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 A11: Turbulence Theory I |
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Chair: Julian Domaradzki, University of Southern California Room: 314 |
Sunday, November 20, 2011 8:00AM - 8:13AM |
A11.00001: Can turbulence closure models come with error bars or uncertainty bounds? Sharath Girimaji The inherent complexity of turbulence -- chaotic and intermittent character -- may render many of the conventional uncertainty quantification norms and procedures ineffective for error assessment in closure models. A concerted alliance between turbulence physics and statistical characterization is imperative to make fundamental progress. In this presentation we first identify the most important sources of uncertainties in turbulence closure modeling and classify them into aleatoric (statistical) and epistemic (systematic) categories in the context of one-point closures. Then we propose a framework for exploiting the closure modeling knowledgebase accumulated over the last several decades and channeling the physical understanding for the purpose of uncertainty quantification. In the long run, such development is critical for the progression of turbulence CFD calculation from ``post-dictive'' nature to high-confidence predictive tools. [Preview Abstract] |
Sunday, November 20, 2011 8:13AM - 8:26AM |
A11.00002: A Study of Structures with Intense Vorticity in Isotropic Turbulence Anthony Leonard We study the characteristics of vortex structures 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). The power law for the observed tail implies a certain average local structure for those regions containing intense vorticity. To obtain a global structure satisfy the solenoidal condition for the vorticity field we add the gradient of a vorticity potential computed using the above-mentioned local structure. Then by assuming that the full vorticity field results from a Poisson distribution in space of these global structures, we can then compute the full PDF of vorticity amplitudes employing techniques used to find the (Holtsmark) distribution of gravitational forces acting on a star due to neighboring stars (see, e.g., S. Chandrasekar, 1943, Rev. Mod. Phys. $\bf{15}$, 1-89). The computed full PDF agrees very well with the observed PDF derived from the DNS data. [Preview Abstract] |
Sunday, November 20, 2011 8:26AM - 8:39AM |
A11.00003: A Lagrangian view of vorticity-strain alignment in turbulent flows Eberhard Bodenschatz, Alain Pumir, Haitao Xu Vortex stretching is arguably the most important aspect of dynamics in 3- dimensional fluid turbulence. Intuitively, one would expect that the vorticity vector is aligned to the direction of the strongest stretching. It is therefore puzzling when numerical simulations and experiments showed that, at any instantaneous time, vorticity preferentially aligns to the intermediate eigenvalues of the rate of strain tensor, corresponding to much weak stretching. Here we show that the dynamics is simplified when the alignment process is studied in a Lagrangian frame, i.e, following a fluid element. Using data from particle tracking experiments and direct numerical simulations, we studied the evolution of 4 fluid tracers that initially form isotropic tetrahedra. The evolution dynamics can be revealed in terms of the velocity gradient tensor perceived by the tetrads. For tetrads with size spanning from the dissipative scale to well in the inertial range, we observed the alignment of the vorticity to the direction of the strongest stretching *at earlier time*, i.e., a demonstration of the expected vortex-stretching in turbulence. For tetrads of sizes within the inertial range, the alignment process occurs at time scales given by the tetrad size and the energy dissipation rate. [Preview Abstract] |
Sunday, November 20, 2011 8:39AM - 8:52AM |
A11.00004: Extracting Coherent Structures from Turbulence Gary Chandler, Rich Kerswell We consider the problem of extracting dynamically-important exact solutions of the Navier-Stokes equations directly from turbulent flows. By monitoring near-recurrences of the flow in direct numerical simulations of 2D body-forced turbulence, we uncover an array of equilibrium points, travelling waves and periodic orbits over a range of Reynolds numbers, which underpin the complicated dynamics seen. Progress will be discussed in determining whether these solutions can then be used to predict the mean statistics of the turbulence (in the spirit of Kawahara \& Kida 2001). [Preview Abstract] |
Sunday, November 20, 2011 8:52AM - 9:05AM |
A11.00005: Wavelet versus Fourier Analysis of the Conditional Vorticity Budget in Homogeneous Isotropic Turbulence Benjamin Kadoch, Michael Wilczek, Kai Schneider, Rudolf Friedrich, Marie Farge We study the conditional balance of vortex stretching and vorticity diffusion of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. This decomposition is achieved by the Coherent Vorticity Extraction (CVE) based on orthogonal wavelets applied to DNS data, which yields insights into the influence of the different contributions as well as their interaction. It is shown that CVE yields an excellent representation of the total flow using a reduced number of degrees of freedom, which is particularly interesting as the conditional budget of vortex stretching and vorticity diffusion represents a dynamical rather than a purely kinematic relation. The results are compared to a decomposition with a standard Fourier filter. [Preview Abstract] |
