Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session G23: Turbulence: Theory IV - Modeling and Simulation |
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Chair: William K. George, Princeton University Room: 318 |
Monday, November 25, 2013 8:00AM - 8:13AM |
G23.00001: On Intense Vortex Structures in Isotropic Turbulence Anthony Leonard We continue our study of vortex structures are having vorticity occupying the high amplitude tail of the distribution of vorticity amplitudes in homogeneous, isotropic turbulence. The data are obtained from the results of a $1024^3$ DNS at $Re_{\lambda} = 433$ residing in the Johns Hopkins web-based public database (http/turbulence.pha.jhu.edu). First, a connection is made between the PDF of a single intense structure and the vorticity distribution within that structure. Second, this PDF for intense structures, coupled with the distribution of finite-time Lyapunov exponents for material deformation in isotropic turbulence, yields a candidate for the full PDF of vorticity amplitudes. [Preview Abstract] |
Monday, November 25, 2013 8:13AM - 8:26AM |
G23.00002: Self-sustaining turbulence in a Restricted Nonlinear (RNL) Model of plane Couette flow Vaughan Thomas, Dennice Gayme, Brian Farrell, Petros Ioannou In this work we develop a restricted non-linear model (RNL) of plane Couette flow based on stochastic structural stability theory (S3T). The S3T system consists of a coupled set of equations for the evolution of a streamwise averaged mean flow forced by the ensemble averaged Reynolds stresses computed from the perturbations. The RNL model calculates the evolution of a single member of the perturbation ensemble interacting with the time varying streamwise averaged mean flow. Simulations of the RNL exhibit self-sustaining turbulent behavior that closely resembles DNS. S3T based analysis of this system shows that this self-sustaining activity arises due to the coupling from the mean flow to the perturbations, in other words the fact that the perturbations depend parametrically on the current state of the streamwise averaged mean flow. Elimination of this interaction reduces the system to the so-called 2D/3C model, which is asymptotically stable and consequently, does not exhibit turbulent behavior in the absence of forcing. Studies of the RNL confirm that the turbulence intensity decreases as the coupling strength is reduced, and that its behavior collapses to that of the 2D/3C model at a non-zero threshold. [Preview Abstract] |
Monday, November 25, 2013 8:26AM - 8:39AM |
G23.00003: A minimal representation of turbulence in plane Couette flow Dennice F. Gayme, Vaughan Thomas, Brian Farrell, Petros Ioannou We describe a stochastic structural stability theory (S3T) based model of fully developed turbulence in plane Couette flow. This model is obtained by partitioning Navier Stokes into a nonlinear equation governing the evolution of the streamwise averaged mean flow and a linearized equation for the covariance of streamwise varying perturbations. When coupled, these equations explicitly model the dynamics of a second order approximation of the probability distribution of the turbulence. We investigate this system using a computationally tractable Restricted Nonlinear (RNL) model that represents the dynamics of a single member of the infinite ensemble of the S3T system. The RNL system has been shown to capture the dynamics of roll/streak structures and to support self-sustaining turbulence. Our results demonstrate that this self-sustaining state naturally collapses to a minimal realization of turbulence that retains only the essential set of streamwise varying perturbations. Comparisons to DNS data show that this minimal representation captures the salient features of fully developed turbulence and that the wavelengths involved in this behavior are independent of the number of streamwise modes used or the channel length. [Preview Abstract] |
Monday, November 25, 2013 8:39AM - 8:52AM |
G23.00004: A ``resonant'' spanwise perturbation frequency in streamwise-constant Couette flow Ismail Hameduddin, Dennice Gayme Turbulence in plane Couette flow is dominated by streamwise elongated structures that are approximately spanwise periodic with a preferred spatial frequency. It has been postulated that these approximately streamwise-constant coherent structures develop due to streamwise vortices in the flow. We investigate this idea by considering a streamwise-constant (2D/3C) model of plane Couette flow. We introduce streamwise vortices by imposing spanwise periodic cross-stream perturbations on the flow field and study it's energy amplification under stochastic disturbances. The periodic nature of the resulting equations allows us to cast the system into a convenient, so-called ``lifted,'' form that retains the periodic coefficients in the analysis. We can then efficiently solve for the energy amplification using a perturbation approach on the associated Lyapunov equation. Our results show the existence of a peak or ``resonant'' spanwise frequency that maximizes the disturbance amplification, suggesting that the 2D/3C equations capture the type of (spanwise frequency) selective mechanism that leads to spanwise periodic structures common in fully developed flows. [Preview Abstract] |
