14:00
Intermittency and Scaling 5
14:00
15 mins
#90
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Weak formulation and scalings in turbulent Rayleigh-Bénard convection
Sergio Chibbaro, Berengere Dubrulle, Alessio Innocenti, Valentina Valori
Abstract: We apply the weak formalism on the Boussinesq equations, to characterise scaling properties of the mean and the standard deviation of the potential, kinetic and viscous energy flux in very high-resolution numerical simulations.
We consider two simulations of a cube with $1024^3$ points at $Ra=10^7,10^8$ and $Pr=1$,
and we investigate the scale-by-scale averaged terms of the weak equations, which are a generalization of the Karman-Howarth-Monin and Yaglom equations.
The local Bolgiano-Oboukhov length $L_{OB}$ is investigated and it is found that its value may change of an order of magnitude through the domain, in agreement with previous results\cite{calzavarini2002evidences,kaczorowski2013turbulent}.
Concerning the small-scale properties, we are able to point out a neat Bolgiano scaling for the temperature, but the scalings are globally compatible with the flow being an effective mixture of Kolmogorov and Bolgiano one, for the velocity follow the Kolmogorov scaling.
This behaviour can be related to the strong heterogeneity of the convective flow, reflected in the wide distribution of Bolgiano-Oboukhov local scales.
The scale-by-scale analysis allows us also to compare the
theoretical Bolgiano-Oboukhov length $L_{OB}$ previously computed with that heuristically extracted through scalings.
The results show that the use of local coarse-graining approach is crucial to have accurate measurements of small-scale properties in turbulent non-homogeneous flows.
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14:15
15 mins
#205
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Energy flux vectors in anisotropic turbulence
Naoto Yokoyama, Masanori Takaoka
Abstract: The energy flux in anisotropic turbulence systems such as rotating turbulence and stratified turbulence depends on the directions of the wave numbers, and should be a geometric vector. The energy-flux vectors in stratified turbulence and rotating turbulence are obtained by using the generalized inverse from the energy-transfer rates in direct numerical simulations. The energy-flux vectors in the present work well reproduce the directions of the energy fluxes in these turbulence systems.
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14:30
15 mins
#373
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Large-scale transitions in fully developed turbulence
Cristian C. Lalescu, Michael Wilczek
Abstract: Please see attached .pdf file.
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14:45
15 mins
#566
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Internal and external fluctuations in a turbulent non-premixed planar flame
Michael Gauding, Dominik Denker, Yacine Brahami, Emilien Varea, Luminita Danaila
Abstract: We analyze the statistics of a turbulent non-premixed flame in the context of Kolmogorov’s scaling theory. The main contribution consists in the derivation of generalized scaling relations for mixed density-velocity structure functions of arbitrary order. Structure functions are non-local statistical quantities, which provide scale-sensitive information at different transversal locations in the flame. The inertial range scaling exponents of structure functions exhibit a growing departure from Kolmogorov’s prediction toward the edge of the flame. We show that this departure is primarily due to the effect of external intermittency. The analysis is based on a highly-resolved direct numerical simulation of a temporally evolving planar jet flame.
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15:00
15 mins
#21
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Flowing fibers as a proxy of two-point statistics of turbulence
Andrea Mazzino, Marco Edoardo Rosti, Stefano Olivieri, Luca Brandt
Abstract: Accurate measurements of multipoint statistics are crucial in order to advance our understanding of turbulent flows and in particular to establish a connection between scaling laws and spatial structures, e.g., vortex filaments~\cite{frisch1995turbulence}. To this end, we consider a fiber of finite size, i.e. whose length is within the inertial range of scales, freely moving in a homogeneous and isotropic three-dimensional turbulent flow (Fig.~\ref{fig1}a). Recently, Rosti et al.~\cite{rosti2018flexible} identified a regime where the flapping motion of a flexible fiber is slaved to turbulent fluctuations and the two-point statistical properties of these latter can be obtained by simply measuring the position and velocity difference between the fiber ends. In this work, those findings are put into an enriched and more general framework~\cite{rosti2019flowing}. We first introduce a phenomenological theory to describe the dynamics of a flexible fiber, predicting two distinct flapping regimes: the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinction between different flapping behaviors, especially in the under-damped case. We validate our theory by means of fully-resolved direct numerical simulations and find that, for both regimes, the fiber is effectively slaved to the flow and can therefore be used as a proxy to measure various two-point statistics of turbulence such as, e.g., the probability density function of longitudinal velocity increments (Fig.~\ref{fig1}b). Moreover, we show that this holds true also in the case of a passive fiber, without any feedback force on the fluid.
Subsequently, we move to the case of rigid fibers: although flapping does not occur in this situation, we show that one can still access two-point statistics of turbulence when the attention is focused on transverse fluctuations. Moreover, the eddy turnover time turns out to be related to the fiber tumbling time. We conclude by discussing the potential application in experimental methods and the generalization of the model for multipoint statistics.
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