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 E23: Turbulence Theory: 2D Turbulence |
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Chair: Marie Farge, LMD-IPSL-CNRS ENS Room: 30D |
Sunday, November 18, 2012 4:45PM - 4:58PM |
E23.00001: Spatial structure of spectral transport in two-dimensional flow Yang Liao, Nicholas Ouellette Recently developed tools based on filtering have begun to allow the spatial localization of spectral activity in turbulent flow. These filter-space techniques (FSTs) have been used, for example, to study the mechanisms responsible for the double cascade in two-dimensional turbulence or the coherence of the spectral energy flux along Lagrangian trajectories. But FSTs can sometimes give results that seem potentially spurious, such as very large signals around vortex cores. Using both a simple analytical model flow field and measurements from a quasi-two-dimensional experimental flow, we study the results of FSTs in detail. In particular, we show that a classic decomposition of the spectral energy flux may be fruitful. [Preview Abstract] |
Sunday, November 18, 2012 4:58PM - 5:11PM |
E23.00002: Fokker-Planck description of the inverse cascade in two-dimensional turbulence Oliver Kamps, Michel Vosskuhle In many approaches the mathematical description of fully developed turbulence relies on the statistical properties of the longitudinal velocity increments $ \xi(r) = U(x+r)-U(x) $. In [1] the increment statistics is described as a Markov process in scale, leading to a Fokker-Planck description of the probability density functions (PDFs) for the velocity increments. The universality of this approach was tested for different kinds of three-dimensional flows like inhomogeneous turbulence, fractal grid generated turbulence and for the transition of a flow from a vortex street to fully developed turbulence in a cylinder wake the flow. In this talk we want to extend the test for the universality of the Markov description by analyzing data from numerical simulations of the inverse energy cascade in two-dimensional turbulence. The central question is whether the velocity field of the inverse cascade can be modeled as Markov process in scale similar to the three-dimensional case. By estimating the coefficients of the Fokker-Planck equation we are able to discuss the role of intermittency and differences to three-dimensional flows. \\[1ex] [1] Friedrich R., Peinke J., \emph{Phys. Rev. Lett, vol. 78, pp. 863-866 (1997)} [Preview Abstract] |
Sunday, November 18, 2012 5:11PM - 5:24PM |
E23.00003: Simple invariant solutions embedded in 2D Kolmogorov turbulence Rich Kerswell, Gary Chandler Ideas from dynamical systems have recently provided fresh insight into transitional and weak turbulent flows where the system size is smaller than the spatial correlation length. Viewing such flows as a trajectory through a phase space littered with invariant solutions and their stable and unstable manifolds has proved a fruitful way of understanding such flows. It is therefore natural to ask whether any ideas attempting to rationalise chaos may have something to say about developed turbulence. One promising line of thinking in low-dimensional, hyperbolic dynamical systems stands out as a possibility - Periodic Orbit Theory (Auerbach et al 1987, Cvitanovic 1988 and the review by Lan 2010). I will discuss an attempt to apply this in 2D Kolmogorov turbulence: body-forced flow (where the forcing is monochromatic and large scale) over a doubly periodic box. [Preview Abstract] |
Sunday, November 18, 2012 5:24PM - 5:37PM |
E23.00004: Exponential decay of a passive tracer variance in a two-dimensional Navier-Stokes flow Farid Ait Chaalal We study numerically the decay of a passive tracer in a dynamically consistent flow solution of the two-dimensional Navier-Stokes equation and in the limit of small diffusion. We observe that the decay of the variance becomes quickly exponential, as previously observed in simple chaotic maps, like the well-studied renewing sine flow proposed by Pierrehumbert in the early nineties. However, after a few tens of large-eddy turnover times, the decay rate changes. We interpret this result in light of theories developed for mixing in simple ergodic flows, in particular local Lagrangian stretching theories. It is found that they only can explain very partially the phenomenology we observe. In particular, they cannot capture the r\^ole of coherent vortices which is crucial, particularly in the very long-term decay, and might explain the decay rate change. [Preview Abstract] |
Sunday, November 18, 2012 5:37PM - 5:50PM |
E23.00005: Comparison of turbulent mixing and chaotic advection in a two-dimensional wall-bounded domain Benjamin Kadoch, Wouter Bos, Kai Schneider The mixing of a passive scalar blob in a confined vessel is studied. A flow is generated by a rod, describing a figure-eight motion. The two-dimensional incompressible Navier-Stokes and advection-diffusion equations are solved using direct numerical simulation with no-slip and no-flux boundary conditions for the velocity and scalar, respectively. These boundary conditions are imposed on the wall and the rod by using a volume penalization method as described in in Ref. [1], in combination with a classical Fourier pseudo-spectral code. The decay of scalar variance in Stokes regime, for different Schmidt numbers, is compared with the one obtained in Ref. [2] for chaotic mixing. Subsequently, the influence of Reynolds and Schmidt numbers on turbulent mixing is investigated. In order to quantify the mixing at infinite Schmidt number, we measure the dispersion of tracer particles. Both the variance and higher moment statistics for the scalar concentration are analyzed. We show that the scalar variance decays in time following a powerlaw.\\[4pt] [1] B. Kadoch, D. Kolomenskiy, K. Schneider and P. Angot. J. Comput. Phys., 231, 4365-4383, 2012.\\[0pt] [2] E. Gouillart, O. Dauchot, B. Dubrulle, S S. Roux, and J.-L. Thiffeault. Phys. Rev. E 78, 026211, 2008. [Preview Abstract] |
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