Monday, November 25, 2013 8:52AM - 9:05AM |
G23.00005: Exact coherent structures in 2D weakly turbulent flow Roman Grigoriev, Ravi Pallantla The description of fluid dynamics in terms of exact coherent structures (ECS) has recently emerged as a promising approach to a deterministic description of weak turbulence. Each ECS corresponds to an exact regular unstable solution of the Navier-Stokes equation and turbulence can be thought of as a walk through neighborhoods of a set of ECS. Although many ECS of different types have been identified numerically for a variety of experimentally realizable 3D flows (e.g., pipe Pouseuille and plane Couette flows), none have been verified to exist in experiment, in part due to the practical difficulties with setting up the appropriate initial conditions. In this talk we discuss numerically computed ECS in a model of a 2D Lorentz force-driven flow in a thin layer of electrolyte, which should be much easier to compare with experiment due to the relative ease with which 2D flow can be manipulation and observed. Special attention is given to enforcing physical boundary conditions and the choice of protocols that can be used in experiment to reproduce unstable flows corresponding to computed ECS. [Preview Abstract] |
Monday, November 25, 2013 9:05AM - 9:18AM |
G23.00006: Universal Realizable Anisotropic Prestress (URAPS) Closure for the Reynolds Stress Charles Petty, Karuna Koppula, Andre Benard The Reynolds-averaged Navier-Stokes (RANS-) equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds (NR-) stress and the turbulent kinetic energy.~Clearly, any solution to an NS-closure model must be a non-negative operator. This longstanding problem has recently been addressed by developing a non-negative algebraic mapping of the NR-stress into itself. Consequently, all solutions of the URAPS NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. Most significantly, unlike the class of Boussinesq closures for the NR-stress, the new theory predicts the redistribution of the turbulent kinetic energy~among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows. Furthermore, the URAPS theory also predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay. [Preview Abstract] |
Monday, November 25, 2013 9:18AM - 9:31AM |
G23.00007: Simultaneous large-scale and sub-grid scale PIV measurements in a turbulent shear flow Oliver Buxton, Bharathram Ganapathisubramani An experimental investigation is undertaken in which the self-similar region of a nominally two-dimensional planar mixing layer is observed at inertial range and dissipative range spatial resolutions simultaneously. This is achieved by performing PIV experiments in which the field of view of three cameras, with a high spatial resolution, overlaps that of another camera with a lower spatial resolution in the far field of a mixing layer in which the Reynolds number based on the Taylor micro-scale is 260. The low-resolution experiment is thus analogous to a large eddy simulation (LES), in which the finest (sub-grid scale) stresses are modelled. This data thus permits an investigation of the effect of the large-scale fluctuations on the sub-grid scale (SGS) stresses, and vice-versa. It is found that the sign of the large-scale fluctuations is significant in determining the sub-grid scale activity, with low momentum (negative) large-scale fluctuations leading to an increase in the sub-grid scale stresses, particularly the $u^\prime v^\prime$ component. A Smagorinsky type SGS model is also compared to the experimental data in order to determine the effects of the large-scale fluctuations on the eddy viscosity. [Preview Abstract] |
Monday, November 25, 2013 9:31AM - 9:44AM |
G23.00008: Turbulence in Taylor-Couette Flow and a Molecule Dependent Transport Equation Luis Ma. Bo-ot, Ludek Jirkovsky We apply a previously derived and utilized a modified Navier-Stokes equation to Taylor-Couette flow, that is fluid flow enclosed between two concentric cylinders where the inner cylinder is rotating with some constant speed and the outer cylinder is stationary or vice versa. We report first analytic solutions describing velocity profiles of such flow in turbulent regime. The analytic profiles are compared with results of the reported first direct numerical simulation of Taylor-Couette flow in turbulent regime [D. Pirro and M. Quadricio, Euro. J. of Mech. B, 27, (2008) 552-566]. PACS: 47.20.Qr, 47.27.-I, 02.30.Gp [Preview Abstract] |
Monday, November 25, 2013 9:44AM - 9:57AM |
G23.00009: Temporal decorrelations in compressible isotropic turbulence Guowei He, Xing Zhang, Dong Li Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components while the classic random sweeping model is proposed for solenoidal components. The swept-wave model shows that the temporal decorrelations in dilatational fluctuations are dominated by two physical processes: random sweeping and wave propagation. These models are supported by the direct numerical simulation of compressible isotropic turbulence, in the sense of that all curves of normalized time correlations for different wavenumbers collapse into a single one using the normalized time separations. [Preview Abstract] |
Monday, November 25, 2013 9:57AM - 10:10AM |
G23.00010: ABSTRACT WITHDRAWN |
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