Christian Geindreau, Univ. Grenoble Alpes, 3SR, Director of the Fed3G, Deputy Director of Tec21

Mickaël Bourgoin,

CNRS, Laboratoire de physique, ENS (Lyon)

In spite of centuries of active research Turbulence remains one of the deepest mysteries of fluid mechanics. The complexity relies on the random and multi-scale nature of the phenomenon. This lecture will review the origin and the characteristics of fluid Turbulence, as well as the phenomenological framework and statistical tools commonly used to describe the phenomenon. These rely on the concept of energy cascade, introduced by L. Richardson in the 1920’s, later refined by A. Kolmogorov, who’s ideas still dominate the Turbulence research community.

Frédéric Pignon,

CNRS, LRP (Grenoble)

Courses objectives are the characterization of the link between the flow mechanical properties (flow field, shear or extensional stresses, viscoelasticity moduli) and the structural organizations (aggregation, orientation, phase changes). The goal is to bring an understanding of the mechanisms controlling the flows properties of colloidal dispersions used in several processes (membrane separation, extrusion, film casting) involved in several industrial applications (chemical, bio- and agro-industries, pharmaceutical, water treatment...)

All participants are kindly asked to prepare a poster about their work that will be exposed over the whole school. During the poster session, the participants will have 5 minutes to present their poster to the audience. 3 poster sessions will be held during the school with around 10 speakers each.

**Please don't forget to bring your poster with you on Thursday morning and a 3-4 slides presentation for the poster session.**

An icebreaker cocktail is organised on Thrusday 13 for the participants and the teachers to share a friendly moment after the first day of the school

Philippe Peyla,

Univ. Grenoble Alpes, LIPhy

Suspensions are encountered in nature as well as in various industrial processes. Suspensions refer to particles immersed in a liquid like mud, fresh concrete, blood, paints or ink to site but a few examples. A very recent interest with an exponential growing number of publications concerns active suspensions where particles can actively swim in the liquid phase like planktonic suspensions. Usually, the small size of the particles often means that the surrounding flow is dominated by viscous effects, and therefore that inertial forces can be neglected relative to viscous forces. This means that the Reynolds number associated with the particles is small and the flow can be considered as a Stokes flow. The present course aims at providing a physically based introduction to the dynamics of particulate suspensions and focuses on hydrodynamical aspects. We will also briefly summarize recent researches concerning active suspensions.

Christian Geindreau,

Univ. Grenoble Alpes, 3SR

The macroscopic mechanical behaviour of heterogeneous material strongly depends on the arrangement of the constituents according to various microstructures (granular or porous media, fibrous network) and the physical phenomena involved at the microscale (heterogeneity scale). A fine scale description of such material is often impossible due to the large number of heterogeneities.

In practice, a macroscopic equivalent modelling is more efficient. An overview of the different methods that can be used to derived such equivalent macroscopic behaviour will be given.

Mickaël Bourgoin,

CNRS, Laboratoire de Physique, ENS (Lyon)

Because of its intrinsic multi-scale nature, the experimental characterization of turbulence requires dedicated metrological tools, capable to resolve (simultaneously if possible) the whole range of relevant involved scales (both in time and space). The present lecture will review the main contemporary instruments used by the scientific community for such high resolution and multi-scale disgnosis. These include Eulerian methods (such as hot-wire anemometry, laser-Doppler velocimetry and Particle Image Velocimetry) as well as new Lagrangian methods, based on acoustical and optical 3D particle tracking.

On Saturday afternoon, the participants will be taken to a nice city tour, with an unforgettable lift to the highest point of Grenoble

On Sunday, an excursion will be organised to take the participants to the great outdoors of the Alps around Grenoble

Guillaume Balarac,

Grenoble-INP, LEGI

Turbulent flows are characterized by a large range of motion scales. When turbulent flows are studied by numerical simulations, the explicit discretization of the overall range of scales is still an issue, even with the exponential rise in computational capability over the last few decades. In this presentation, some methods to overcome this limitation will be presented. The methods can consist to model a part of the turbulent fields (RANS and LES approaches), but the methods can also consist to develop numerical algorithm to allow direct numerical simulation with a lower computational cost (hybrid method for turbulent mixing).

