Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session M6: Turbulence Theory IV |
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Chair: Alan Kerstein, Sandia National Laboratories Room: 309 |
Tuesday, November 22, 2011 8:00AM - 8:13AM |
M6.00001: Linear flow dynamics near a T/NT interface Miguel Teixeira, Carlos Silva The characteristics of a suddenly-inserted T/NT interface separating a homogeneous and isotropic shear-free turbulence region from a non-turbulent flow region are investigated using rapid distortion theory (RDT), taking full account of viscous effects. Profiles of the velocity variances, TKE, viscous dissipation rate, turbulence length scales, and pressure statistics are derived, showing very good agreement with DNS. The normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. In the non-turbulent region, where the flow is irrotational (except within a thin viscous boundary layer), the dissipation rate decays as $z^{-6}$, where $z$ is distance from the T/NT interface. The mean pressure exhibits a decrease towards the turbulence due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and dissipation rate display large maxima at the T/NT interface due to the existing inviscid discontinuities of the tangential velocity, and these maxima are quantitatively related to the thickness of the viscous boundary layer (VBL). At equilibrium, RDT suggests that the thickness of the T/NT interface scales on the Kolmogorov microscale. [Preview Abstract] |
Tuesday, November 22, 2011 8:13AM - 8:26AM |
M6.00002: PDF Equation Approach to the Lagrangian Velocity Increment Statistics of Fully Developed Turbulence Michael Wilczek, Haitao Xu, Nicholas T. Ouellette, Eberhard Bodenschatz The Lagrangian velocity increment statistics of fully developed three-dimensional turbulence is known to be highly intermittent, i.e., the probability density functions (PDFs) undergo a transition from a nearly Gaussian shape for large time lags to a highly non-Gaussian shape with pronounced tails for small time lags. We study this shape deformation across scale in the framework of the corresponding PDF equation, which is readily derived from the Lagrangian equations of motion. Here, the conditional acceleration plays a key role. The unclosed acceleration term is determined from experimental and direct numerical simulation data and is investigated with respect to the possibility of a simple mechanism for the origin of Lagrangian intermittency. [Preview Abstract] |
Tuesday, November 22, 2011 8:26AM - 8:39AM |
M6.00003: The role of helicity on the turbulent energy flux Federico Toschi, Luca Biferale, Stefano Musacchio Three-dimensional turbulence is characterized by two inviscid constants of motion, kinetic energy and helicity. Helicity (i.e. the correlation between velocity and vorticity) is a key quantity in fluid turbulence, and has not a definite sign. This mere fact have since long been associated with the different phenomenology of 3d vs. 2d turbulence, which in contrast has two positive defined conserved quantities, energy and enstrophy (the square vorticity). In this study we investigate the role of helicity on the turbulent cascade process by decomposing the velocity field on the eigenmodes of the curl operator which have definite-sign helicity. We present numerical results on the statistical properties of the energy flux and velocity field in turbulent flows in which interactions between modes are selected according to their helicity. Minimal bibliography: P. D. Ditlevsen and P. Giuliani (2001) ``Cascades in helical turbulence'' PRE, 63(3), 036304. Q. Chen, S. Chen, and G.L. Eyink (2003) ``The joint cascade of energy and helicity in three-dimensional turbulence'' Physics of fluids, 15(2), 361. R. Benzi, L. Biferale, R. M. Kerr, and E. Trovatore (1996) ``Helical shell models for three- dimensional turbulence'' Phys. Rev. E 53, 3541. F. Waleffe (1992) ``The nature of triad interactions in homogeneous turbulence'' Phys. Fluids A, 4(2), 350. [Preview Abstract] |
Tuesday, November 22, 2011 8:39AM - 8:52AM |
M6.00004: Lagrangian Acceleration Statistics in Curvilinear Coordinates Oliver Kamps, Michael Wilczek In this talk we present results from the analysis of the Lagrangian acceleration statistics in curvilinear coordinates. The investigation is based on numerical simulations of isotropic, homogeneous turbulence in three dimensions for a certain range of Reynolds numbers. We focus on the effect of curvilinear coordinates on statistical observables like the cross correlation between acceleration components and the long time memory of the acceleration. Beside this we compare our observations to the corresponding observables in simulations of two-dimensional turbulence in the inverse cascade regime. [Preview Abstract] |
Tuesday, November 22, 2011 8:52AM - 9:05AM |
M6.00005: Turbulence in an inhomogeneous medium Robert Rubinstein In some compressible turbulent flows, it is appropriate to assume that density fluctuations are negligible. The additional assumption that the mean density is known independently of the velocity field defines a model problem of turbulent fluctuations in an inhomogeneous medium in which the solenoidal condition on velocity of the constant density case is replaced by a solenoidal condition on the product of density and velocity. Because the fluctuations are inhomogeneous, the correlation function is not diagonal in the Fourier representation. Closure theories for this problem will be formulated and applied to analyze the possibility of inhomogeneous steady states and the applicability of gradient transport models. A generalized self-similarity for variable density will be developed and applied to the compressible law of the wall for boundary layers at moderate Mach numbers. Implications of the breakdown of this type of self-similarity as Mach number is increased will be drawn for understanding the behavior of cold-wall boundary layers. [Preview Abstract] |
Tuesday, November 22, 2011 9:05AM - 9:18AM |
