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 L18: Turbulence Theory: General |
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Chair: Susan Kurien, LANL Room: 400 |
Monday, November 25, 2019 1:45PM - 1:58PM |
L18.00001: A symmetry of the pressure Hessian in the incompressible Euler and Navier-Stokes equations Maurizio Carbone, Andrew Bragg, Michele Iovieno The Lagrangian dynamics of the velocity gradient is examined in the strain-rate eigenframe, in three-dimensional (3D) and incompressible flows. The equations highlight a symmetry of the pressure Hessian. Indeed, the component of the eigenframe angular velocity along the vorticity direction does not play any role in the Lagrangian dynamics of the velocity gradient invariants. Such symmetry involving the eigenframe angular velocity turns into a gauge symmetry for the pressure Hessian, which is determined up to a term proportional to the commutator between the symmetric and anti-symmetric part of the velocity gradient tensor. Therefore, only four numbers are necessary to specify the effective pressure Hessian in 3D flows. The gauge term is exploited to simplify the geometry of the non-local pressure Hessian, reducing it to a tensor of rank two. This simplifies the geometric interpretation of the pressure Hessian effect on the dynamics of the velocity gradient invariants and allows to compare two- and three-dimensional flows. We characterize the geometry of the effective pressure Hessian by means of DNS results, focusing on the statistics of its independent eigenvalue and the alignment between the plane on which the effective pressure Hessian acts and the strain-rate eigenframe. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L18.00002: Velocity gradient (VG) decomposition into normal-strain, pure shear, solid-body-rotation tensors: new insights into turbulence VG dynamics Rishita Das, Sharath Girimaji Velocity gradient tensor (VGT, $A_{ij}$) decomposition into symmetric ($S_{ij}$) and anti-symmetric ($W_{ij}$) tensors is unable to segregate the effect of shear present in both the “strain-rate” and “rotation-rate” tensors. In this study, an additive decomposition of VGT into normal strain-rate ($N_{ij}$), solid body rotation ($R_{ij}$) and pure shear ($H_{ij}$) tensors, is employed. In this decomposition, shear is clearly demarcated from pure rotation and pure normal strain effects. Then, we use direct numerical simulation data of incompressible forced isotropic turbulence in Taylor Reynolds number range $Re_\lambda \in (200-600)$, to examine statistical and dynamical aspects of velocity gradient dynamics. We investigate (i) the probability distribution of the magnitude (Frobenius-norm) of these pure strain, pure shear and solid-body rotation tensors; (ii) the preferential alignment of the axis of solid-body rotation with the normal strain-rate eigenvectors; (iii) the conditional statistics of different VG processes as a function of these tensors; and (iv) intermittency phenomenon. The study develops unique and novel insights into turbulence processes which are not evident from previous VGT decompositions. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L18.00003: Area Rule for velocity circulation Kartik Iyer, Katepalli Sreenivasan, P.K. Yeung The statistical theory of velocity circulation at high Reynolds numbers has witnessed renewed interest following recent studies, both empirical (Iyer et al., arXiv:1902.07326, 2019) and theoretical (Migdal, arXiv:1903.08613, 2019). A central tenet in the scaling theory of circulation is the Area Rule which states that the probability distribution of the circulation around closed contours, whose characteristic dimensions reside in the inertial range, depends solely on the minimal spanning surface of the contour. We examine the Area Rule for both low and high order circulation moments, for different contour shapes and sizes, using the DNS of the three-dimensional Navier-Stokes equations within a cube with periodic boundary conditions, with the integral-scale Reynolds number spanning over two decades. Useful comparisons with other fields such as the Gaussian random fields will be discussed to highlight the simplicity afforded by circulation in the statistical description of small-scale turbulence. [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L18.00004: Intermittency of Incompressible Passive Vector Convected by Homogeneous Turbulence Toshiyuki Gotoh, Jingyuan Yang, Hideaki Miura, Takeshi Watanabe \def\w{\mbox{\boldmath $w$}} It is known that the fluctuation of passive scalar convected by turbulence is stronger than that of the turbulent velocity. In order to understand the physical mechanism yielding this difference we have studied the fluctuations of an incompressible passive vector $\w$ convected by the isotropic turbulence by comparing them with the passive scalar. It is found that the passive vector spectrum obeys the Obukhov-Corrsin spectrum $k^{-5/3}$ with constant $C=0.99$ and the low order statistics is close to the velocity at large scales and resembles the passive scalar at small scales. Strength of the intermittency of the passive scalar is intemediate between the velocity and the passive scalar. The domain shape of intense $|\nabla\times \w|^2$ is found to be sheet like and similar to the scalar gradient. It is argued that the linearity of the equation is the key to generate the stronger intermittency of the passive fields. