Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session HS: Turbulence Theory II |
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Chair: Charles Meneveau, Johns Hopkins University Room: Hilton Chicago Stevens 4 |
Monday, November 21, 2005 1:20PM - 1:33PM |
HS.00001: Multi-Scale Gradient Expansion of the Turbulent Stress Tensor Gregory Eyink Turbulent stress is the fundamental quantity in the filtered equation for large-scale velocity that reflects its interactions with small-scale velocity modes. We develop a convergent expansion of the turbulent stress tensor into a double series of contributions from different scales of motion and different orders of space-derivatives of velocity, a Multi-Scale Gradient (MSG) expansion. We describe several important applications of our methods, starting with the inverse energy cascade of 2D turbulence. To first order in velocity-gradients we find that the turbulent stress in 2D is proportional not to strain but instead to ``skew-strain,'' i.e. the strain tensor rotated by 45 degrees. We show that this result is consistent with a simple ``vortex-thinning'' mechanism of inverse cascade, proposed by Kraichnan in 1976. In 3D turbulence the stress has three contributions to first order in gradients: a tensile stress along principal directions of strain, a contractile stress along vortex lines, and a shear stress proportional to skew-strain. Our 3D results are consistent with Taylor's ``vortex-stretching'' mechanism of forward energy cascade, but imply also a second, less scale- local contribution from skew-strain. For 3D helicity cascade our results are consistent with a mechansm of ``twisting'' of small-scale vortex filaments due to a large-scale screw. In contrast to energy flux, helicity flux arises scale-locally from skew-strain while the stress along vortex-lines gives a secondary, less scale-local contribution. Supported in part by NSF grant \#ASE-0428325. [Preview Abstract] |
Monday, November 21, 2005 1:33PM - 1:46PM |
HS.00002: Deterministic large-eddy simulation Robert Rubinstein, Timothy Clark By `deterministic large-eddy simulation' we mean the abridgment of a spectral closure theory by replacing small scales of motion by a simplified subgrid model. As in standard LES, this abridgment reduces the number of resolved scales; the important question is how well the subgrid model preserves the dynamics of the resolved scales. This question will be addressed for the transient development of a Kolmogorov spectrum under steady forcing in a fluid initially at rest. This problem poses a simple yet severe test of the physical ideas behind subgrid models. Deterministic analogs of the classical Smagorinsky, dynamic Smagorinsky, and Yoshizawa-Horiuti one-equation subgrid models will be considered. The classical Smagorinsky model does not reproduce the transient dynamics well. Both the dynamic model and the one-equation model are considerably better. Perhaps surprisingly, the best results are obtained with a dynamic procedure that expresses everything in terms of the resolved scales alone. [Preview Abstract] |
Monday, November 21, 2005 1:46PM - 1:59PM |
HS.00003: Spectral eddy viscosity and diffusivity in a turbulent shear Hyung-Suk Kang, Charles Meneveau Experimental measurements were performed of the spectral eddy viscosity and diffusivity in a heated wake flow, using an array of four X-wire and four cold-wire probes. The data were analyzed by applying two-dimensional box-filtering in the streamwise and cross-stream directions and using assumptions of local isotropy. The results show that the spectral eddy viscosity and diffusivity approach zero at large wavenumbers (qualitatively consistent with Leslie \& Quarini's classic analysis for graded filters). We find that it also decreases at low wavenumbers approaching the integral scale. To compare the experimental results with EDQNM predictions in more detail, the EDQNM computations are performed using the experimentally obtained spectra. Also, the sensitivity of the EDQNM predictions to eddy-damping parameters and to the flow integral scale is explored. Overall, we find reasonable qualitative agreement between measurements and EDQNM. However, we find that the low- wavenumber decrease of the measurements is not reproduced well by the EDQNM within reasonable ranges of the adjustable parameters. Some discrepancies between our EDQNM calculations and those of Leslie \& Quarini are also pointed out. [Preview Abstract] |
Monday, November 21, 2005 1:59PM - 2:12PM |
HS.00004: Experimental Measurement of Single-Particle Dispersion in High Reynolds Number Turbulence Kelken Chang, Haitao Xu, Nicholas Ouellette, Mickael Bourgoin, Eberhard Bodenschatz We report Lagrangian measurements of single-particle dispersion in a high Reynolds number (up to a Taylor microscale Reynolds number of $R_{\lambda} = 815$) turbulence experiment. The motion of tracer particles is followed optically in three dimensions using multiple high speed cameras. Such direct measurement is not possible from Eulerian techniques. We compare our measurements with previous experimental data, stochastic models and DNS. This work is supported by the National Science Foundation and the Max Planck Society. [Preview Abstract] |
Monday, November 21, 2005 2:12PM - 2:25PM |
HS.00005: Material deformations and scalar intermittency in restricted Euler dynamics Yi Li, Charles Meneveau We explore the implications of Restricted Euler dynamics on the intermittency of the velocity and passive scalar fields, and on the geometry of material deformations. Following the pioneering work of Cantwell (1992), we find a number of exact solutions for the Lagrangian evolution of material elements, velocity increments, and passive scalar increments. For the latter, the probability density functions calculated from the model system display a rapid evolution from Gaussian to exponential, to stretched exponential distributions. This is in good qualitative agreement with the intermittent statistics of scalar increments in turbulent flows. We show how the analysis can be generalized to include linear viscous damping. The analytical predictions for material deformations based on restricted Euler are compared with results obtained from filtered direct numerical simulations, in which geometry of deforming material elements is tracked in a Lagrangian frame. [Preview Abstract] |
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