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 M23: Turbulence Theory: General II |
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Chair: Duo Xu, Purdue University Room: 30D |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M23.00001: Experimental Test of Revised Similarity Hypotheses without Taylor's Hypothesis Jun Chen, Duo Xu Simultaneous velocity and scalar fields of a turbulent jet, measured by combined Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF), are used to test Refined Similarity Hypotheses (RSH) and its extension to passive scalar (RSH-P). Without introducing artificial effects introduced by Taylor's hypothesis in traditional single-point measurements, RSH is successfully validated in this study by direct examinations of its three hypotheses. However, RSH-P is partially supported, where the hypothesis of independent behavior of stochastic variable is not supported. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M23.00002: An infinity of microscales for turbulence William K. George It is has long been accepted that the Kolmogorov microscale $\eta = (\nu^3/\varepsilon)^{1/4}$ is the smallest dynamically significant length scale of turbulence (e.g.,[1]), where $\nu$ is the kinematic viscosity and $\varepsilon$ is the dissipation. Following George [2] it is argued that there are an infinity of smaller scales, say $\eta_n =(\nu^{n+3}/\varepsilon_n)^{1/(2n+4)}$ where $\varepsilon_1$ is the dissipation of the dissipation, $\varepsilon_2$ is the dissipation of the dissipation of the dissipation, etc. Each of these is equal to a spectral moment in homogeneous turbulence, $(2 \nu)^{n+1}\int_0^\infty k^{2n+2} E(k) dk$. Time scales can be similarly defined. It is demonstrated how these play an important role, especially in non-stationary turbulence where Kolmogorov's equilibrium hypothesis is invalid.\\[4pt] [1] Tennekes and Lumley (1972) A First Course in Turbulence, MIT Press.\\[0pt] [2] George, W.K (2012) Asymp. Effect of Initial and Upstream Conditions on Turbulence, J. Fluids Engr, 134, 1061203-1--27. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M23.00003: Experimental test of a missing spectral link in turbulence Pinaki Chakraborty, Hamid Kellay, Tuan Tran, Walter Goldburg, Nigel Goldenfeld, Gustavo Gioia Although the cardinal attribute of turbulence is the velocity fluctuations, these fluctuations have been ignored in theories of the frictional drag of turbulent flows. Our goal is to test a new theory that links the frictional drag to the spectral exponent $\alpha$, a property of the velocity fluctuations in a flow. We use a soap-film channel wherein for the first time the value of $\alpha$ can be switched between 3 and 5/3, the two theoretically possible values in soap-film flows. Remarkably, the new theory holds in both soap-film flows and ordinary pipe flows, even though these types of flow are governed by different equations. We conclude that even where the governing equations are unknown and $\alpha$ can take anomalous values (as in sediment-laden rivers and polymer-doped oil pipelines), the frictional drag might be estimated from simple measurements of $\alpha$. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M23.00004: Linear stability analysis of homogeneous three-dimensional turbulent flows Anand Mishra, Sharath Girimaji We examine the stability characteristics of homogeneous three-dimensional mean flows. Such mean fields can be categorized based on the invariants of the velocity gradient tensor. In this study, the linear stability of different three-dimensional mean-flow topologies and the action of pressure in each category are investigated. Expressly, this entails an analysis of the Kelvin-Moffat system in Fourier space. The concomitant invariant sets and their appurtenant bifurcations are explicated. Thence, the stability characteristics of the system are analyzed, apropos individual modes (i.e., Hydrodynamic stability) and the statistical ensemble (Rapid Distortion Theory). Such understanding can lead to improved pressure-strain correlation models. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M23.00005: Multiscale Characterisation of Helical Properties in Homogeneous Turbulence Wouter Bos, Frank Jacobitz, Kai Schneider, Marie Farge This study investigates the helical properties of five prototypical homogeneous turbulent flows: statistically steady forced isotropic turbulence, decaying isotropic turbulence, decaying rotating turbulence, growing sheared turbulence, and growing rotating sheared turbulence. A solenoidal uncorrelated Gaussian random field is included in the analysis as a sixth comparison case. The scale-dependent helical properties of the cases are studied using an orthogonal wavelet decomposition. It was observed that flows with growing turbulent kinetic energy and turbulent motion at large scales show a maximum in the velocity helicity probability distribution functions (PDFs) at zero, corresponding to a trend to local two-dimensionalization of the flow with vorticity and velocity being perpendicular. Flows with decaying turbulent kinetic energy and turbulent motion at small scales, however, show maxima of the velocity helicity PDFs at plus and minus one, indicating a preference for helical motion with alignment or anti-alignment of vorticity and velocity. Joint PDFs of relative velocity helicity and relative vorticity helicity show that the quantities tend to have the same sign for all flows including the random field, indicating that vorticity helicity dissipates velocity helicity. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M23.00006: Measurements of Anisotropy in Turbulence using SO(3) decomposition Greg Voth, Susantha Wijesinghe We use SO(3) decomposition of 3D particle tracking measurements to study the anisotropy of turbulence in a flow between oscillating grids. SO(3) decomposition is a powerful tool for determining the anisotropy as a function of scale, but experimental measurements of 3D anisotropy have proven to be difficult. Barriers that have hindered previous efforts to make these measurements include contamination from anisotropic sampling and the large data sets required for convergence of higher order anisotropic sectors. We use a real-time image compression system to obtain very large data sets of high speed video and to detect and correct for anisotropic sampling. We measure scaling exponents in the anisotropic sectors of the longitudinal structure functions up to j=4. Our results are consistent with previous results from numerical simulations and hot wire anemometry indicating that the scaling exponents at all orders increase with increasing $j$, so the small scales approach isotropy. We also condition the SO(3) decomposed structure functions on the instantaneous state of the large scales which provides an alternative way to probe the decay of anisotropy. We find that although smaller scales are not becoming independent of the large scales, but they are becoming isotropic. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M23.00007: Mean shear regulates the intermittency of energy dissipation rate Khandakar Morshed, Lakshmi Dasi We studied the multi-fractal properties of the instantaneous fluctuations of the turbulent kinetic energy dissipation rate, $\varepsilon $ in the strongly anisotropic flow past a backward facing step. Measurements correspond to time-resolved PIV at Reynolds number, Re= 13600, 9000, and 5500 based on the free stream velocity and step height. Results indicate a significant dependence of the intermittent dissipation rate signal with respect to Re and local mean shear, S. Probability analysis showed that the fluctuations in $\varepsilon $ are less skewed around its mean in regions of intense shear. The frequency of relatively intense bursts of intermittent fluctuations in $\varepsilon $ appear to be dependent on the magnitude of these events. Lacunarity, a measure that characterizes such magnitude and temporal scale dependent intermittency of fluctuating signals, revealed that intermittency in $\varepsilon $ reduces with S across all temporal scales. However, the intermittency of $\varepsilon $ appears to increase with burst magnitudes. We discuss the implications of these results on the established multi-fractal picture of small-scale turbulence and the effects of large scale anisotropy. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M23.00008: Energy spectrum in the wavenumber-frequency domain from Kraichnan's random sweeping hypothesis with mean flow Michael Wilczek, Yasuhito Narita The energy spectrum in the wavenumber-frequency domain for turbulent flows is derived based on Kraichnan's random sweeping hypothesis with additional mean flow. The resulting model spectrum is parametrized by two parameters, the mean flow velocity and the sweeping velocity associated with Doppler shift and Doppler broadening, respectively. Among others, it has the interesting property that the power-law index of the one-dimensional wavenumber spectrum translates to the frequency spectrum, invariant for arbitrary choices of mean and sweeping velocity. In this talk, various properties of the model including implications for single- and multi-point measurements of turbulent flows are discussed, and the relation to the recently introduced elliptic model for space-time correlations is highlighted. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M23.00009: Scaling of the mean length of streamline segments in various turbulent flows Philip Sch\"afer, Markus Gampert, Jonas Boschung, Norbert Peters Streamlines constitute natural geometries in turbulent flow fields. The latter can be partitioned into segments based on the zero crossings of the gradient of the absolute value of the velocity field along the streamline. Streamline segments can further be characterized by the sign of the gradient of the absolute value into positive and negative ones. Then, most of the statistical properties of streamline segments are captured in the joint probability density function of the arclength between and the velocity difference at the ending points. An analysis based on a model equation for the length distribution of streamline segments and the characteristic size of extreme points of the absolute value of the velocity field along the streamline yields that the mean length of the latter should scale with the geometrical mean of the Kolmogorov microscale and the Taylor microscale. This theoretical prediction is confirmed based on four different direct numerical simulations of turbulent flow fields with Taylor based Reynolds numbers ranging from 50 -- 300. The database consists of two homogeneous isotropic decaying and one forced field. Furthermore, the case of a homogeneous shear flow is investigated. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M23.00010: Turbulence theory and infrared images falsify the 2011 Nobel Prize in Physics Carl Gibson Turbulence defined by the inertial vortex force explains Planck scale big bang processes as temporary, rendering a permanent Einstein cosmological constant $\Lambda$ and a positive expansion rate of the universe driven by anti-gravitational dark energy forces unnecessary. Large kinematic viscosity stresses during the plasma epoch from $10^{11}$ s to $10^{13}$ s cause fragmentation by proto-super-cluster-voids at $10^{12}$ s and proto-galaxies at the $10^{13}$ s transition to gas. Fragmentation of gas proto-galaxies is at Earth-mass planet viscous scales in Jeans mass clumps of a trillion planets. These Proto-Globular-star-Clusters (PGCs) freeze to form the dark matter of galaxies according to the Gibson (1996) Hydro-Gravitational-Dynamics (HGD) theory, and as observed by Schild (1996) by quasar microlensing. White dwarf carbon stars explode as Supernovae Ia events (SNeIa) when their mass increases to 1.44 solar, providing the standard candles used to justify the Nobel Prize claim of a positive expansion rate. However, if all stars form from primordial planet mergers in PGC clumps as claimed by HGD cosmology, the SNeIa become subject to a systematic dimming error depending on the line of sight to the event. New space telescope infrared images strongly support HGD cosmology. [Preview Abstract] |
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