Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session A23: Turbulence Theory: Isotropic Turbulence |
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Chair: Saba Almalkie, University of Massachusetts Amherst Room: 30D |
Sunday, November 18, 2012 8:00AM - 8:13AM |
A23.00001: Invariants of the reduced velocity gradient tensor in turbulent flows Jose Cardesa, Dhiren Mistry, Lian Gan, James Dawson In this paper we examine the invariants $p$ and $q$ of the reduced $2\times 2$ velocity gradient tensor formed from a 2D slice of an incompressible 3D flow. Based on 2D PIV measurements and 3D DNS, we show that the joint probability density function of $p$ and $q$ exhibits a common characteristic shape shared across various turbulent flows. This is confirmed by data from a turbulent jet, a turbulent channel flow, isotropic turbulence in a periodic cube and mixing tank shear turbulence. The asymmetry in the shape of the resulting scatter plot is studied and proved to follow from the predominance of vortex stretching in all these flows. The only assumptions required for the proof are local homogeneity and local isotropy applied to the velocity gradients. We compare this $p-q$ scatter plot for which only 2D data is required with the widely known $Q-R$ scatter plot based on 3D information. Finally, we explore the properties of the strain rates deduced from the 2D velocity gradient tensor only. We find in which cases these can be used to unambiguously discriminate between sheet-forming or tube-forming configurations of the full 3D strain rates. [Preview Abstract] |
Sunday, November 18, 2012 8:13AM - 8:26AM |
A23.00002: Evolution of the velocity gradient invariants of fractal-generated turbulence Rafael Fernandes, Bharathram Ganapathisubramani, Christos Vassilicos An experimental study of turbulence generated by low-blockage space-filling fractal square grids was performed using cinematographic Stereo Particle Image Velocimetry in a water tunnel. Velocity gradient tensors were determined using Taylor's hypothesis and their invariants were computed at different distances downstream of the grid. It is shown that the classical tear-drop shape of the second and third invariant (Q and R) diagram is not seen throughout all measured stations but, instead, develops to the well known shape with downstream distance from the grid. Surprisingly, the averages of the Q and R remain zero throughout the measurements in space, even in highly inhomogeneous regions of the flow. The structure function achieves the 2/3 power law when conditioned on a very active sub-region of the flow, well before where the classical shape of the Q-R diagram is established, and in a non-Gaussian, inhomogeneous part of the turbulent flow. Finally, the alignment of the vorticity vector with the eigen vectors of the strain rate tensor in specific quadrants of the Q-R diagram is studied as a function of downstream position. [Preview Abstract] |
Sunday, November 18, 2012 8:26AM - 8:39AM |
A23.00003: The Forward-Backward Time Asymmetry in Shape Deformation of Tetrahedra in Fully Developed Turbulence Jennifer Mutschall, Haitao Xu, Alain Pumir, Eberhard Bodenschatz The analysis of shape deformations of multi-particle clusters can serve as an important tool for gaining insights in turbulent mixing. Recent experiments and numerical simulations on clusters of four particles (i.e. tetrahedra) observe a tendency for initially isotropic tetrahedra to deform into coplanar structures and thereby to enhance the mixing process. A quantitative understanding was to date missing. Further, the understanding of the forward-backward time asymmetry in shape deformation can elucidate the time-irreversibility of fully developed turbulence. Here we present an explanation of the observations and extend the analysis to the dynamics of tetrahedra backwards in time. We report our analytical results and compare them with our particle tracking experiments in a von Karman swirling flow and with direct numerical simulations of homogeneous isotropic turbulence in a periodic box. [Preview Abstract] |
Sunday, November 18, 2012 8:39AM - 8:52AM |
A23.00004: Intense dissipative mechanisms of strong thin shear layers in high Reynolds number turbulence Takashi Ishihara, Julian C.R. Hunt, Yukio Kaneda Direct numerical simulation of box turbulence at the Taylor micro-scale Reynolds number $R_\lambda =1131$ on $4096^3$ grid points was used to show that strong thin shear layers are the significant intermittent structures of high Reynolds number turbulence. Both the distance between the layers and their widths are comparable with the integral length scale $L$. The layers' thicknesses $\ell $ are of the order of the Taylor micro-scale $\lambda $. Typically $\ell \sim 4\lambda $, where $\lambda \sim 35L/R_\lambda $. Across the significant layers there are jumps in large-scale velocities of the order of the rms velocity $u_o $. Within the layers, much thinner intermittent, elongated vortical eddies are generated, with microscale thickness $\ell _v \sim 178L/R_\lambda ^{3/2}$ with associated large peak values of vorticity of order $u_o /\ell _v (<35\omega _{\mbox{rms}} )$ and velocities of the order of $u_o (<3.4u_o )$, where $\omega _{\mbox{rms}} $ is the rms vorticity. The vorticity of these micro-scale eddies have components predominantly parallel to the average vorticity of the thin shear layers. Their spacing is of order $\ell _v $, so that vortices within the layers are reasonably close packed. The high relative magnitude of dissipation in the significant thin layers balances with the high relative magnitude of energy transfer (across the wave number $k)$ for $k$ larger than $\pi /\ell $. The marked increase in the energy transfer inside the layer for $k$ comparable with $\pi /\ell $ defines the eddy scales where the maximum energy transfer occurs from outside to inside. [Preview Abstract] |
