Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session RA: Turbulence Theory III |
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Chair: Carl H. Gibson, University of California, San Diego Room: Long Beach Convention Center 101A |
Tuesday, November 23, 2010 3:05PM - 3:18PM |
RA.00001: Effect of scalar-field boundary conditions on the Markovian properties of passive scalar increments Jason Lepore, Laurent Mydlarski Lepore and Mydlarski\footnote{Lepore and Mydlarski, 2009, {\it Phys. Rev. Lett.}, {\bf 103}, 034501.} recently investigated the influence of the scalar-field boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions ($\xi_n$). The latter was accomplished by injecting the scalar field into the flow (i.e., the turbulent wake of a circular cylinder) using two different scalar injection methods: (i) heating the cylinder, and (ii) using a ``mandoline''. The authors concluded that all previous estimates of $\xi_{n}$ are sensitive to the scalar field boundary conditions, given the finite Reynolds numbers of the flows under consideration, and, therefore, do not constitute a universal measure of the internal intermittency of the passive scalar field. The present work examines the Markovian properties of passive scalar increments, and their dependence on the scalar injection method, to provide additional insight into the small-scale structure of the turbulent passive scalar. In particular, the current research examines the relationship between the high-order terms of the Kramers-Moyal expansion and the internal intermittency of the passive scalar field. [Preview Abstract] |
Tuesday, November 23, 2010 3:18PM - 3:31PM |
RA.00002: Tomographic Particle-Image Velocimetry To Investigate Dissipation Elements Lisa Schaefer, Uwe Dierksheide, Wolfgang Schroeder A new method to describe the nature of turbulence has been proposed by Wang and Peters (JFM 2006). Based on fluctuating scalar fields, local minimum and maximum points are determined via gradient trajectories starting from every grid point in the direction of the steepest ascending and descending gradients. Then, so-called dissipation elements are indentified as the region of all the grid points the trajectories of which share the same pair of minimum and maximum points. The statistical properties of these space-filling elements are evaluated focusing on the linear distance and the scalar difference between their extrema. The procedure is also applied to various DNS fields using u', v', w', and k' as scalar fields (Wang and Peters JFM 2008). In this spirit, dissipation elements are derived from experimental 3D velocity data of a fully developed turbulent channel flow gained by Tomographic Particle-Image Velocimetry. The statistical results, inter alia, regarding the distribution of the element length are compared to those from the DNS. [Preview Abstract] |
Tuesday, November 23, 2010 3:31PM - 3:44PM |
RA.00003: Forced Turbulence, Multiscale Dynamics, and Variational Principles Haris J. Catrakis We consider theoretically fundamental aspects of forced turbulence as well as unforced turbulence, with emphasis on the multiscale properties of turbulent level crossings as well as emphasis on connections to variational principles. The connection between power spectral exponents and level crossing scales in forced turbulence, as well as unforced turbulence, is explored. Also, the connection between variational principles and the behavior of level crossing scales is investigated in both forced and unforced turbulence. In addition, we explore testing of our theoretical considerations using computations and visualizations. [Preview Abstract] |
Tuesday, November 23, 2010 3:44PM - 3:57PM |
RA.00004: Recent Analytical and Numerical Results for The Navier-Stokes-Voigt Model and Related Models Adam Larios, Edriss Titi, Mark Petersen, Beth Wingate The equations which govern the motions of fluids are notoriously difficult to handle both mathematically and computationally. Recently, a new approach to these equations, known as the Voigt-regularization, has been investigated as both a numerical and analytical regularization for the 3D Navier-Stokes equations, the Euler equations, and related fluid models. This inviscid regularization is related to the alpha-models of turbulent flow; however, it overcomes many of the problems present in those models. I will discuss recent work on the Voigt-regularization, as well as a new criterion for the finite-time blow-up of the Euler equations based on their Voigt-regularization. Time permitting, I will discuss some numerical results, as well as applications of this technique to the Magnetohydrodynamic (MHD) equations and various equations of ocean dynamics. [Preview Abstract] |
Tuesday, November 23, 2010 3:57PM - 4:10PM |
RA.00005: Is drift-wave turbulence intermittent from a Lagrangian point of view? Kai Schneider, Benjamin Kadoch, Wouter Bos Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated by means of direct numerical simulation in the context of the Hasegawa-Wakatani model. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This exponential distribution is shown to be a robust feature independent of the Reynolds number. For small adiabaticity, algebraic tails are observed, suggesting the strong influence of point-vortex-like dynamics on the acceleration. A causal connection is found between the shape of the probability density function and the auto-correlation of the norm of the acceleration. For further details we refer to Bos et al., Physica D 239, 2010 and Kadoch et al., Phys. Rev. Lett., 2010, in press. [Preview Abstract] |
Tuesday, November 23, 2010 4:10PM - 4:23PM |
RA.00006: Maximum Enstrophy Growth in Burgers Equation Diego Ayala, Bartosz Protas The regularity of solutions of the Navier--Stokes equation is controlled by the boundedness of the enstrophy $\mathcal{E}$. The best estimate for its rate of growth is $d\mathcal{E}/dt \leq C\mathcal{E}^{3}$, for $C>0$, leading to the possibility of a finite--time blow--up when straightforward time integration is used. Recent numerical evidence by Lu \& Doering (2008) supports the sharpness of the instantaneous estimate. Thus, the central question is how to extend the instantaneous estimate to a finite--time estimate in a way that will incorporate the dynamics imposed by the PDE. We state the problem of saturation of finite--time estimates for the enstrophy growth as a PDE--constrained optimization problem, using the Burgers equation as a ``toy model''. The following problem is solved numerically: \begin{displaymath} \max_{\phi}[\mathcal{E}(T) - \mathcal{E}(0)]\quad\mbox{subject to}\quad\mathcal{E}(0) = \mathcal{E}_0 \end{displaymath} where $\phi$ represents the initial data for Burgers equation, for a wide range of values of $T>0$ and $\mathcal{E}_0$ finding that the maximum enstrophy growth in finite time scales as $\mathcal{E}^{\alpha}_0$ with $\alpha\approx 3/2$, an exponent different from $\alpha = 3$ obtained by analytic means. [Preview Abstract] |
Tuesday, November 23, 2010 4:23PM - 4:36PM |
RA.00007: Turbulence in more than two and less than three dimensions Antonio Celani, Dario Vincenzi, Stefano Musacchio We investigate the behavior of turbulent systems in geometries with one compactified dimension. A novel phenomenological scenario dominated by the splitting of the turbulent cascade emerges both from the theoretical analysis of passive scalar turbulence and from direct numerical simulations of Navier-Stokes turbulence. (Phys. Rev. Lett. 104, 184506 (2010), J. Stat. Phys. 138, 579-597 (2010)) [Preview Abstract] |
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