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 D23: Turbulence Theory: General I |
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Chair: Gregory Eyink, Johns Hopkins University Room: 30D |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D23.00001: Analytical Model for Pair Dispersion in Gaussian Models of Eulerian Turbulence Gregory Eyink, Damien Benveniste Synthetic models of Eulerian turbulence are often used as computational shortcuts for studying Lagrangian properties of turbulence (e.g. Elliott \& Majda, 1996). These models have been criticized by Thomson \& Devenish (2005), who argued on physical grounds that their sweeping effects are very different from true turbulence. We give analytical results for Eulerian turbulence modeled by Gaussian fields. Our starting point is an exact integrodifferential equation for the particle pair separation distribution obtained from Gaussian integration-by-parts. When velocity correlation times are short, a Markovian approximation leads to a Richardson-type diffusion model. We obtain a time-dependent pair diffusivity tensor of the form $K_{ij}({\bf r},t)=S_{ij}({\bf r})\tau(r,t)$ where $S_{ij}({\bf r})$ is the structure-function tensor and $\tau(r,t)$ is an effective correlation time of velocity increments. Crucially, this is found to be the minimum value of three times: the intrinsic turnover time $\tau_{eddy}(r)$ at separation $r$, the overall evolution time $t,$ and the sweeping time $r/v_0$ with $v_0$ the rms velocity. We thus verify the main argument of Thomson \& Devenish (2005), but we predict scaling laws for pair dispersion different from theirs for zero-mean velocity ensembles. [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D23.00002: Deviations from Kolmogorov-Kraichnan similarity theory in the energy cascade of two-dimensional alpha turbulence Bel Helen Burgess, Theodore Shepherd We study energy cascades in 2D $\alpha$ turbulence, for which ``vorticity'' $\theta$ is related to streamfunction $\psi$ by $\theta(\mathbf{x}) = (-\Delta)^{\alpha/2} \psi(\mathbf{x})$, where $(-\Delta)^{\alpha/2}$ is the fractional Laplacian. Using the eddy damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions. The energy flux is finite and the similarity solution self-consistent for $\alpha < 4$. In keeping with strain rate arguments, this suggests a spectrally local and self-similar energy cascade for $\alpha < 4$. However, the transfers vanish identically for $\alpha = 2.5$ and $\alpha = 10$. Comparison with statistical equilibrium spectra elucidates this: for $\alpha = 2.5$ and $\alpha = 10$, the similarity spectra coincide with enstrophy and energy equipartition respectively, and the similarity ranges are equilibrium solutions with Gaussian statistics. Moreover, the similarity range energy flux is toward small scales for $\alpha \in (2.5,10)$, suggesting that any inverse cascade for $\alpha \geq 2.5$ cannot be self-similar. Numerical simulations confirm this: for $\alpha < 2.5$, one can obtain the similarity spectrum, while for $\alpha \ge 2.5$, the inverse cascade spectrum is significantly steeper than the similarity solution. [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D23.00003: On the decay of homogeneous nearly isotropic turbulence behind active fractal grids Adrien Thormann, Charles Meneveau The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results appear to favor power-law decay with exponents between -1.2 and -1.4, approximately. More recently, fractal-generated turbulence (Hurst \& Vassilicos, PoF 2007, and subsequent papers) using multi-scale passive grids suggest possible faster decay, and non-trivial behavior especially near the grid, where the mean velocity is spatially evolving. In order to generate spatially homogeneous flow using multi-scale injection of kinetic energy at high Reynolds numbers, we use a new type of active-grid consisting of winglets with various fractal shapes. We test space-filling fractal shaped winglets as well as Sierpisky-carpet and Apollonian packing type fractal shapes. Data are acquired using X-wire thermal anemometry. Tests of homogeneity of mean flow and turbulence intensity will be presented as well as decay of kinetic energy and spectral characteristics of the flow. [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D23.00004: Can a flow be turbulent in microfluidics with Reynolds number in the order of 1? Guiren Wang, Fang Yang, Wei Zhao Traditionally, it is believed that turbulence occurs in relatively high Re number flow. For instance, the critical Re number is about 2100 in a pipe flow. Although there can be elastic turbulence in low Re, it is conventionally believed that the flow in mirofluidics, where typical Re is in the order of 1 or less, can only be laminar. Here, we demonstrate that features of turbulent flows can be achieved in a microchannel with Re in the order of 1, when the flow is electrokinetically forced. To measure the flow velocity, we developed a confocal microscopic velocimeter with high tempo-spatial resolution, i.e. molecular tracer based Laser Induced Fluorescence Photobleaching Velocimeter. We measured the general features in turbulent flows: fast diffusion or mixing, irregular flow velocity, high dissipation rate, 3-D flow and continuous power spectrum of velocity fluctuation indicating multiscale structures of small eddies. Interesting is that a -5/3 power spectrum with about one decade span in frequency is also observed. The results indicate that turbulence can be realized as well in microfluidics with Re in the order of 1. The study could open a new perspective view on turbulence and transport phenomena in microfluidics. [Preview Abstract] |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D23.00005: On the collision of small particles in isotropic turbulence Satoshi Yokojima, Takashi Mashiko, Kenjiro Baba, Takashi Miyahara Collisions of small particles in isotropic turbulence are closely investigated by direct numerical simulations. In the talk, the relationship between particle collision events and the background turbulent flow field will be discussed. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D23.00006: Turbulent 2-Particle Dispersion Laws in Kinematic Simulations Damien Benveniste, Gregory Eyink Kinematic Simulations (KS) are often used as a shortcut for studying Lagrangian properties of turbulence (e.g. Elliott {\&} Majda, 1996) but have been criticized by Thomson {\&} Devenish (2005), who pointed out that KS sweeping effects are very different from true turbulence. We study numerically by a Monte Carlo method a Richardson-like diffusion equation recently derived analytically by us for KS models, which exhibits such sweeping effects. With moderate inertial-ranges like those achieved in current KS, our model is found to reproduce the $t^{9/2}$ power-law for pair dispersion predicted by Thomson {\&} Devenish and observed in those KS. However, for much longer ranges, our model exhibits three distinct pair-dispersion laws in the inertial-range: a Batchelor $t^2$-regime, followed by a Kraichnan-model-like $t^1$ diffusive regime, and then a $t^6$ regime. Finally, outside the inertial-range, there is another $t^1$ regime with particles undergoing independent Taylor diffusion. These scalings are exactly the same as those predicted by Thomson {\&} Devenish for KS with large mean velocities, which we argue hold also for KS with zero mean velocity. Our results support the basic conclusion of Thomson {\&} Devenish (2005) that sweeping effects make Lagrangian properties of KS completely different from true turbulence for very extended inertial-ranges. [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D23.00007: Turbulence modulation through the interface of a deformable drop Luca Scarbolo, Dafne Molin, Alfredo Soldati The transport of momentum across the interface of a large deformable droplet immersed in a turbulent liquid is investigated using Direct Numerical Simulation of turbulence (pseudo-spectral method) coupled with the Diffuse Interface Model to track the droplet interface. We explored a wide range of Weber numbers (ratio between inertial forces and surface tension) always limiting the analysis to cases of non-breaking droplets where the droplet and the surrounding fluid have the same density and viscosity. We quantify turbulence modulation across the interface in terms of velocity fluctuations and turbulent kinetic energy, showing that turbulence is always weaker inside the droplet. We also determine how the turbulent kinetic energy budget terms are influenced by the surface tension and how the local vorticity is affected by the presence of the interface. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D23.00008: Turbulence close to the critical point of a fluid Gautier Verhille, Cecile Lachize, Patrice Le Gal Most of experiments in turbulence deal with liquid or gas. With classical fluids it is quite difficult to have both a high Reynolds number and a Mach number high enough to have compressible effects ($Ma \ga 0.3$). In water the sound speed is too large to permit compressible effects ($c\sim1500$m/s at room temperature and atmospheric pressure) and in air the viscosity is not so small ($\nu\sim10^{-5}$m$^2$/s) so it is difficult to have high Reynolds number in a laboratory experiments. On the contrary, a fluid close to its critical point has a small kinematic viscosity, typically 20 times smaller than the water viscosity for SF6, and a small sound speed as the compressibility diverges, $c\sim70$m/s for SF6. Other properties of the fluid are diverging close to the critical point, as the correlation length of the density fluctuation and other goes to zero, as the thermal conductivity. We present here the first study of the modification of a turbulent flow close to the critical point. This flow is created in a rotor stator cavity, a one disk version of the ``french washing machine,'' in a pressurized and thermalized vessel filled up with SF6. Pressure and velocity measurements show an increase of the large scale dynamic whereas the inertial range does not seem to be affected. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D23.00009: Chaos Synchronization in Navier-Stokes Turbulence Cristian C. Lalescu, Charles Meneveau, Gregory L. Eyink Chaos synchronization (CS) has been studied for some time now (Pecora \& Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al. 2002). CS in general is said to be present in a pair of coupled dynamical systems when a specific property of each system has the same time evolution for both, even though the evolution itself is chaotic. There have been some studies of CS for systems with an infinite number of degrees of freedom (Kocarev et al. 1997), but CS for Navier-Stokes (NS) turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. We present DNS results which show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. We compare our results with related ideas of ``approximate inertial manifolds.'' The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we show are recoverable even at very high Reynolds number from simulations that only resolve down to about the Kolmogorov scale. [Preview Abstract] |
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