Sunday, November 20, 2011 9:05AM - 9:18AM |
A11.00006: Convergence of third-order velocity structure functions in axisymmetric turbulence Fabien Godeferd, Alexandre Delache Kolmogorov theory (1941) for isotropic turbulence establishes asymptotic scaling laws for the statistics of $n$-th order structure functions at high Reynolds number, in terms of dissipation $\epsilon$ and separation distance $r$ for the velocity increment $\delta u$. A famed relationship is the -4/5 law. When the turbulent flow is anisotropic, due to external distortions (background rotation,...) to inhomogeneities or initial conditions (jets, ``isotropic'' grid turbulence), such laws may fail. We examine the applicability of the K41 predictions for third-order moments of velocity structure functions, and evaluate low Reynolds number effects and anisotropic effects on the departure with the -4/5 law. We consider rotating or stably stratified turbulence, whose statistics are obtained by Direct Numerical Simulations or by a two-point statistical model allowing to reach high Reynolds numbers. We link anisotropic spectral statistics for energy transfer with $<(\delta u)^3>$ and derive physical space statistics from spectral data of the statistical model. Although K41 scalings may arguably not apply to anisotropic turbulence, some justifications for anisotropic turbulence statistics can be provided (Taylor et al. PRE 2003) by specific data processing in DNS. [Preview Abstract] |
Sunday, November 20, 2011 9:18AM - 9:31AM |
A11.00007: Does the Kolmogorov scaling bridge hydrodynamic linear stability and turbulence? Stefania Scarsoglio, Francesca De Santi, Daniela Tordella The way in which the kinetic energy is distributed over the multiplicity of scales is a fundamental feature of turbulence. According to Kolmogorov's 1941 theory, by dimensional analysis, the only possible form for the energy spectrum function is the -5/3 spectrum. Experimental evidence has accumulated that supports it. Until now, such a power-law decay was considered a specific treat of the nonlinear interaction overlooking turbulence dynamics. We show here that this picture is also present in the linear interaction relevant to three-dimensional stable perturbation waves. Through extensive computation of the transient life of these waves in typical shear flows, we observe that the energy they own when, out of the transient phase, enter the final exponential decay shows a spectrum very close to the -5/3 spectrum. Moreover, also the observation times show a similar scaling. [Preview Abstract] |
Sunday, November 20, 2011 9:31AM - 9:44AM |
A11.00008: Statistically non-stationary turbulence William K. George Of all the assumptions in Kolmogorov 1941 the most fundamental is the assumption (or postulate) that that the smallest scales of the turbulence are in statistical equilibrium. This is usually justified by heuristic arguments based on the decreasing time scales as the eddy size is decreased relative to that of the energy containing eddies so that they can be assumed to be in {\it local equilibrium}. This argument can be shown to be fundamentally flawed since it does not account for the decreasing energy of the smaller scales. Moreover there are well-documented counter-examples to local equilibrium in non-stationary flows. It will be suggested that the K41 scaling arguments (or variations upon it) for the dissipative scales are in fact only applicable to flows in strict statistical equilibrium (i.e., statistically stationary), and should not be expected to apply to non-equilibrium flows. At least three types of non-equilibrium flows will be identified, one of which curiously enough satisfies Kolmogorov scaling at all scales. [Preview Abstract] |
Sunday, November 20, 2011 9:44AM - 9:57AM |
A11.00009: Restricted Euler moments in a pre-turbulent state Robert M. Kerr, Andrew N. Ferguson, Miguel D. Bustamante The evolution of the velocity stress moments of the `restricted Euler' equations with an isotropic pressure Hessian are compared with their evolution under the three-dimensional Hessian of the full nonlinear terms for a flow with changing structures. Past analysis of numerical data in a fully developed flows has shown that the second and third invariants, $Q$ and $R$ are distributed in the manner predicted by this model. In this work, we ask how these distributions depend upon whether the underlying vortex structures are sheets or tubes. Distributions will also be used to compare the time-derivatives of the individual terms, as predicted by the restricted Euler model, with their values when the full Hessian is applied. Both types of distributions are time-dependent, that is dependent on the underlying vortical structures. When vortex tubes dominate and the turbulence is becoming fully-developed, the predictions of the restricted Euler model are approximately obtained. However, when vortex sheets are dominant, another paradigm is needed. At a minimum, these results suggest that while the restricted Euler model might be a good representation of turbulence once it is fully developed, during the period when the turbulence is still developing, modifications to the usual picture will be needed. [Preview Abstract] |
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