M6.00006: Flow-thermodynamics interactions in compressible shear-driven turbulence: Linear analysis of possible flow control strategies Rebecca Bertsch, Gaurav Kumar, Sharath Girimaji Flow-thermodynamics interaction in turbulent flows can be classified into three categories based on the action of pressure fluctuations. In very high Mach number flows, pressure fluctuations play an insignificant role as momentum far exceeds pressure forces. At very low Mach numbers, pressure is determined by the Poisson equation and flow-thermodynamics interactions are dynamically not very important. However, at intermediate Mach numbers, pressure exhibits wave character leading to critical flow-thermodynamics interactions and concurrent modification in the nature of turbulence. In our previous works, we have established that inhibiting influence of compressibility on turbulence is due to the intermediate Mach number regime. In this work, we use RDT (rapid distortion theory) linear equations to examine some strategies for flow control in the intermediate Mach number regime by exploiting flow-thermodynamic interactions. The results have important implications for inhibiting onset of turbulence in hypersonic external flows and intensifying mixing in internal propulsion flows. [Preview Abstract] |
Tuesday, November 22, 2011 9:18AM - 9:31AM |
M6.00007: Statistics of incremental averages of passive scalar fluctuations Colin Meyer, Laurent Mydlarski Whereas statistics of differences in turbulent quantities measured over a given separation have been extensively studied, statistics of the incremental averages of the same quantities (e.g., $\Sigma \theta \equiv [\theta(x+r) + \theta(x)]/2$) have only been the focus of recent research. The present work studies incremental averages of a fluctuating passive scalar (temperature) in nearly homogeneous, isotropic turbulence, generated by an active grid, with an imposed mean scalar gradient. Following the arguments of Mouri and Hori ({\it Phys. Fluids}, 2010) for the velocity field, we derive a scale-dependent budget for the incremental average of the scalar field fluctuations, $\Sigma \theta$. We discuss its relationship to Yaglom's four-thirds law (which pertains to differences of passive scalar fluctuations) and compare the results with the experimental data. Furthermore, the statistics of $\Sigma \theta$ are compared with those of the incremental averages of the velocity fluctuations ($\Sigma u_\alpha$). [Preview Abstract] |
Tuesday, November 22, 2011 9:31AM - 9:44AM |
M6.00008: Nonlinear stochastic advection and structure generation in two-dimensional ideal fluids Madalina Vlad, Florin Spineanu We show that trajectory trapping or eddying in the structure of the turbulence is the main physical reasons for the strong nonlinear effects that are observed in two-dimensional ideal fluids. This conclusion is drawn from a study of the statistics of test particles in turbulent Euler fluids, which is based on a new analytical method. Trajectory trapping determines non-Gaussian distribution of the displacements, quasi-coherent motion and local flows. This nonstandard statistical properties of trajectories determine the evolution of turbulence toward large correlation lengths (inverse cascade) and long correlation times. Thus, trajectory trapping explains the tendency of structure generation in two-dimensional Euler fluids. [Preview Abstract] |
Tuesday, November 22, 2011 9:44AM - 9:57AM |
M6.00009: Universal constants and equations of turbulent motion Helmut Baumert For turbulence at high Reynolds number we present an analogy with the kinetic theory of gases, with dipoles made of vortex tubes as frictionless, incompressible but deformable quasi-particles. Their movements are governed by Helmholtz' elementary vortex rules applied locally. A contact interaction or ``collision'' leads either to random scatter of a trajectory or to the formation of two likewise rotating, fundamentally unstable whirls forming a dissipative patch slowly rotating around its center of mass, the latter almost at rest. This approach predicts von Karman's constant as 1/sqrt(2 pi) = 0.399 and the spatio-temporal dynamics of energy-containing time and length scales controlling turbulent mixing [Baumert 2005, 2009]. A link to turbulence spectra was missing so far. In the present contribution it is shown that the above image of dipole movements is compatible with Kolmogorov's spectra if dissipative patches, beginning as two likewise rotating eddies, evolve locally into a space-filling bearing in the sense of Herrmann [1990], i.e. into an ``Apollonian gear.'' Its parts and pieces are are frictionless, excepting the dissipative scale of size zero. Our approach predicts the dimensionless pre-factor in the 3D Eulerian wavenumber spectrum (in terms of pi) as 1.8 , and in the Lagrangian frequency spectrum as the integer number 2. Our derivations are free of empirical relations and rest on geometry, methods from many-particle physics, and on elementary conservation laws only. [Preview Abstract] |
Tuesday, November 22, 2011 9:57AM - 10:10AM |
M6.00010: Nonlinear Mechanisms in Streamwise Constant Plane Couette Flow Dennice F. Gayme, Bassam Bamieh, Beverley J. McKeon, John C. Doyle The dominance of streamwise constant features was previously used to motivate input-output analysis of a streamwise constant (2D/3C) model of plane Couette flow (Gayme et. al 2011). Periodic spanwise-wall normal (z-y plane) stream functions acted as the input and led to a forced 2D/3C streamwise velocity field qualitatively similar to a fully turbulent spatial field of DNS data, in particular having a spanwise mean consistent with the time-averaged mean turbulent velocity profile. In this work, we further explore the relationship between the nonlinearity in the model and the mechanisms involved in creating the turbulent velocity profile's shape. We combine similar input functions with a weakly nonlinear (perturbation) analysis to determine analytical expressions for the leading terms in the streamwise velocity expansion. Our results provide further evidence of the importance of each of the nonlinear streamwise constant terms in the momentum transfer required to generate the turbulent mean velocity profile. \textbf{Acknowledgements:} This research is supported by AFOSR. B.J.M. gratefully acknowledges NSF-CAREER award no. 0747672 (program managers W. W. Schultz \& H. H. Winter). [Preview Abstract] |
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