Cino Viggiani,

Univ. Grenoble Alpes, 3SR

Various advanced modeling approaches have been proposed to describe intriguing phenomena in solid mechanics. However, such models require experimental results, at the appropriate scales, with the appropriate sensitivities and under the appropriate loading conditions, to identify and characterize the important mechanisms controlling the material responses, to provide ground truth and to identify model input parameters. Unfortunately, traditional experimental methods often fall short of providing the necessary data for the increasingly ambitious modeling approaches. To address such shortcomings, new (advanced) experimental methods have been under development in recent years. This lecture summarizes some of the key developments in this area, with specific examples mostly (but not only) from geomechanics.

Bruno Chareyre,

Grenoble-INP, 3SR

The macroscopic effective properties or behaviour of heterogeneous materials are commonly invstigated by solving specific boundary value problem on Representative Elementary Volume (i.e. at the microscale) arising from the homogenization process. Nowadays, these boundary value problems (BVP) are commonly solved on 3D images of the material obtained by microtomography or idealized microstructure. Different numerical methods (Finite volume differences, Finite Element method, Discret Element method…) can used to solved the BVP. An overview of these methods is presented and illustrated.

The participants will attend 2 out of the 8 proposed lab-courses (1 on Tuesday, the other one on Wednesday). Groups of 4-5 participants will be made and each group will be given its planning and location depending on the chosen topic. The lab-courses will be held in parallel sessions at different places on the campus. The detailed description of the lab-courses can be seen here.

The Gala dinner will take place at the Restaurant "le 5" near the art museum of Grenoble.

The Restaurant is easily accessible by tram, line B, "Notre Dame Musée" stop (about 15 minutes from the university campus). View the map

Invited lectures: Instabilities in fluid and solid mechanics

Anne De Wit

Non Linear Physical Chemistry Unit

Université Libre de Bruxelles

To mitigate climate changes and global warming on Earth, Carbon Capture and Sequestration (CCS) methods are increasingly considered as one of the various measures needed to decrease the atmospheric concentration of greenhouse gases. In CCS, CO2 is captured at the exit of CO2-emitting industries instead of being released in the atmosphere. It is next injected into soils in combination with enhanced oil recovery techniques or in saline aquifers, widely distributed around the globe.

In the specific case of injection in saline aquifers, chemical reactions can impact the efficiency of the sequestration process. Indeed, when dissolved in water, CO2 produces carbonate ion (CO32- ) which can subsequently produce solid precipitates upon reaction with Ca2+ or Mg2+ ions for instance [1]. This mineralization process is welcome to increase the safety of the sequestration process. To understand the injection conditions optimizing the production of solid precipitates, we conduct laboratory-scale experimental studies of precipitation patterns obtained when a solution of carbonate ions is injected into an aqueous solution of calcium ions in a confined geometry (Fig.1). We show that the amount and spatio-temporal distribution of the solid calcium carbonate (CaCO3) phase produced strongly depends on the concentrations and injection flow rate [2, 3, 4].

If gaseous or supercritical CO2 is injected in an aquifer, it can first rise to the top of the the salt water layer, up to the impermeable cap rock containing the aquifer. It next slowly starts dissolving into the lower aqueous solution. Upon dissolution, the denser boundary layer of CO2-rich water starts to sink convectively into the less dense salt water beneath it, because of a Rayleigh-Taylor instability (Fig.2). We have experimentally and theoretically investigated the influence of chemical reactions on this convective dissolution of CO2 by analyzing density fingering patterns developing in the gravity field when gaseous CO2 is put in contact with aqueous solutions of reactants. We show that the reactions can enhance convection inducing a more efficient sequestration [5, 6, 7]. On the contrary, an increase in salinity of the host solution decreases the intensity of convection [8].

These results evidence the possibility to control the convective and precipitation fingering pattern properties by varying the very nature of the chemicals or injection conditions. Implications on the choice of optimal sequestration sites in CCS techniques will be discussed.

[1] J.M. Matter et al., Rapid carbon mineralization for permanent disposal of anthropogenic carbon dioxide emissions, Science 352, 1312 (2016).

[2] G. Schuszter, F. Brau and A. De Wit, Calcium Carbonate Mineralization in a Confined Geometry, Environm. Sci. Tech. Letters 3, 156−159 (2016).

[3] G. Schuszter, F. Brau and A. De Wit, Flow-driven control of calcium carbonate precipitation patterns in a confined geometry, Phys. Chem. Chem. Phys. 18, 25592 (2016).

[4] F. Brau, G. Schuszter and A. De Wit, Flow control of A + B → C fronts by radial injection, Phys. Rev. Lett. 108, 134101 (2017).