Sunday, November 18, 2012 8:52AM - 9:05AM |
A23.00005: On the angle between relative velocity and relative acceleration between two fluid particles in turbulence Haitao Xu, Alain Pumir, Eberhard Bodenschatz In turbulence study, it is often desirable to know if locally the flow is strain-dominated or vorticity-dominated. This information not only is related to the local flow topology, it also reveals where small particles with weak inertia accumulate. However, to determine whether strain or vorticity is dominating requires access to the velocity gradient tensor, which is difficult to measure experimentally. By using results from direct numerical simulation of fully developed turbulence we show that the angle between the relative velocity and the relative acceleration between two fluid particles can be used as an indicator of strain-dominated versus vorticity-dominated flow structure. This new indicator has the advantage that it is much more easily accessible experimentally than measuring the velocity gradients. We also present further turbulence statistics from both DNS and experiments conditioned on the angle between relative velocity and relative acceleration and compare them with those conditioned on strain and vorticity. [Preview Abstract] |
Sunday, November 18, 2012 9:05AM - 9:18AM |
A23.00006: Wind tunnel measurements of scale-by-scale energy transfer, dissipation, advection and production/transport in equilibrium and nonequilibrium decaying turbulence Pedro Valente, Christos Vassilicos The cornerstone assumption that $C_{\epsilon} \equiv \epsilon L/u^3 \approx constant$ was found to breakdown in certain nonequilibrium regions of decaying grid-generated turbulence with wide power-law near -5/3 spectra where the behaviour of $C_\epsilon$ is, instead, very close to $C_\epsilon \sim Re_L^{-1}$ (Valente \& Vassilicos, 2012 [Phys. Rev. Lett. 108, 214503]). We investigate nonequilibrium turbulence by measuring with two cross wire anemometers the downstream evolution of the scale-by-scale energy transfer, dissipation, advection, production and transport in the lee of a square-mesh grid and compare with a region of equilibrium turbulence. For the nonequilibrium case it is shown that the production and transport terms are negligible for scales smaller than about a third of $L$. For both cases it is shown that the peak of the scale-by-scale energy transfer scales as $u^3/L$ which is the expected behaviour for equilibrium turbulence. However, for the nonequilibrium case this implies an imbalance between the energy transfer to the small scales and the dissipation. This imbalance is reflected on the small-scale advection which becomes larger in proportion to the maximum energy transfer as the turbulence decays whereas it stays proportionally constant in the equilibrium case. [Preview Abstract] |
Sunday, November 18, 2012 9:18AM - 9:31AM |
A23.00007: The Reynolds number dependence of classical grid turbulence Eberhard Bodenschatz, Gregory Bewley, Michael Sinhuber, Margit Vallikivi, Marcus Hultmark, Alexander Smits We measured inertial and dissipation range statistics in the decaying turbulence generated by a biplanar grid of crossed bars. We did so at Taylor Reynolds numbers between 130 and 1700, reaching higher than any previous study of reasonably homogeneous and isotropic turbulence. The measurements were made in the Variable Density Turbulence Tunnel at the Max Planck Institute in G\"{o}ttingen with both traditional hot-wire anemometers and the new nano-fabricated NSTAP anemometers developed at Princeton. We fixed the large-scale conditions of the flow while changing the Reynolds number only by changing the viscosity of the fluid. To do this, we used two gases, air and sulfur hexafluoride, and adjusted the pressure of the gases to between 1 and 15 bar. The data confirm that even when the large-scale conditions are controlled as the Reynolds number is raised, scaling ranges are not well-defined unless Extended Self-Similarity is employed. [Preview Abstract] |
Sunday, November 18, 2012 9:31AM - 9:44AM |
A23.00008: Local and distant interactions in the Batchelor regime of scalar turbulence Robert Rubinstein, Wouter Bos Kraichnan's 1968 paper on the passive scalar reconsidered Batchelor's classic analysis of the persistence of scalar fluctuations in the dissipation range of the velocity field when the scalar diffusivity is much smaller than the fluid viscosity. Adopting the premise that the velocity field fluctuates rapidly, instead of Batchelor's hypothesis that the velocity field is essentially static, Kraichnan found that although Batchelor's prediction of a $k^{-1}$ spectrum remains intact, the subsequent diffusive range falls off as $\exp(-k)$ instead of Batchelor's prediction $\exp(-k^2)$. We will show that these two hypotheses also make significantly different predictions of higher order statistics in the $k^{-1}$ range, namely that in Kraichnan's analysis, a reduction of mean square advection analogous to the `suppression of nonlinearity' in Navier-Stokes turbulence occurs, but that this effect is absent in Batchelor's analysis. This difference will be interpreted in the light of a suggestion of Yukio Kaneda that the difference between Kraichnan's and Batchelor's analysis originates in treating velocity-scalar interactions either as local (Kraichnan) or as asymptotically distant (Batchelor). [Preview Abstract] |
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