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 L19: Turbulence: Theory  Cascades & Multiscale InteractionTurbulence

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Chair: Kathy Prestridge, Los Alamos National Laboratory Room: 702 
Monday, November 20, 2017 4:05PM  4:18PM 
L19.00001: A K\`{a}rm\`{a}nHowarthMonin equation for variabledensity turbulence Chris Lai, John Charonko, Kathy Prestridge We present a generalisation of the von K\`{a}rm\`{a}nHowarthMonin (KHM) equation to include variable density (VD) effects. The derived equation: (i) reduces to the original KHM equation when density is a constant and (ii) leads to a VDanalogue of the 4/5law with the same value of constant (=4/5) appearing as the prefactor of dissipation rate. The equation is employed to understand negative turbulent kinetic energy production in a SF$_6$ turbulent round jet with an initial density ratio of 4.2; from a Reynoldsaveraged NavierStokes (RANS) perspective, negative production is indicative of an inverse energy cascade. We show that an inverse cascade exists in the development region of the jet and is captured by the linear scalebyscale energy transfer term in the variabledensity KHM equation. There is a redistribution of scale energy among turbulent eddies such that offaxis eddies lose their energies to the forwardcascading eddies oriented in the streamwise direction.The nonlinear transfer term of the VDKHM equation depicts a conventional forward cascade for all eddies having a size less than the Eulerian integral length scale, regardless of their orientation. The net effect is a retarded energy cascade that has not been accounted for by existing turbulence theories. [Preview Abstract] 
Monday, November 20, 2017 4:18PM  4:31PM 
L19.00002: The nature of triad interactions in active turbulence Jonasz Slomka, Piotr Suwara, Jorn Dunkel Generalized NavierStokes (GNS) equations describing threedimensional active fluids with flowdependent spectral forcing possess numerical solutions corresponding to parityviolating Beltramitype chaotic flows that can sustain an upward energy transfer. To rationalize these findings, we study the triad truncation of two GNS models. Utilizing a previously unknown cubic invariant, we show that the asymptotic triad dynamics reduces to that of a forced rigid body coupled to a particle moving in a magnetic field. This analogy allows us to classify the triadic interactions by their asymptotic stability: unstable triads correspond to rigidbody forcing along the largest and smallest principal axes, whereas stable triads arise from forcing along the middle axis. This suggests that the unstable triads dominate the initial relaxation stage of the full GNS equations, which is characterised by helicity growth, whereas the stable triads determine the statistically stationary state. To support this hypothesis, we introduce and simulate a new active turbulence model, which develops an energy spectrum with Kolmogorovtype 5/3 scaling. Our results suggests that Beltramitype flows and an inverse energy cascade are generic features of 3D active turbulence models with flowdependent forcing. [Preview Abstract] 
Monday, November 20, 2017 4:31PM  4:44PM 
L19.00003: The Inviscid Criterion for Scale Decomposition in Variable Density Flows Dongxiao Zhao, Hussein Aluie The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a `lengthscale.' A choice can be made according to the \emph{inviscid criterion}, which requires a scale decomposition to guarantee that viscous effects are negligible at large enough `lengthscales.' This is necessary to unravel inertialrange dynamics and the cascade in variable density turbulence. It has been proved recently that a densityweighted decomposition, or a Favre decomposition, satisfies the inviscid criterion. Here, we present numerical verification of that result. We also show that two other commonly used decompositions violate the inviscid criterion and, therefore, are not suitable to study inertialrange dynamics in variabledensity turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled if the smallest resolved scale is large enough. [Preview Abstract] 
Monday, November 20, 2017 4:44PM  4:57PM 
L19.00004: A New Cascade Mechanism in Compressible Turbulence Aarne Lees, Hussein Aluie Baropycnal work has been recently identified as a new cascade process that can participate in the transfer of energy across scales in compressible turbulence. We will explain the physical mechanism behind this cascade process. We will use a series of high resolution direct numerical simulations (DNS) of isotropic turbulence at varying degrees of compressibility to analyze baropycnal work and its relative significance. [Preview Abstract] 
Monday, November 20, 2017 4:57PM  5:10PM 
