchmidtnumber scalar fields Mohammad Mohaghar, Lakshmi P Dasi, Donald R Webster This experimental study has investigated effects of Reynolds number ($5000\leq Re\leq 20,000$) and initial release diameter ($2.2mm\leq D\leq 9.4mm$) on scalar power spectra and turbulent length scales of highSchmidtnumber passive scalar fields resulting from an isokinetic release in a turbulent boundary layer. The turbulence analysis is based on 12,000 scalar fields collected using the PLIF technique for each case at 6 locations downstream. Although the spectral slope at intermediate scales is found to increase to an asymptotic value higher than 5/3 farther downstream, there is an increase in spectral slope from approximately 1.5 for $Re=5000$ to roughly 1.2 for $Re=20,000$ while fixing the release diameter at 4.7 mm. A similar trend is observed for the effect of nozzle diameter on spectral slope, as it increases from almost 1.5 to 1.2 when the nozzle diameter changes from 9.4 mm to 2.2 mm while fixing $Re=10,000$. The scalar integral scale and scalar Taylor microscales are calculated directly from the scalar fields using the correlation function. It was found that the Taylor microscale decreases and the integral scale increases to an asymptotic value respectively, farther downstream. This indicates a larger range of scales exists as flow becomes more turbulent. [Preview Abstract] 
Sunday, November 24, 2019 8:13AM  8:26AM 
C15.00002: Frozen waves in turbulent mixing layers BenoitJoseph Grea Strong timeperiodic accelerations applied tangentially to an infinite horizontal plane layer between two miscible fluids trigger a parametric instability leading to remarkable sawtooth patterns known as frozen waves. The resulting turbulent mixing zones grow in time and then saturate when the resonance conditions of internal gravity waves are no longer fulfilled. The Floquet analysis of a model equation and direct numerical simulations reveal that the final mixing zone sizes evolve as the square of the forcing amplitude while, by contrast, the horizontal wavelengths grow nearly linearly. This explains why frozen waves sharpen with increasingly intense horizontal oscillations. It also suggests that an horizontal forcing mixes more efficiently fluids than a vertical one at large forcing accelerations. [Preview Abstract] 
Sunday, November 24, 2019 8:26AM  8:39AM 
C15.00003: Complex networkbased Lagrangian analysis of turbulent mixing in channel flows at different Reynolds numbers Giovanni Iacobello, Stefania Scarsoglio, Hans Kuerten, Luca Ridolfi Turbulent mixing is a fundamental issue in many applications, from natural phenomena to industry. In the Lagrangian viewpoint, typical investigations involve the temporal evolution of pairwise meansquare separation or multiparticle shape evolution. In this work, recent advances in complex networks are exploited to study turbulent mixing in a Lagrangian framework. The dynamics of a set of fluid particles is geometrized in a timedependent complex network, in which nodes correspond to groups of particles and link activation is based on particle spatial proximity. A turbulent channel flow setup is considered at different Reynolds numbers, with the aim to highlight the relative intensity of advection and mixing. Specifically, accurate direct numerical simulations of turbulent channel flows are performed, with Reynolds number between 180 and 950. By doing so, the networkbased approach is able to capture the temporal development of particle dynamics due to the turbulent motion, as well as transient and longterm features of wallnormal turbulent mixing. Based on present findings, Lagrangianbased networks can pave the way for a systematic networkbased investigation of turbulent mixing, thus extending the level of information of classical statistics. [Preview Abstract] 
Sunday, November 24, 2019 8:39AM  8:52AM 
C15.00004: Alignment Analysis of Passive Scalar Mixing in Shock Turbulence Interaction Xiangyu Gao, Ivan BermejoMoreno, Johan Larsson The transport of passive scalar fields by an initially isotropic turbulent flow passing through a nominally planar shock wave is investigated via shockcapturing DNS for different Mach numbers (1.5 to 5), turbulence Mach numbers (0.1 to 0.4), and Taylor microscale Reynolds numbers (40, 70), with unitary Schmidt number, including both wrinkled and brokenshock regimes. The effects of the shockturbulence interaction on alignments between the strainrate eigenvectors and vorticity, scalar gradient, and the mean streamwise direction are studied, aided by a novel barycentric map representation. Across the shock, the scalar gradient shows an increased alignment with the most extensive eigenvector of strain rate at the expense of a reduced alignment with the most compressive eigenvector (which still dominates) and with the intermediate eigenvector (which becomes nearly perpendicular). This trend is more obvious with larger Mach number and smaller Taylor microscale Reynolds number. Also, across the shock, the most probable alignment between the passive scalar gradient and the eigenvectors of the strainrate tensor is found to converge towards the alignment that provides the largest scalar dissipation, which is correlated with the enhanced scalar mixing observed downstream of the shock. [Preview Abstract] 
Sunday, November 24, 2019 8:52AM  9:05AM 
C15.00005: Differential diffusion and spectral transfer in turbulent mixing at high Schmidt numbers Kiran Ravikumar, P.K YEUNG, M.P. Clay Many applications of turbulent mixing involve differential diffusion between scalars of different molecular diffusivities. We study this phenomenon using direct numerical simulation, employing a dualgrid computational approach to meet stringent resolution requirements for scalars of low diffusivity (high Schmidt number, $Sc$). The largest Schmidt number ratio considered is 64, occurring between two scalars of $Sc=4$ and 256, whose fluctuations are produced by velocity fluctuations acting upon a uniform mean scalar gradient. Spectral transfer characteristics examined individually for each scalar show robust evidence of a forward cascade, where local transfer by nonlocal interactions modulated by lowwavenumber velocity modes is readily observed at the small scales. Contributions to the coherency spectra from moderately nonlocal velocityscalar triads were found to produce a net decorrelating effect at small scales which is balanced by the coherent mean gradient forward cascade leading to a stationary state. The scalings of the twoscalar difference spectrum and joint dissipation rate are investigated in detail. The role of differential diffusion in doublediffusive convection is briefly addressed. [Preview Abstract] 
