Bérengère Dubrulle,
Service de Physique de l’Etat Condensé, CNRS, CEA Saclay, Université Paris-Saclay

Revisiting Kolmogorov Theory

Turbulent flows are characterized by a self-similar energy spectrum, signature of fluid movements at all scales. This organization has been described for more than 70 years by the phenomenology of "Kolmogorov cascade": the energy injected on a large scale by the work of the force that moves the fluid (e. g. a turbine) is transferred to smaller and smaller scales with a constant dissipation rate, up to the Kolmogorov scale, where it is transformed into heat and dissipated by viscosity.
I will explain why this image, which Landau questioned in the 1950s, is false. I will use recent velocity measurements obtained by very high resolution laser velocimetry to show that the energy "cascade" is in fact driven by extreme events on a very small scale, which are the signature of quasi-singularities of the Navier-Stokes equations existing under the Kolmogorov scale.

John Bell, Lawrence Berkeley National Laboratory

Modeling Electrolytes at the Mesoscale

At small scales, the standard deterministic equations used for modeling fluids break down and thermal fluctuations play an important role in the dynamics. Landau and Lifshitz proposed a modifi ed verion of the Navier-Stokes equations, referred to as the fluctuating hydrodynamics equations that incorporate stochastic flux terms designed to incorporate the eff ect of fluctuations. These stochastic fluxes are constructed so that the equations are consistent with equilibrium fluctuations from statistical mechanics. In this talk, we present a generalization of fluctuating hydrodynamics to electrolytes. We then discuss some of the properties of the resulting system and show how fluctuations naturally incorporate some of the distinguishing characteristics of electrolytes. We then introduce a finite-volume method for solving the fluctuating hydrodynamics equations and present numerical results illustrating the behavior of electrolytes in some canonical flows.

Johannes von Lindheim, Technische Universität Berlin

"What is... a coherent structure?"

Although a formal definition of a coherent (or turbulent) structure has so far been elusive, it is generally thought to be a region of space and time within which the flow field exhibits a characteristic coherent pattern. With the contribution from flow visualization experiments and DNS simulations, Pope (2001) classifies these structures into eight categories. In this talk, I will give a brief overview on turbulent structures and then shift the focus to identifying one category of such structures, namely vortices, both in the Eulerian and Lagrangian specification of the flow field.

Gilles Vilmart, Université de Genève

Long time integration of stochastic differential equations: the interplay of geometric integration and stochastic integration

The preservation of geometric structures, such as the symplecticity of the flow for deterministic Hamiltonian systems, often reveals essential for an accurate numerical integration, and this is the aim of geometric integration.
In this talk we highlight the role that some geometric integration tools that were originally introduced in the deterministic setting play in the design of new accurate integrators to sample the invariant distribution of ergodic systems of stochastic ordinary and partial differential equations. In particular, we show how the ideas of modified differential equations and processing techniques permit to increase at a negligible overcost the order of accuracy of stiff integrators, including implicit schemes and explicit stabilized schemes.

This talk is based on joint works with Assyr Abdulle (EPF Lausanne), Ibrahim Almuslimani (Univ. Geneva), Charles-Edouard Béhier (Univ. Lyon), Adrien Laurent (Univ. Geneva), Gregorios A. Pavliotis (Imperial College London), Konstantinos C. Zygalakis (Univ. Edinburgh). Preprints available at http://www.unige.ch/~vilmart

Abhishek Harikrishnan, Freie Universität Berlin

"What is... a shearlet?"

Shortcomings in Fourier or Wavelet representations of multivariate data, most commonly images, have lead to the development of shearlets, originally introduced for the sparse approximation of functions from  L2(R2).  They are a multiscale geometric framework tuned to efficiently encode anisotropic features of such functions using parabolic scalings and shearings of some mother shearlet psi. In this talk, I will show the construction of shearlet frames, as well as a theorem showing almost-optimal sparse approximation behavior of shearlets with respect to a model class of images with anisotropic features (so-called cartoon-like functions). Moreover, I will present a few examples of applications of shearlets from image processing (denoising, inpainting, super-resolution, medical imaging...) by means of sparse regularization, which has been proven to be a useful prior in such imaging problems.

Back to top