Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session A23: Turbulence: Theory I - General |
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Chair: Antonio Attili, King Abdullah University of Science and Technology Room: 318 |
Sunday, November 24, 2013 8:00AM - 8:13AM |
A23.00001: The definition of turbulence and the direction of the turbulence energy cascade Carl Gibson Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. Because vorticity is produced at the Kolmogorov scale, turbulent kinetic energy always cascades from small scales to large. Irrotational flows that supply kinetic energy to turbulence from large scale motions are by definition non-turbulent. The Taylor-Reynolds-Lumley cascade of kinetic energy from large scales to small is therefore a non-turbulent cascade. The Reynolds turbulence poem must be revised to avoid further confusion. Little whorls on vortex sheets, merge and pair with more of, whorls that grow by vortex forces, Slava Kolmogorov! Turbulent mixing and transport processes in natural fluids depend on fossil turbulence and fossil turbulence waves, which are impossible by the TRL cascade direction. Standard models of cosmology, astronomy, oceanography, and atmospheric transport of heat, mass, momentum and chemical species must be revised. See journalofcosmology.com Volumes 21 and 22 for oceanographic and astro-biological examples. [Preview Abstract] |
Sunday, November 24, 2013 8:13AM - 8:26AM |
A23.00002: On Lagrangian and Eulerian Acceleration in Rotating and Sheared Homogeneous Turbulence Frank Jacobitz, Kai Schneider, Wouter Bos, Marie Farge The Lagrangian and Eulerian acceleration properties of turbulence are of importance for problems ranging from fundamental theoretical considerations to modeling of dispersion processes. The acceleration statistics of rotating and sheared homogeneous turbulence are studied here using direct numerical simulations. The study focusses in particular on the influence of the Coriolis to shear rate ratio and also on the scale dependence of the statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian acceleration show a strong and similar influence on the rotation ratio. The flatness further quantifies this influence and yields values close to three for strong rotation. For moderate and vanishing rotation, the flatness of the Eulerian acceleration is larger than that of the Lagrangian acceleration, contrary to previous results for isotropic turbulence. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian acceleration increases as scale decreases. For strong rotation, the Eulerian acceleration is more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. [Preview Abstract] |
Sunday, November 24, 2013 8:26AM - 8:39AM |
A23.00003: Scale-Dependent Stress-Strain Rate Alignment and Spectral Transport in 2D Turbulence Yang Liao, Nicholas T. Ouellette The flux of quantities such as energy or enstrophy between different scales can be expressed as the scalar product of an appropriate scale-dependent stress and a rate of strain. But regardless of their magnitudes, spectral transfer can be suppressed if the stress and strain rate are geometrically misaligned. Working with experimental data obtained from an experimental quasi-two-dimensional weakly turbulent flow, we explore the impact of geometric alignment on the spectral transfer of energy and enstrophy using filter-space techniques. We decompose the scale-dependent stress into three distinct components, and show that they tend to drive spectral transport in different directions. We also show that the net observed directionality of the inverse energy and forward enstrophy cascades are controlled by the scale-dependet geometric alignment of these quantities. [Preview Abstract] |
Sunday, November 24, 2013 8:39AM - 8:52AM |
A23.00004: Classical Turbulence Scaling and Intermittency in Strongly Stratified Turbulence Steve de Bruyn Kops A -5/3 slope in the velocity and scalar spectra of stratified turbulence has long been taken as a sign that turbulence in this regime may scale as hypothesized by Kolmogorov, Oboukhov, and Corrsin (KOC). It has also been observed, however, that if the flow is in the strongly stratified regime then the buoyancy force is not insignificant and so some of the assumptions that underlie the KOC scaling hypotheses do not hold. The KOC hypotheses imply more than just -5/3 slope in spectra, though. We consider scaling of the second- and third-order velocity structure functions, the second-order scalar structure function, and the third-order mixed velocity-scalar structure functions. In addition, we examine the scaling of the dissipation rate in light of Kolmogorov's hypotheses on internal intermittency. Direct numerical simulations in the strongly stratified regime with buoyancy Reynolds numbers between 13 and 220 are examined, along with isotropic homogeneous turbulence with similar dynamic range. The simulations are resolved on up to $8192 \times 8192 \times 4096$ grid points. For unstratified turbulence, the dynamic range that these large grids enable is sufficient for KOC scaling to be evident, and for the intermittency exponent to be close to its textbook value. [Preview Abstract] |