Sunday, November 24, 2019 9:05AM  9:18AM 
C15.00006: Largescale anisotropic structure of a passive scalar in turbulence under a uniform mean gradient at low Schmidt numbers Tatsuya Yasuda, Toshiyuki Gotoh, Takeshi Watanabe, Izumi Saito We have run direct numerical simulations (DNS) of passive scalar turbulence in a triply periodic box with various parameter sets. The homogeneous isotropic turbulent velocity field is achieved by a Gaussian whitenoise forcing, and passive scalar fluctuations are sustained with a uniform mean scalar gradient. In so doing, we discover that the degree of anisotropy in passive scalar fluctuation is well predicted by not the Schmidt number $\textrm{Sc} = \nu/\kappa$ but the Peclet number $\textrm{Pe}_{\lambda} = u^{\prime} \lambda_{\theta}/\kappa$, where $\nu$, $\kappa$, $u^{\prime}$ and $\lambda_{\theta}$ are the kinematic viscosity, molecular diffusivity, rootmeansquare velocity and Taylormicro scale for turbulent scalar field, respectively. We also find that, at sufficiently low Peclet numbers, very largescale scalar structures, which elongate along the direction of the uniform mean scalar gradient, are generated and sustained by the action of scalar diffusion and the mean scalar gradient. They can emerge irrespective of Reynolds numbers as long as the Peclet number is sufficiently low. [Preview Abstract] 
Sunday, November 24, 2019 9:18AM  9:31AM 
C15.00007: A FractionalOrder NonFickian Transport Model For Scalar Turbulence Ali AkhavanSafaei, Mehdi Samiee, Mohsen Zayernouri Anomalous features such as spotty behavior of coherent vortex structures, rampcliff structures and scaling of the structure functions have been shown to be significantly effective on passive scalars mixing and transport in turbulent flows. It has experimentally and numerically been pointed out that such anomalies are imprinted on the statistical features of passive scalar as nonGaussian statistics, i.e., heavytailed and asymmetric distributions. According to the physics, these anomalies are described as nonlocal phenomena such as longrange interactions in passive scalar properties during the mixing process. We propose a heavytailed stochastic transport model which is employing the fractional calculus that intrinsically is designed to consider nonlocal effects and intermittent behavior. In this talk, we present the Eulerian and Lagrangian implementations of the proposed framework and discuss their numerical considerations. As an important canonical problem, we study the passive scalar mixing on a wellresolved homogeneous isotropic turbulence (HIT) in a periodic computational domain. We show the performance of our stochastic transport model for a variety of Reynolds and Schmidt numbers including a discussion on the statistics of passive scalar and its structure functions. [Preview Abstract] 
Sunday, November 24, 2019 9:31AM  9:44AM 
C15.00008: The influence of propagation angle on vortex ringinduced mixing Benjamin Jackson, Stuart Dalziel The propagation angle of a vortex ring travelling towards the interface in a twolayer density stratification has a considerable influence on the mixing induced by the interaction that ensues. For example, at bulk Richardson number equal to 1, a vortex ring propagating at 75 degrees to the vertical produces an interfacial wave when sufficiently close to the interface. The ring is unable to penetrate the interface, the flow remains largely laminar and the ring acts minimally to mix the stratification. Conversely, for the same Richardson number, a vertically downward propagating vortex ring will cause significant volumes of lower layer fluid to be ejected into the upper layer as the vortex ring destabilises, leading to a turbulent energy cascade and considerable mixing. Here, we present new experimental results investigating the mixing induced by the periodic generation of vortex rings fired at an angle in a twolayer stratification. We demonstrate how deviating from the vertically propagating case impacts the evolution of the density field and the longterm mixing regime. [Preview Abstract] 

C15.00009: ABSTRACT WITHDRAWN 
Sunday, November 24, 2019 9:57AM  10:10AM 
C15.00010: Local Wave Number Model for Inhomogeneous Turbulence Nairita Pal, Susan Kurien, Ismael Boureima, Praveen Ramaprabhu, Andrew Lawrie We provide a systematic characterization of buoyancydriven twofluid system in the RayleighTaylor configuration using a spectral turbulence model. In the system, we have a heavy fluid accelerated into a light fluid by grav itational acceleration. In the spectral turbulence model, known as ``Local Wave Numbe'' or LWN model, we compute the timeevolution of the spectral distribution in wave number $k$ of the correlation of density and specific volume $b(k)$, the velocity associated with the turbulent mass flux $a(k)$, and the turbulent kinetic energy $E(k)$, using a set of coupled equations. We next assess the accuracy of the model relative to Implicit Large Eddy Simulations of the same system using $b$, $a$ and $E$ as metrics. We show that the model is able to capture the gross features of the flow, like the evolution of the mixing layer and the evolution of the mean mass flux velocity with time. In particular the wellknown quadratic growth of the mix layer is captured by the LWN model. [Preview Abstract] 
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