L19.00005: Tensor Geometry in the Turbulent Cascade Joseph Ballouz, Nicholas Ouellette The defining characteristic of highly turbulent flows is the net directed transport of energy from the injection scales to the dissipation scales. This cascade is typically described in Fourier space, obscuring its connection to the mechanics of the flow. Here, we recast the energy cascade in mechanical terms, noting that for some scales to transfer energy to others, they must do work on them. This work can be expressed as the inner product of a turbulent stress and a rate of strain. But, as with all inner products, the relative alignment of these two tensors matters, and determines how strong the energy transfer will be. By comparing the observed energy flux to the maximum possible if the tensors were in perfect alignment, we define an efficiency for the energy cascade. Using data from a direct numerical simulation of isotropic turbulence, we show that this efficiency is surprisingly low, with an average value of about 25% in the inertial range, though it is spatially heterogeneous. Our results have implications for how the stress and strain rate magnitudes influence the flux of energy between scales. [Preview Abstract] 
Monday, November 20, 2017 5:10PM  5:23PM 
L19.00006: From 2D to 3D turbulence through 2D3C configurations Michele Buzzicotti, Luca Biferale, Moritz Linkmann We study analytically and numerically the geometry of the nonlinear interactions and the resulting energy transfer directions of 2D3C flows. Through a set of suitably designed Direct Numerical Simulations we also study the coupling between several 2D3C flows, where we explore the transition between 2D and fully 3D turbulence. In particular, we find that the coupling of three 2D3C flows on mutually orthogonal planes subject to smallscale forcing leads to a stationary 3D outofequilibrium dynamics at the energy containing scales where the inverse cascade is directly balanced by a forward cascade carried by a different subsets of interactions [L. Biferale et al, Physics of Fluids 29, 111101 (2017)]. [Preview Abstract] 
Monday, November 20, 2017 5:23PM  5:36PM 
L19.00007: A fluctuation relation for the probability of energy backscatter Alberto VelaMartin, Javier Jimenez We simulate the large scales of an inviscid turbulent flow in a triply periodic box using a dynamic Smagorinsky model for the subgrid stresses. The flow, which is forced to constant kinetic energy, is fully reversible and can develop a sustained inverse energy cascade. However, due to the large number of degrees freedom, the probability of spontaneous mean inverse energy flux is negligible. In order to quantify the probability of inverse energy cascades, we test a local fluctuation relation of the form $\log{P(A)}=c(V,t)A$, where $P(A)=p(C_s_{V,t}=A)/p(C_s_{V,t}=A)$, $p$ is probability, and $C_s_{V,t}$ is the average of the leastsquared dynamic model coefficient over volume $V$ and time $t$. This is confirmed when $C_s$ is averaged over sufficiently large domains and long times, and $c$ is found to depend linearly on $V$ and $t$. In the limit in which $V^{1/3}$ is of the order of the integral scale and $t$ is of the order of the eddyturnover time, we recover a global fluctuation relation that predicts a negligible probability of a sustained inverse energy cascade. For smaller $V$ and $t$, the local fluctuation relation provides useful predictions on the occurrence of local energy backscatter. [Preview Abstract] 
Monday, November 20, 2017 5:36PM  5:49PM 
L19.00008: The cascade of energy in homogeneous turbulence: a 5D approach Jose CardesaDuenas, Alberto VelaMartin, Javier Jimenez The inherent multidimensional nature of the turbulent cascade is a major challenge to its study. In order to characterize a process occurring in space, time and scale, we present a new approach where we track coherent structures representing energy in different scales from a timeresolved simulation of isotropic turbulence lasting $66$ largeeddy turnovers. We couple the dynamics at different scales by computing the geometric intersection between individual coherent structures from any two scales. Statistically, we find that eddies at scale $r$ intersect those at scales $2r$ and $r/2$ preferentially at the beginning and at the end of their life, respectively. With our simulation at $Re_{\lambda}=315$, we could check this trend to hold for $r$ values spanning a ratio of $8$. We thus report on $4$ generations of eddies that trace the transfer of energy from scale $8r$ to scale $r$ via intermediate steps through a scalelocal, spatiallylocalized process. We found the geometric intersection between scales separated by ratios of $4$ or larger to be of the same order of magnitude as the random intersection levels found for those scale combinations. [Preview Abstract] 
Monday, November 20, 2017 5:49PM  6:02PM 
