• Home
• Program
• Contact

14:00   Intermittency and Scaling 2 14:00 15 mins #69 SCALE ANALYSIS OF A NUMERICAL VON KÁRMÁN FLOW Hugues FALLER, Bérengère Dubrulle, Caroline Nore, Loïc Cappanera, Jean Luc Guermond Abstract: Turbulent flows are characterized by the coexistence of multiple scales between the injection scale and the energy dissipation scale as one may see in figure 1. The local interscale energy transfer down to the Kolmogorov scale has been studied experimentally by Saw et al in [2] using the tool developed by J. Duchon and R. Robert in [1]. They found that the local energy transfer has a very wide distribution and reaches extreme values at locations where the velocity field has front like or spiral topology. In this talk, I show how to recover such results in a high resolution direct numerical simulation of the experimental Von Kármán flow of [2]. The numerical code (SFEMaNS) uses a hybrid spatial discretization combining spectral and finite elements. The approximation in space is done by using a Fourier decomposition in the azimuthal direction and the continuous Hood-Taylor Lagrange elements for the pressure and velocity fields in the meridian section. The approximation in time is done by using a prediction-correction method described in [4]. The moving counter-rotating impellers are accounted for by using a pseudo-penalty technique described in [5]. In this talk, we discuss the problem of computing interscale transfer on a finite element mesh, often used to simulate real turbulent flows. We show the distribution of the interscale transfer term and the structure of the velocity fields around extreme local energy transfers and discuss the comparison with experimental results. References [1] J. Duchon & R. Robert : Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations. Nonlinearity 13 249–255, 2000. [2] E.-W. Saw, D. Kuzzay, D. Faranda, A. Guittonneau, F. Daviaud, C. Wiertel-Gasquet, V. Padilla & B. Dubrulle: Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow. Nature Communications, 2016. [3] Nore, C. and Castanon Quiroz, D. Cappanera, L. and Guermond, J.-L: Numerical simulation of the von Karman sodium dynamo experiment. Journal of Fluid Mechanics 854 DOI 10.1017, 2018. [4] J. L. Guermond, R. Laguerre, J. Léorat & C. Nore: Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method. J. Comp. Physics 228 2739–2757, 2009. [5] R. Pasquetti, R. Bwemba, and L. Cousin: A pseudo-penalization method for high Reynolds number unsteady flows. Appl. Numer. Math. 58(7):946–954, 2008. 14:15 15 mins #139 LOCAL ESTIMATES OF HÖLDER EXPONENTS IN TURBULENT VECTOR FIELDS Florian Nguyen, Jean-Philippe Laval, Bérengère Dubrulle, Pierre Kestener, Alexey Cheskidov, Roman Shvydkoy Abstract: It is still an open question whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is H\"older continuous with some exponent $h < 1$ (i.e. not necessarily differentiable) at small scales, i.e. to find under which conditions the following holds: \begin{equation} \vert \bm u\left(\bf x + {\bm \ell}\right) - \bm u\left(\bf x\right) \vert < C \ell^h. \label{holder} \end{equation} Different methods have already been proposed to estimate the regularity properties of the velocity field, and the estimate of its H\"older exponent $h$. A first method is to use Onsager' remark \cite{Onsager49} that singularities, if they exist, can produce an "inertial" dissipation $D^*=\lim_{\ell\to 0}D_\ell^I$ that is independent on viscosity \cite{D00}. This dissipation has already been used as a criterion for detection of potential singularities \cite{[K16]}. Another possibility is to use the concept of multifractal analysis. Using e.g. the \textit{Wavelet Transform Modulus Maxima} (WTMM) method \cite{ Kestener2004,xsmurf} one can compute the fractal dimensions of the subspace of singularity exponents $h$ where this coefficient $h$ corresponds to a measure of the regularity of the flow. However, the WTMM method is a \textit{global statistical} method that only provides a {\sl global} information about local H\"older exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a \textit{local statistical} analysis, that estimates locally the H\"older continuity. We have compared outcomes of our analysis, with results using the inertial energy dissipation $D_\ell^I$ (see Figure \ref{fig1}). We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local H\"older exponents however shows non trivial behavior and does not exactly match the distribution of the inertial dissipation (see Figure \ref{fig2}). 14:30 15 mins #186 On the fine structure of turbulence determined by entropy variation Andre Fuchs, Matthias Wächter, Joachim Peinke, Swapnil Kharche, Alain Girard, Jean-Paul Moro Abstract: Using a non-equilibrium thermodynamical approach [3, 4, 5, 7] together with a stochastic description of the turbulent cascade process [1, 2, 6] allow a new access via entropy variation to the dynamic fluctuations of small scale structures. Positive and negative entropy fluctuation occur like it is known from microscopic systems. Furthermore, these entropy fluctuations fulfill accurately the elementary "integral fluctuation theorem" [7]. Here we used the entropy values to investigate special cascade events. Therefore we determine the average of all measured absolute velocity increment scale trajectories conditioned on a specific total entropy variation (shown in Fig.1(a-b)). Our investigation shows that entropy-consuming trajectories are correlated to extreme events in the increment statistics on the smallest scales and thus are correlated to small-scale