[5] V. Loodts, C. Thomas, L. Rongy, and A. De Wit, Control of Convective Dissolution by Chemical Reactions: General Classification and Application to CO2 Dissolution in Reactive Aqueous Solutions, Phys. Rev. Letters 113, 114501 (2014).

[6] C. Thomas, V. Loodts, L. Rongy, A. De Wit, Convective dissolution of CO2 in reactive alkaline solutions: Active role of spectator ions, Int. J. Greenhouse Gas Control 53, 230 (2016).

[7] V. Loodts, B. Knaepen, L. Rongy and A. De Wit, Enhanced steady-state dissolution flux in reactive convective dissolution, Phys. Chem. Chem. Phys. 19, 18565 (2017).

[8] C. Thomas, S. Dehaeck, A. De Wit, Convective dissolution of CO2 in water and salt solutions, Int. J. of Greenhouse Gas Control 72, 105 (2018).

Catherine Quilliet

Laboratory of Interdisciplinary Physics (LIPhy)

Université Grenoble Alpes

A brief summary of possible deformation modes for thin elastic shells under external overpressure will be done, and examples given where such a simple deflating ball can be a model for objects of biology and soft matter.

Then I will focus on the swift deformation (buckling) that can be induced this way : due to scale independency of shape studies, symmetry considerations allow to forecast that micronic shells could provide a smart solution for making artificial microswimers.

Indeed, swimming at small scale generally happens at low Reynolds number (viscous regime) and thus requires non-reciprocal strokes, i.e. the deforming body follows a sequence of shapes which are not the same back and forth. A deflation-reinflation cycle, now known to induce buckling and an hysteresis in the shape of the shell it is submitted to, seemed then to be a simple and elegant way to remotely power a displacement on a microscopic object in a fluid.

The first experiments in this purpose were upscaled in order to allow a careful study of swimming through buckling. They showed the importance of postbuckling shape oscillations, that can boost the swimming for some values of the dimensionless numbers to be considered.

The whole study led to a model that draws the big lines for the conception of a steerable nanosubmarine, the first results on which will be presented.

Davide Bigoni

Dipartimento di Ingegneria Civile, Ambientale e Meccanica,

University of Trento

When a ductile material is subject to severe strain, failure is preluded by the emergence of shear bands, which initially nucleate in a small area, but quickly extend rectilinearly and accumulate damage, until they degenerate into fractures. Therefore, research on shear bands yields a fundamental understanding of the intimate rules of failure, so that it may be important in the design of new materials with superior mechanical performances.

Modelling of a shear band as a slip plane embedded in a highly prestressed material and perturbed by a mode II incremental strain, reveals that a highly inhomogeneous and strongly focussed stress state is created in the proximity of the shear band and aligned parallel to it. This evidence, together with the fact that the incremental energy release rate blows up when the stress state approaches the condition for ellipticity loss, may explain the rectilinear growth of shear bands and the reason why they are a preferred mode of failure for ductile materials [1,2]

A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J2–deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band, Fig. 1, [3].

The same mathematical tools developed for the analysis of shear bands in ductile materials will be shown to lead to folding and faulting in constrained Cosserat materials, when these have a strong anisotropy, so that they are close to the elliptic boundary. In fact, folding is a process in which bending is localized at sharp edges separated by almost undeformed elements and folding in these materials can originate from ellipticity loss, Fig. 2, [4-6]

Acknowledgement: Financial support from the ERC advanced grant ‘Instabilities and nonlocal multiscale modelling of materials’ FP7-PEOPLE-IDEAS-ERC-2013-AdG is gratefully acknowledged.

[1] D. Bigoni (2012) Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge

University Press.

[2] Bigoni, D. and Dal Corso, F. (2008) The unrestrainable growth of a shear band in a prestressed material.

Proc. Royal Soc. A. 464, 2365-2390.

[3] Giarola, D., Capuani, D. Bigoni, D. (2018) The dynamics of a shear band. J. Mech. Phys. Solids, In Press.

[4] D. Bigoni and P.A. Gourgiotis (2016) Folding and faulting of an elastic continuum.

Proc. Royal Soc. A, 472, 20160018.

[5] P.A. Gourgiotis and D. Bigoni (2016) Stress channelling in extreme couple-stress materials Part I: Strong

ellipticity, wave propagation, ellipticity, and discontinuity relations. J. Mech. Phys. Solids 88, 150-168.

[6] P.A. Gourgiotis, D. Bigoni (2016) Stress channelling in extreme couple-stress materials Part II: Localized

folding vs faulting of a continuum in single and cross geometries J. Mech. Phys. Solids 88, 169-185.

