10:45
Intermittency and Scaling 4
10:45
15 mins
#260
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On the stochastic modeling of the spatio-temporal structure of homogeneous and isotropic turbulence
Jason Reneuve, Laurent Chevillard
Abstract: Based on a Direct Numerical Simulation, we analyse a spatio-temporal map of the longitudinal velocity component. We characterize the overall correlation structure of this two-dimensional map, and higher-order statistical quantities (i.e. energy transfers and intermittent corrections). We then propose a stochastic modeling of these observed fluctuations using a two-dimensional Gaussian field as a first approximation, and then a more sophisticated multifractal version of it, that is shown to reproduce the main statistical features.
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11:00
15 mins
#381
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EXPERIMENTAL STUDY OF INERTIAL INTERMITTENCY USING FOKKER-PLANK EQUATION IN VON KARMAN CRYOGENIC TURBULENT FLOWS
Swapnil Kharche, Alain Girard, Joachim Peinke, André Fuchs, Bernard Rousset, Michel Bon-Mardion, Jean-Paul Moro, Christophe Baudet
Abstract: The study presented here deals with the experimental data from the large size von Karman apparatus called Superfluid
High REynolds von Karman experiment (SHREK) at CEA-Grenoble[1]. Within this experiment, the data is acquired
using a technique of hot wire anemometry at an operating pressure of 3 bar and temperature of 2.2 K in a medium
of liquid helium (HeI). The large eddy turnover times are in the range of O(104) to O(106) which accounts for the
maximum time of data acquisition up to 20 hours. Typically for this experiment, the ratio of integral length scale and the
Taylor’s length scale lies within O(102). Hence, this allows us to study the energy cascade along a wide range of scales
within inertial subrange. The statistical approach of velocity increments (ur) at multiscales (r) has been used in order
to estimate the joint and conditional probability density functions(PDFs). These conditional PDFs of velocity increment
at different scales dictates the stochastics of energy cascade which is governed by the Fokker-Plank equation (FPE). This
Fokker-Plank equation can be solved using the present experimental data defining a Drift function, D1 and Diffusion
function, D2. The dependence of D1 and D2 with respect to ur and r is addressed here in detail.
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11:15
15 mins
#424
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Energy budget in wall-bounded turbulent flows
Rakesh Yuvaraj, Jean-Marc Foucaut, Jean-Philippe Laval, Christos Vassilicos
Abstract: The present work focuses on obtaining the instantaneous energy budget by using the instantaneous Kármán-Howarth-Monin-Hill (KHMH) equation to analyse DNS of channel flow and of a turbulent boundary layer at similar Reynolds number (Re τ ≈ 550). This KHMH equation is a direct reflection of the Navier-Stokes equations without averaging and without assumptions.
Our analysis reveals a very strong spatio-temporal intermittency for all the terms in this equation as also observed in homogeneous turbulence. The different terms in this equation quantify different physical processes, including effects of pressure fluctuations, inter-scale and inter-space energy transfers, unsteadiness and dissipation. We carry out our study at various distances from the wall and find significant correlations between the fluctuations of the time-derivative (unsteadiness) term and the inter-space energy transfer term. This strong correlation reflects the sweeping effect expressed in the way that is appropriate for wall turbulence. There is also a significant correlation between the fluctuating pressure-velocity term and the fluctuating inter-scale energy transfer term. This correlation reflects the relevance of pressure fluctuations in the cascade process. Similar correlations have been found in homogeneous turbulence. They extend over a wide range of length-scales which, in the present case of wall turbulence, are affected by the distance to the wall. We therefore also study the effects of wall-attached coherent structures on these dynamics.
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11:30
15 mins
#426
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Energy transfer in Rayleigh-Bénard cell
David DUMONT, Bérengère DUBRULLE, Olivier LIOT, Julien SALORT, Francesca CHILLÀ
Abstract: Rayleigh-Bénard convection cells have been studied for several decades because it is considered as a useful model to understand the physics of thermal turbulent flows. However, in experimental setups, boundaries are smooth while in nature or industries they are mostly rough. Therefore, boundary roughness in Rayleigh-Bénard setup is an intense research topic to understand how roughness affects energy transfer and flows properties.
Turbulent flow is strongly inhomogeneous in our Rayleigh-Bénard cell because of the system itself: a fluid layer heated from below and cooled from the top. Even in flows deemed to be homogeneous, inhomogeneities appear due to energy dissipation which seems to occur at intermittent spots. Because of that, many tools were developped by Onsager, Leray and more recently Duchon-Robert to take into account these singularities and their consequences on the energy transfer and dissipation. Duchon-Robert methods were widely used in turbulent flows but not yet in turbulent thermal convection.
We want to map our inhomogenous flow, especially its energy transfer and dissipation. Accordingly, we applied Duchon-Robert approach to our two Rayleigh-B\'enard cells, made of a smooth plate at the top and a smooth (or rough) plate at the bottom. Many topics are studied : Are Duchon-Robert scalings similar to isothermal turbulence ? What is the effect of surface roughness of hot plate on the energy transfer map ?
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11:45
15 mins
#458
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Extracting the Spectrum by Spatial Filtering
Mahmoud Sadek, Hussein Aluie
Abstract: We show that the spectrum of a flow field can be extracted within a local region by straightforward filtering in physical space. We find that for a flow with a certain level of regularity, the filtering kernel must have a sufficient number of vanishing moments for the "filtering spectrum" to be meaningful. Our derivation follows a similar analysis by Perrier et al. (1995) for the wavelet spectrum, where we show that the filtering kernel has to have at least $p$ vanishing moments in order to correctly extract a spectrum $k^{-\alpha}$ with $\alpha < p+2$. For example, any flow with a spectrum shallower than $k^{-3}$ can be extracted by a straightforward average on grid-cells of a stencil. We construct two new "simple stencil" kernels, M1 and M2, with only two and three fixed stencil weight coefficients, respectively, and that have sufficient vanishing moments to allow for extracting spectra steeper than $k^{-3}$.
Our method guarantees energy conservation and can extract spectra of non-quadratic quantities self-consistently, such as kinetic energy in variable density flows, which the wavelet spectrum cannot. The method can be useful in both simulations and experiments when a straightforward Fourier analysis is not justified, such as within coherent flow structures covering non-rectangular regions, in multiphase flows, or in geophysical flows on Earth's curved surface.
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12:00
15 mins
#585
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Projection method for the analysis of small-scale intermittency in hydrodynamic turbulence
Jan Friedrich Friedrich, Holger Homann, Rainer Grauer
Abstract: We present an alternative to the usual structure function approach for the investigation of small-scale intermittency in turbulence. To this end, we rely on a description of the turbulent energy cascade in terms of a Markov process of the velocity increments in scale. It will be shown that the associated Kramers-Moyal expansion of the velocity increment PDF is capable of reproducing all currently known phenomenological models of turbulence. Furthermore, we will provide a projection on the small-scale scaling features of turbulence by means of a decomposition of the Kramers-Moyal coefficients that were evaluated form direct numerical simulations of 3D turbulence.
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12:15
15 mins
#469
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Bolgiano-Obukhov scaling in Rayleigh-Taylor turbulence at moderate Atwood number
Takeshi Matsumoto
Abstract: We report the Bolgiano-Obukhov scaling in the three dimensional Rayleigh-Taylor turbulence with Atwood number 1/2.
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