Sunday, November 24, 2013 8:52AM - 9:05AM |
A23.00005: Scaling of Lyapunov Exponents in Homogeneous, Isotropic DNS Nicholas Fitzsimmons, Nicholas Malaya, Robert Moser Lyapunov exponents measure the rate of separation of initially infinitesimally close trajectories in a chaotic system. Using the exponents, we are able to probe the chaotic nature of homogeneous isotropic turbulence and study the instabilities of the chaotic field. The exponents are measured by calculating the instantaneous growth rate of a linear disturbance, evolved with the linearized Navier-Stokes equation, at each time step. In this talk, we examine these exponents in the context of homogeneous isotropic turbulence with two goals: 1) to investigate the scaling of the exponents with respect to the parameters of forced homogeneous isotropic turbulence, and 2) to characterize the instabilities that lead to chaos in turbulence. Specifically, we explore the scaling of the Lyapunov exponents with respect to the Reynolds number and with respect to the ratio of the integral length scale and the computational domain size. [Preview Abstract] |
Sunday, November 24, 2013 9:05AM - 9:18AM |
A23.00006: Using information theory for turbulence prediction: a statistical approach Walter Goldburg, Rory Cerbus Information theory provides a tool for quantifying the amount of uncertainty or disorder in physical systems through the entropy density h. Going beyond this, physics is often concerned with prediction. The goal here is to predict a subsequent string of velocity measurements on the basis of a set of prior observations. The predictability is captured in a function called the system's statistical complexity C, which is the average information needed for the prediction. There have been very few attempts to use this theory with experimental data. We have measured C in a quasi-2D soap film flow as a function of Reynolds number Re. The measurements point to a sharp transition in C(Re) when the turbulence becomes fully developed. This approach to complexity through predictability promises to be an interesting way of looking at turbulence and other complex systems. [Preview Abstract] |
Sunday, November 24, 2013 9:18AM - 9:31AM |
A23.00007: Turbulent scaling laws as solutions of the multi-point correlation equation using statistical symmetries Martin Oberlack, Andreas Rosteck, Victor Avsarkisov Text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Most important, theses new symmetries have important consequences for our understanding of turbulent scaling laws. The symmetries form the essential foundation to construct exact solutions to the infinite set of MPCE, which in turn are identified as classical and new turbulent scaling laws. Examples on various classical and new shear flow scaling laws including higher order moments will be presented. Even new scaling have been forecasted from these symmetries and in turn validated by DNS. Turbulence modellers have implicitly recognized at least one of the statistical symmetries as this is the basis for the usual log-law which has been employed for calibrating essentially all engineering turbulence models. An obvious conclusion is to generally make turbulence models consistent with the new statistical symmetries. [Preview Abstract] |
Sunday, November 24, 2013 9:31AM - 9:44AM |
A23.00008: Comparing nearly singular vorticity moments in Euler and Navier-Stokes numerical solutions Robert M. Kerr The inviscid growth of a range of vorticity moments in Navier-Stokes and Euler calculations are compared for simulations using a new anti-parallel initial condition. One goal is to understand the origins of a new hierarchy of rescaled vorticity moments in several Navier-Stokes calculations where the rescaled moments obey $D_m\geq D_{m+1} $, the reverse of the usual $\Omega_{m+1}\geq\Omega_m$ H\"older ordering. Two temporal phases have been identified for the Euler calculations. In the first phase the $1 |
Sunday, November 24, 2013 9:44AM - 9:57AM |
A23.00009: Detrended Structure-Function in Fully Developed Turbulence Yongxiang Huang A detrended structure-function (DSF) method is proposed to
extract scaling exponent by constraining the influence of large-scale structures. This is accomplished by removing a $q$th-order
polynomial fitting within a window size $\tau$ before calculating the velocity increment. By doing so, the scale larger than $\tau$,
i.e., $r\ge \tau$, is expected to be removed. The detrending process is equivalent to a high-pass filter.
We first validate the DSF by using synthesized fractional Brownian motion
for mono-fractal process and lognormal process for multifractal random
walk process.
When applying the DSF to a turbulent velocity obtained from a high Reynolds number wind tunnel experiment with $Re_{\lambda}\simeq 720$, the third-order DSF demonstrates a clear inertial range with $\mathcal{B}_3(\tau)\sim \tau$ on the range $0.001<\tau<0.1\,$sec, corresponding to a frequency range $10 |
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