15th European Turbulence Conference 2015
August 25-28th, 2015, Delft, The Netherlands

Invited speakers:

Prof. Marc Brachet. Ecole Normale Superieure, Paris, France

Prof. Peter G. Frick, Institute of Continuous Media Mechanics, Perm, Russia

Prof. Bettina Frohnapfel,  Karlsruher Institut fur Technology, Germany

Prof. Andrea Mazzino, Dipartimento di Fisica, University of Genova, Italy

Prof. Bernhard Mehlig. Department of Physics, University of Gothenburg, Sweden

Prof. Lex Smits, Mechanical and Aerospace Engineering, Princeton University, USA

Prof. Chao Sun Physics of Fluids, University of Twente, The Netherlands

Prof. Steve Tobias, Applied Mathematics, University of Leeds, United Kingdom

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15:00   Intermittency and scaling 2
Chair: Alex Liberzon
15 mins
Carlos B. da Silva, Ryo Onishi, Pedro C. Valente
Abstract: We present data from direct numerical simulations of homogeneous isotropic decaying turbulence showing both the non-equilibrium and the classical dissipation scalings reported in wind-tunnel experiments of both regular and fractal grid-generated turbulence, i.e. Cε ∼ (Re0/Reλ)n with n of order unity and Cε ∼ constant, respectively (Re0 and Reλ are global and local Reynolds numbers). These two dissipation behaviours lead to different power-law decay exponents in both regimes also in accord with the experiments. Finally, we show that in both regimes the maximum non-linear energy cascade flux, Π, reasonably satisfies the classical expectation that Π ∼ K3/2/l.
15 mins
Continuous representation for shell models of turbulence
Alexei A. Mailybaev
Abstract: In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models split into an infinite number of uncoupled subsystems, which are all identical to the same shell model. The two shell models, which allow such a construction, are considered: the dyadic (Desnyansky--Novikov) model with the intershell ratio $\lambda = 2^{3/2}$ and the Sabra model of turbulence with $\lambda = \sqrt{2+\sqrt{5}} \approx 2.058$. The continuous models allow understanding various properties of shell model solutions and provide their interpretation in physical space. We show that the asymptotic solutions of the dyadic model with Kolmogorov scaling correspond to the shocks (discontinuities) for the induced continuous solutions in physical space, and the finite-time blowup together with its viscous regularization follow the scenario similar to the Burgers equation. For the Sabra model, we provide the physical space representation for blowup solutions and intermittent turbulent dynamics.
15 mins
Markov processes linking stochastic thermodynamics and turbulent cascades
Daniel Nickelsen, Nico Reinke, Joachim Peinke
Abstract: An elementary example of a Markov process (MP) is Brownian motion. The work done and the entropy produced for single trajectories of the Brownian particles are random quantities. Statistical properties of such fluctuating quantities are central in the field of stochastic thermodynamics \cite{seifert_ov}. Prominent results of stochastic thermodynamics are so-called fluctuation theorems (FTs) which express the balance between production and consumption of entropy \cite{seifert_ft}. Turbulent cascades of eddies are assumed to be the predominant mechanism of turbulence fixing the statistical properties of fully developed (boundary-free) turbulent flows. These properties typically adress the two-point statistics of the flow field and hold universally for any kind of turbulence generation \cite{frisch}. Various models of turbulence aim at reproducing the observed universal properties. An intriguing phenomenon of developed turbulence are violent small-scale fluctuations in flow velocity that exceed any Gaussian prediction, commonly referred to as small-scale intermittency \cite{frisch}. The correct reproduction of small-scale intermittency by models of turbulence is of particular importance in turbulence research \cite{frisch,sreenivasan}. In analogy to Brownian motion, we show how the assumption of the Markov property leads to a MP for the turbulent cascade that is equivalent to the seminal K62 model \cite{k62}. In addition to the K62 model, we demonstrate how many other models of turbulence can be written as a MP, including scaling laws, multiplicative cascades, multifractal models and field-theoretic approaches. Based on the various MPs, we discuss the production of entropy and the corresponding FTs. In particular, an experimental analysis indicates that entropy consumption is linked to small-scale intermittency and, as a consequence, the corresponding FT probes the correct modeling of small-scale intermittency of the underlying model of turbulence \cite{nickelsen}. Using the FT as a citerion, we demonstrate in another experimental study that the three-point statistics of a developed turbulent flow field is universal only for the same kind of turbulence generation \cite{reinke}.
15 mins
Temperature fluctuations induced by frictional heating in isotropic turbulence
Robert Chahine, Wouter Bos, Andrey Pushkarev, Robert Rubinstein
Abstract: The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that the scaling of their variance with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results.
15 mins
Scaling and intermittency in ocean turbulence: analysis of coastal water optical properties and sea surface temperature (SST).
P.R. Renosh, Francois Schmitt, Hubert Loisel
Abstract: We consider here some scaling and intermittency properties of oceanic turbulence, with a general aim of considering the impact of turbulence on the bio-optical dynamics. For that purpose, we tried two different approaches, using in situ and satellite data. For the in situ study we adopted one dimensional and for the satellite two dimensional approaches. Different techniques such as Fourier power spectrum, Empirical mode of decomposition (EMD), Hilbert spectral analysis (HSA) have been used for analyzing the intermittency characteristics of the in situ data. For analyzing the multi-scale properties of the satellite images, we have considered Structure functions (SF) and Fourier power spectrum (1D and 2D). The general objective is to understand the multi-scale oceanic variability using scaling tools developed in the field of intermittent turbulence studies.
15 mins
Jonas Boschung, Michael Gauding, Fabian Hennig, Norbert Peters, Heinz Pitsch
Abstract: While Kolmogorov's similarity hypothesis suggests that velocity structure functions scale with the mean dissipation $\left< \varepsilon \right>$ and the viscosity $\nu$, we find that the $2m.$ even order scales with $\left< \varepsilon^m \right>$. This implies that there are other cut-off lengths than the Kolmogorov length $\eta$. These cut-off lengths are smaller than $\eta$ and decrease with increasing order and Reynolds-number. They are compared to a previous definition of order dependent dissipative scales by Schumacher~et.~al\cite{schumacher2007asymptotic}.