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 L11: Turbulence Theory III |
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Chair: Blair Perot, University of Massachusetts, Amherst Room: 314 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L11.00001: Effects of Outer Scales on Near-Wall Reynolds Stresses and Higher-Order Statistics M.H. Buschmann, M. Gad-el-Hak The classical view of wall-bounded turbulence suggests that the near-wall region should be scaled with characteristic scales that are closely related to that region. For the last decade, however, alternative concepts considering the influence of outer scales were proposed. Herein, we show that the near-wall Reynolds stresses as well as higher-order statistics in different geometries (e.g., zero-pressure-gradient boundary layers, and pipe and channel flows) collapse in single Reynolds-number-independent curve when scaled with an alternative mixed scaling based on $\bf{u_{\tau}^{3/2}u_{e}^{1/2}}$. [Preview Abstract] |
Monday, November 21, 2011 3:48PM - 4:01PM |
L11.00002: Relevant length scales and time scales in shear flow turbulence Subhas Venayagamoorthy, Lakshmi Dasi, Benjamin Mater Shear flow turbulence has been the subject of fundamental research due to its ubiquitous presence in engineering and natural flows. In this study, we take a fresh approach using dimensional arguments tempered by physical reasoning to gain further insights on their phenomenology. Beginning with the four basic quantities: turbulent kinetic energy $k$, dissipation rate $\epsilon$, kinematic viscosity $\nu$ and mean shear $S$, we construct six length scales and two time scales that are most relevant to this classical problem and discuss their implications on phenomenology. Analysis of the variation of all six length scales and two timescales using high-resolution DNS data of turbulent channel flow and homogeneous shear flow are used to highlight important transitions in the flow dynamics and provide a framework to explain the energy cascade process. [Preview Abstract] |
Monday, November 21, 2011 4:01PM - 4:14PM |
L11.00003: On the smallest sub-kolmogorov mean length scale and its implications on phenomenology Lakshmi Dasi, Subhas Venayagamoorthy The smallest scale in turbulence has been predicted to be less than the Kolmogorov scale $\eta$ by a factor of Re$^{1/4}$ and attributed to the intermittency of the turbulent kinetic energy dissipation rate $\varepsilon$. We show through dimensional arguments that this smallest limit corresponds to a new mean length scale based on turbulent kinetic energy $k$ and kinematic viscosity $\nu$, given by ($\nu^{2}$/$k)^{1/2}$. The independence of this scale with $\varepsilon$ raises the issue of physical dependence of length scales and challenges classical phenomenology. Thus the notion that the smallest scales are set by the intermittent fluctuations of dissipation rate may be physically in-accurate. Given that $\varepsilon$ is also set independently by the large scale and the turbulent kinetic energy, the physical consequence is that the dissipative portion of energy cascade is constrained between $\eta$ and ($\nu ^{2}$/$k)^{1/2}$. Another important implication stems from the fact that ($\nu ^{2}$/$k)^{1/2}$ is a mean length scale. This alludes to the existence of even smaller scales of motion in the instantaneous field that are governed by the fluctuations in turbulent kinetic energy. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L11.00004: Length scales in anisotropic turbulence Gregory Bewley, Kelken Chang, Eberhard Bodenschatz In isotropic turbulence, a single scalar function fully describes the velocity correlation tensor. The characteristic scales of this correlation function, the Taylor scale and the integral scale, then have an unambiguous interpretation. The integral scale, for example, is a measure of the most energetic scale of turbulence. Anisotropic turbulence is more complicated. We examined theoretically and experimentally the relationships between correlation functions measured in two directions in anisotropic turbulence. We found that the ratio of characteristic scales measured in the different directions was a function of the ratio of fluctuating velocities in the two directions. In the case of the integral scale, the inertial range scaling law controls the relationship. In other words, not only is the integral scale a measure of the large scale, but it is also connected to inertial range dynamics. [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L11.00005: Stirring turbulence with turbulence Willem van de Water, Hakki Ergun Cekli, Rene Joosten We stir wind--tunnel turbulence with an active grid that consists of rods with attached vanes. The time--varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer--Ohkitani--Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial--range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the large eddies in the wind--tunnel turbulence. A large mismatch of these times creates a flow with interesting statistics, but it is not turbulence. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L11.00006: PIV study of turbulence generated by fractal grids in a water tunnel Rafael Fernandes, Bharathram Ganapathisubramani, Christos Vassilicos An experimental study of turbulence generated by low-blockage space-filling fractal square grids was performed using 2D Particle Image Velocimetry (PIV) in a water tunnel. In addition to the experimental technique (PIV) and the fact that it was carried out in water, this study has also the particularity of having considerable incoming free stream turbulence with an intensity, in the streamwise (u'/U) and spanwise (v'/U)~ directions, of 2.8 and 4.4 {\%} respectively. Results on turbulence intensity and Taylor microscale of the flow generated by our fractal grids are in good agreement with the previous wind tunnel study of Mazellier and Vassilicos [``Turbulence without the Richardson-Kolmogorov cascade,'' \textit{Phys. Fluids} \textbf{22}, 075101 (2010)] provided that a different normalization scale is used which takes into account the free stream turbulence characteristics. This normalisation scale is a good estimator of the turbulence peak downstream of not only fractal but also regular grids. Finally, local isotropy of fractal generated turbulence was checked based on the gradients estimated from the 2D velocity field and compared with the ones from regular grids. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L11.00007: Extraction of nonequilibrium -7/3 energy spectrum in experimental measurement turbulence data Kiyosi Horiuti, Yuichi Masuda A perturbation expansion for the energy spectrum about a base Kolmogorov $k^{-\frac{5}{3}}$ steady state yields an additional $-7/3$ power component which is induced by the fluctuation of the dissipation rate $\varepsilon$ and represents a nonequilibrium state. DNS study revealed actual existence of $- 7/3$ spectrum in homogeneous shear flow at $Re_\lambda \approx 150$ (\textit{Phys. Fluids} \textbf{23}, 035107 (2011)). In this study, an attempt is made to extract the same spectrum in the data measured using the hot wire anemometer in the experiment of the driving mixing layer, in which nearly constant mean shear is established ($Re_\lambda \approx 468$, Y. Tsuji (2008)). The time series data are converted to the spatially evolving data employing the Taylor's hypothesis and $\varepsilon$ is obtained. To be in accordance with the statistical theory, the variations of $\varepsilon$ in the time scale comparable to the integral length scale are considered. Nonequilibrium component is extracted applying a conditional sampling on $d \varepsilon/dt$, and it is shown that the deviation from the base $-5/3$ spectrum fits the $-7/3$ power slope. The temporal development of the spectrum is divided into two regimes, Phases 1 and 2. Large energy contained in the low- wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of -7/3 power component. These results agree well with the DNS. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L11.00008: Concentration dependence of the effects of polymer additives on bulk turbulence Heng-Dong Xi, Haitao Xu, Eberhard Bodenschatz We present an experimental study of the polymer concentration dependence of the effects of minute long chain polymer additives on bulk turbulent flow. It is found that the measured Eulerian structure function of the velocity field is strongly modified by the presence of the polymer additives. And there exists a critical concentration below which only small scales are modified while above which both small scales and large scales are modified. We found that the critical concentration depends on the energy dissipation rate of the flow, this dependence can be explained by de Gennes' elastic theory on turbulence of dilute polymeric solution. [Preview Abstract] |
Monday, November 21, 2011 5:19PM - 5:32PM |
L11.00009: What correlations between velocity differences and velocity sums tell us about small scale universality Greg Voth An ongoing question about turbulent flows is the degree to which the small scales are universal because they become independent of the details of the forcing at large scales. Recent work has explored these issues by measuring correlations between velocity differences over a distance r (whose variance is dominated by scales near r) and velocity sums over the same distance (whose variance is dominated by the large scales). Some correlations between velocity differences and sums are required by the Navier-Stokes equations (Hosokawa, Prog. Theor. Phys. Lett., 118:169, 2007.) This talk will look at experimental measurements of correlations between velocity differences and velocity sums from several flows. The correlations which are required by Navier-Stokes dynamics do not appear to violate the assumption of independence between the large and small scales. However, there are other correlations in the experimental data which can only be explained by dependence of the small scales on the details of the forcing of the flows. The variance of the velocity differences shows a strong conditional dependence on the velocity sum that is different in different flows. The anisotropy of the velocity differences also shows conditional dependence on the velocity sum. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L11.00010: POD models for turbulent convection in rectangular cells Jorge Bailon-Cuba, Joerg Schumacher Two low-dimensional models (LDM) for turbulent convection in rectangular cells, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, are presented. The empirical eigenfunctions are obtained from a Proper Orthogonal Decomposition (POD) of the fields using the Snapshot Method. The first case is a three-dimensional cell in which a classical turbulent Rayleigh-B\'{e}nard flow evolves. The second case is based on two-dimensional DNS data of mixed convection in a cell with heated obstacles as well as in- and outlets of air. In both cases, a quadratic inhomogeneous coupled ODE system is obtained for the evolution of the modal amplitudes. The truncation to a finite number (a few hundred) of degrees of freedom, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statistical stationarity and a total dissipation that corresponds with the original DNS data. We introduce a mode-dependent eddy viscosity-diffusivity, which turns out to reproduce the large-scale properties of the turbulent convection qualitatively well. [Preview Abstract] |
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