intermittency of turbulence. Most remarkably such increment trajectories have the tendency to diverge as the scale approaches the Taylor length, i.e. the dissipation regime, which might be interpreted as local singularities. Moreover, the presented results indicate a link between the statistical description of turbulence and the characterization via local turbulent flow structures. In this contribution we will investigate these features of the turbulent cascade for different turbulent flows (generated experimentally in a wind tunnel) like free jets, wake flows of regular and fractal grids as well as low-temperature, large size forced von Kármán liquid helium flows (performed in the SHREK experiment). This work could be performed through the program Chair of Excellence of Laboratoire d'Alliances Nanosciences-Energies du Futur (LANEF, ANR funded contract ANR-10-LABX-51-01). References [1] Friedrich R. and Peinke J., (1997), Description of a turbulent cascade by a Fokker–Planck equation, Physical Review Letters, 78:863 [2] Lueck, S., Renner, C., Peinke, J., Friedrich, R., et al., (2006), The markov-einstein coherence length a new meaning for the taylor length in turbulence, Physics Letters A, 359(5), 335-338 [3] Nickelsen D. and Engel A., (2013), Probing small-scale intermittency with a fluctuation theorem, Physical Review Letters, 110, 214501 [4] Peinke, J., Tabar, M. R. R. and Wächter, M., (2018), The Fokker–Planck Approach to Complex Spatiotemporal Disordered Systems, Annual Review of Condensed Matter Physics [5] Reinke, N., Fuchs, A., Nickelsen, D. and Peinke, J. (2018), On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics, Journal of Fluid Mechanics, 848, 117-153 [6] Renner, C., Peinke, J., Friedrich, R., (2001), Experimental indications for markov properties of smallscale turbulence, Journal of Fluid Mechanics, 433, 383-409 [7] Seifert, U., (2012), Stochastic thermodynamics, fluctuation theorems and molecular machines, Reports on Progress in Physics, 75(12) 14:45 15 mins #213 ON THE INERTIAL RANGE SCALING IN THE HIGH-Rλ LIMIT Christian Küchler, Gregory Bewley, Eberhard Bodenschatz Abstract: The scaling behaviour of fully developed turbulence has been a subject of research ever since Kolmogorov predicted in his milestone estimates in 1941 [6] that universal scaling laws emerge in the inertial range if the Taylor-scale Reynolds number Rλ is large enough. In the past it has been found that this limit - if existent - requires extreme Rλ, which are difficult and expensive to create in a well-controlled turbulent flow. The Variable Density Turbulence Tunnel [3] is the first wind tunnel capable of producing Rλ > 3000 at fully resolved inertial scales. It combines the low kinematic viscosity of pressurized sulfur-hexaflouride and a unique mosaic-like active grid with individually controllable tiles [5]. The Kolmogorov scale η can be as low as 10 μm in the tunnel demanding a high spatial resolution of the measurement instruments to faithfully report small-scale statistics. We use Nanoscale Thermal Anemometry Probes developed and generously provided by Princeton University [1, 4, 7]. We present results that the two-point statistics (namely energy spectrum and structure functions up to order 3) follow universal scaling laws that differ from both, the K41 theory and common intermittency-corrections. Following the tradition of extended self-similarity [2], we find this universal behaviour in the local slope of these statistics, e.g. d log E(k)/d log(k) (see 1). The local slopes appear as lines in a semilogarithmic plot, whose parameters become Rλ-independent for Rλ > 2000. Interestingly, this can be observed at larger length scales than typically considered to be part of the inertial range. 15:00 15 mins #246 ANALYZING AND INFLUENCING THE WAKE OF AN ACTIVE TURBULENCE GRID Lisa Rademacher, Gerd Gülker, Michael Hölling, Joachim Peinke Abstract: In recent years, the meaning of active turbulence grids has changed from a wind tunnel tool for turbulence generation to a versatile instrument for the design of inflow conditions. Active grids have been also used to produce shear layers [1] and mean flow direction deviations [2]. For consistent wind tunnel experiments a homogeneous velocity flow field with uniform turbulence intensity across the measuring section is desired. Compared to passive grids, the large structures of the active grid lead to a longer relaxation area in front of the usable measuring section. A special focus is set on the wake of the underlying physical structure of the grid. Therefore, we investigated the flow field behind an active grid, with mesh size M = 5 cm consisting of five horizontal and vertical shafts each, in a closed-loop wind tunnel test section of 25 by 25 cm2 cross section and 150 cm length. A 2D-Laser Doppler Anemometer system was used to record the main and one lateral velocity component. The Y-Z-plane, lateral to the main flow direction X, was traversed for different downstream positions behind the grid. We observed the mean velocities 〈𝑢𝑋 〉, 〈𝑢𝑍 〉 and their fluctuations 〈𝑢𝑥 ′2〉, 〈𝑢𝑦 ′2〉 respectively the turbulence intensity. The analysis of the flow behavior revealed the non-uniformity of the mean flow and lateral flow profile as illustrated in Figure 1, where the velocity field at a distance of 12.2 M is shown. The non-uniformity leads to irregular inflow conditions which produces areas of vortices. The influence of the wake of the active grid on the distribution of mean longitudinal and lateral velocities shows the need for flow-homogenizing methods. Therefore, we investigated the influence of the active grid flaps oscillating slightly around zero position. A parameter study of varying amplitudes and frequencies of an oscillating, sinusoidal flap excitation has been evaluated. We found that different combinations of amplitude and frequency could notably smooth the lateral and longitudinal nonuniformities. Simultaneously, we observed an increase of turbulence intensity for different downstream distances in relation to the varying parameter settings. 