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L18.00005: Toward investigation of local vortex line topology in turbulence Bajrang Sharma, Rishita Das, Sharath Girimaji Current vortex identification methods employ $Q$ or $\lambda_2$ criterion to investigate vortical structures in turbulent flows. We propose an alternate method to examine the local vortex structure. Specifically, we construct the vorticity vector field ($\vec\omega$) and compute the vorticity gradient tensor ($J_{ik}\equiv \partial\omega_i/\partial x_k$). The tensor ($J_{ik}$), similar to the velocity gradient tensor ($A_{ij}\equiv\partial u_i/\partial x_j$), is trace free. In a manner similar to streamline topology analysis using the second and third invariants of $A_{ij}$, the second ($Q_\omega$) and third ($R_\omega$) invariants of $J_{ik}$ are used to develop the topological description of local vortex line structure. Such a representation is not only useful for investigation of the local vortex-line structure but is also useful in identifying key turbulence phenomena such as vortex line reconnection. Direct numerical simulation (DNS) data of incompressible forced isotropic turbulence and perturbation-evolution in plane-Poiseuille flow are analysed in this study. We investigate the following: (i) distribution in these two key canonical turbulent flows; and (ii) the formation of hair-pin vortices in transitioning plane Poiseuille flow using the aforementioned method. [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L18.00006: Origin and implications of odd-spin contributions in rapidly distorted turbulence Susan Kurien, Timothy Clark, Robert Rubinstein We present mathematical calculations and supporting data from numerical simulations to demonstrate the emergence of reflexion-symmetry breaking along the polar axis in flows, in the rapid distortion limit. The mathematical decomposition of second-rank tensors (eg. velocity correlations in wavenumber space) is done in the SO3 basis. We show the appearance of symmetry breaking for various reflexion-symmetric initial conditions including isotropic and axisymmetric turbulence. The strain-rate tensor used to achieve rapid distortion also remains symmetric in all our test cases. These results help to elucidate the mechanism by which the so-called odd-spin (reflexion-symmetry breaking) terms arise in the SO3; they also clarify the separate role of this type of symmetry breaking from other explicitly reflexion-symmetric forcings such as helical or rotational strains. [Preview Abstract] |
Monday, November 25, 2019 3:03PM - 3:16PM |
L18.00007: How the ramp-cliff structures in scalar turbulence vary with the Schmidt number and how to model that variation Dhawal Buaria, M.P. Clay, K.R. Sreenivasan, P.K. Yeung In turbulent mixing of passive scalars, the ramp-cliff structures observed in one-dimensional cuts of the scalar field are responsible for a few important consequences, such as, departure from local isotropy, saturation of scaling exponents with respect to the moment-order. These results are established for the case of unity Schmidt number ($Sc$), given by the ratio of the kinematic viscosity of the fluid to the scalar diffusivity. In this talk, our first goal is to show how the above results vary with increasing $Sc$. We utilize a massive DNS database with the Taylor-scale Reynolds number in the range $140-650$, and Sc in the range $1-512$, for the case of passive scalar with a uniform mean scalar gradient, mixed by forced isotropic turbulence. In particular, we investigate how the odd moments of the scalar derivatives (which are the symptoms of the ramp-cliff structures) vary with $Sc$. A model based on the changing ramp-cliff structures is presented to describe the observed scaling of the scalar derivative statistics. We also address the scaling of scalar increments for varying $Sc$ and particularly explore the saturation of exponents with respect to the order of their moments. [Preview Abstract] |
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