L19.00009: Transition from Direct to Inverse Cascade in ThreeDimensional Turbulence Ganapati Sahoo, Alexandros Alexakis, Luca Biferale We study a model system [1] where the triadic interactions in NavierStokes equations are enhanced or suppressed in a controlled manner without affecting neither the total number of degrees of freedom nor the ideal invariants and without breaking any of the symmetries of original equations. Our numerical simulations are based on the helical decomposition of velocity Fourier modes. We introduced a parameter (0 ≤ λ ≤ 1) that controls the relative weight among homochiral and heterochiral triads in the nonlinear evolution. We show that by using this weighting protocol the turbulent evolution displays a sharp transition, for a critical value of the control parameter, from forward to backward energy transfer but still keeping the dynamics fully three dimensional, isotropic, and parity invariant. [1] G Sahoo, A Alexakis and L Biferale, Phys. Rev. Lett 118, 164501 (2017). [Preview Abstract] 
Monday, November 20, 2017 6:02PM  6:15PM 
L19.00010: Culmination of the inverse cascade  mean flow and fluctuations Anna Frishman, Corentin Herbert An inverse cascadeenergy transfer to progressively larger scales  is a salient feature of twodimensional turbulence. If the cascade reaches the system scale, it terminates in the self organization of the turbulence into a large scale coherent structure, on top of small scale fluctuations. A recent theoretical framework in which this coherent mean flow can be obtained will be discussed. Assuming that the the quasilinear approximation applies, the forcing acts at small scales, and a strong shear, the theory gives an inverse relation between the average momentum flux and the mean shear rate. It will be argued that this relation is quite general, being independent of the dissipation mechanism and largely insensitive to the type of forcing. Furthermore, in the special case of a homogeneous forcing, the relation between the momentum flux and mean shear rate is completely determined by dimensional analysis and symmetry arguments. The subject of the average energy of the fluctuations will also be touched upon, focusing on a vortex mean flow. In contrast to the momentum flux, we find that the energy of the fluctuations is determined by zero modes of the meanflow advection operator. Using an analytic derivation for the zero mo [Preview Abstract] 
Monday, November 20, 2017 6:15PM  6:28PM 
L19.00011: A generalized selfsimilar spectrum for decaying homogeneous and isotropic turbulence Pingfan Yang, Alain Pumir, Haitao Xu The spectrum of turbulence in dissipative and inertial range can be described by the celebrated Kolmogorov theory. However, there is no general solution of the spectrum in the large scales, especially for statistically unsteady turbulent flows. Here we propose a generalized selfsimilar form that contains two lengthscales, the integral scale and the Kolmogorov scale, for decaying homogeneous and isotropic turbulence. With the help of the local spectral energy transfer hypothesis by Pao (Phys. Fluids, 1965), we derive and solve for the explicit form of the energy spectrum and the energy transfer function, from which the second and thirdorder velocity structure functions can also be obtained. We check and verify our assumptions by direct numerical simulations (DNS), and our solutions of the velocity structure functions compare well with hotwire measurements of highReynolds number windtunnel turbulence. [Preview Abstract] 
Monday, November 20, 2017 6:28PM  6:41PM 
L19.00012: Estimation of turbulent spacetime energy spectra using local wavenumber intervals Guowei He, Ting Wu Spacetime energy spectra describe the energy distributions over spatial and temporal scales in turbulent flows. However, the estimation of spacetime energy spectra from partially resolved velocity fields remains a great challenge. In this paper, we propose a local wavenumber interval (LWI) method to estimate spacetime energy spectra. This method can accurately predict the first and second moments of energy spectra, where the first moment can be used to calculate turbulent convection velocity and the second moment can be used to measure turbulent spectral broadening. We first show that both phase velocity and amplitude modulation make the significant contributions to spectral bandwidths. Therefore, the local wavenumber method that only utilizes the phase velocity is insufficient to determine spectral bandwidths. We further develop the LWI method than includes the contributions of both phase velocity and amplitude modulation to spectra bandwidths. Finally, we use the existing DNS data of turbulent channel flows to validate the LWI method, which accurately predicts spectral bandwidths. [Preview Abstract] 
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