15:15 15 mins #248 High Reynolds number turbulence generation by active grid and wind tunnel control Lars Neuhaus, Joachim Peinke, Michael Hölling Abstract: To experimentally investigate the impact of atmospheric turbulence on objects under laboratory conditions, high Reynolds number turbulence is needed [1]. To generate defined turbulence in wind tunnels grids are used. Passive grids generate one specific type of turbulence and are also limited in the achievable Taylor scale Reynolds number Reλ. Active grids on the other hand allow for generating higher Re due to a higher degree of freedom [2]. The Taylor Reynolds number e.g. in the atmospheric boundary layer is known to be in the order of couple thousands [3]. The objective of this study is to reproduce comparable flows in the wind tunnel. To do so, a 3 x 3m² active grid is used in the Oldenburg wind tunnel with a closed test section [4]. The grid exhibits 80 individually controllable shafts with attached square-shaped vanes. In this approach the motion of the shafts is given by a Langevin process to imitate a turbulent like excitation. The active grid is driven in a constant blockage mode, which allows for changes in the local blockage but keeps the global blockage across the wind tunnel outlet constant. To further increase the energy in the large scale fluctuations, the wind tunnel speed is varied by changing the wind tunnel fan speed. The fan speed is also controlled based on a Langevin process but with different parameters and time scales. The generated flow is measurement by a hot-wire probe in the centerline of the wind tunnel 100 mesh width downstream the active grid, which corresponds to roughly 14.3m. The measurements are analyzed regarding their one and two point statistics by means of velocity increments. The generated flow is found to be stationary on the 10 minutes measured (Fig. 1(a)). In the power spectral density the generated flow fulfills the -5/3 power law for a wide range of frequencies (approximately four decades) (Fig. 1(b)). This results in a Taylor Reynolds numbers Reλ of roughly 6400. The shape factor λ² = 1/4 log(/(3²) of the velocity increments uτ = u(t+τ)-u(t) shows high values, which correspond to a highly intermittent flow (Fig. 1(c)). At large τ the increment distribution becomes gaussian (λ² = 0). For smaller τ the shape factor exhibits a constant slope in the semi-log plot on the scales 2.5x10^(-3)s < τ < 10s. This region coincides with the one in the power spectral density where the -5/3 power law is fulfilled - the inertial subrange - and indicates a fully developed turbulence with an intermittency factor of µ = 0.23 (expected 0.2 < µ < 0.3 [5]). The presented approach allows for an easy generation of high Reynolds number turbulence in the wind tunnel. Integral length scales larger than the wind tunnel width can be produced. At the small scales, features of homogeneous and isotropic turbulence by means of power spectra and intermittency are well reproduced. This is promising for lab-scale studies of the impact of atmospheric turbulence on objects. References [1] A.N. Kolmogorov. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers. Dokl. Akad. Nauk., 30,4: 299-303, 1941. [2] P. Knebel, A. Kittel, and J. Peinke. Atmospheric wind field conditions generated by active grids. Experiments in fluids, 51(2), 471-481, 2011. [3] E.F. Bradley, R.A. Antonia, and A.J. Chambers. Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer. Boundary-Layer Meteorology, 21(2): 183-197, 1981. [4] L. Kröger, J. Frederik, J.W. van Wingerden, J. Peinke, and M. Hölling. Generation of user defined turbulent inflow conditions by an active grid for validation experiments. Journal of Physics: Conference Series, 1037, 5: 052002, 2018. [5] A. Arneodo, and 23 other. Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett., 34(6): 411-416, 1996. 15:30 15 mins #167 Cascades and transitions in turbulent flows Alexandros Alexakis, Luca Biferale Abstract: Turbulent flows are characterized by the non-linear cascades of energy and other inviscid invariants across scales, from where they are injected to where they are dissipated. Recent experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal cases of strictly forward cascade of three dimensional turbulence or the strictly inverse cascade of two dimensional turbulence. In the presence of confinement, rotation, stratification or magnetic fields (to mention a few examples) the direction of cascade can change direction and possibly display a "split cascade" where energy cascades to both small and large scales. In this talk, I will present a short summary of these recent results from a unified point of view and attempt a classification of all different cascading states and all possible transitions from one scenario to another as the control parameters are varied. The presentation will be based on a set of paradigmatic examples. I will conclude with a series of open problems and challenges that future theoretical and experimental work needs to address in this new direction of turbulence research.