François Nicot

ETNA Group

IRSTEA (Grenoble)

Summary coming soon...

François Charru

Toulouse institute of Fluid Mechanics

University of Toulouse

The pioneering works of O. Reynolds and G. I. Taylor first recognized that laminar flows may become unstable, giving birth to remarkable organized patterns or to highly disordered turbulent flows. Since then, the field of hydrodynamic instabilities has been constantly renewed by the consideration of a wide variety of flows, encountered in aerodynamics, mechanical and chemical engineering, as well as in the natural environment (meteorology, geophysics). The analysis was also enriched by connections with other fields of physics, such as phase transitions, optics and astrophysics, and with the bifurcation theory of dynamical systems [1].

We will first consider the simplest situation of instabilities of fluids at rest, where a small disturbance may be amplified by the gravitational field, or by thermal or capillary effects. Dimensional analysis here provides the characteristics of the emerging spatial pattern and a physical understanding of the mechanisms involved. We will then turn to instabilities in open flows, where fluid inertia comes into play : the inviscid instability of shear layers – as first studied by Kelvin and Helmholtz – (Figure 2), and the viscous instability of flows near a solid wall (Poiseuille flow, boundary layers). For open flows, it appears that the predictions of linear stability analyses agree with experiments only if the flow disturbances coming from upstream are very small and carefully controlled – in particular for the critical Reynolds number –. Otherwise – that is, in usual situations – instability and transition to turbulence occur at much lower Reynolds number. In order to overcome the observed discrepancies, new concepts have been introduced, such as those of convective and absolute instability, and the “by-pass” transition involving the

transient growth of some “optimal” combinations of stable eigenmodes [2]. However, in spite of considerable theoretical and experimental efforts, the transition to turbulence is not fully understood yet [3]. Beyond the initial growth of disturbances of infinitesimal amplitude, which are described by linear stability analyses, nonlinear effects come into play. No general theory

is here available. However, weakly nonlinear analysis, based on perturbation methods, provide model equations – such as the Schrödinger or the Ginzburg–Landau equations – governing the spatio-temporal evolution of the amplitude or the envelope of modulated patterns. These equations allow the calculation, close to the threshold of the primary instability, of finite-amplitude patterns, and reveal some of their generic features such as the Eckhaus secondary instability of dissipative structures (e.g. in Rayleigh–Bénard convection or Couette–Taylor flow), or the Benjamin-Feir instability of finite-amplitude dispersive

waves (e.g. gravity waves). In the last part of the presentation, a focus will be given on the instability of plane sand beds sheared by fluid flows, which gives rise to sand ripples and dunes [4].

The mechanism of the instability – which is governed by fluid inertia – will be discussed, as well as the importance, for the wavenumber selection, of relaxation phenomena within the moving sand layer.

[1] F. Charru 2011 Hydrodynamic Instabilities, Cambridge University Press.

[2] Schmid, P. J. & Henningson, D. S. 2001 Stability and transition in shear flows, Springer-Verlag.

[3] Kerswell, R. R. 2005 Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity 18, 17–44.

[4] F. Charru, B. Andreotti & Ph. Claudin 2013 Sand ripples and dunes. Annu. Rev. Fluid Mech. 45, 469–493.

Patrice Le Gal

Institut de recherche sur les phénomènes hors équilibre

Université d'Aix Marseille

In this lecture, I will present the different types of classical waves and instabilities that can occur in astro and geophysical ﬂows. Inertial waves, caused by the rotation of the ﬂuid, will ﬁrst be introduced as well as their 2D version called Rossby waves. Then, it will be shown how a density stratiﬁcation of the ﬂuid can make internal gravity waves appear. In each case and in the case where both rotation and stratiﬁcation are present, the dispersion relations of the waves will be derived. A direct consequence of the presence of inertial waves in ﬂows is their possible resonance with for instance, the elliptic deformation of the rotating container in which they propagate: this resonance will give rise in this case to the so-called elliptic or tidal instability that may appear in celestial bodies [1] (see Figure 1-a) and 1-b)).

A diﬀerential rotation will then be added on the ﬂow. The classical Rayleigh criterium for the centrifugal instability is naturally recovered in the case of an homogeneous ﬂuid but it will be shown that a new instability, called the strato-rotational instability (SRI), can occur in a Taylor-Couette device when the ﬂuid is stratiﬁed [5, 4] (see ﬁgure 1-b)). Again, this instability arises because of the resonance of internal gravity waves which are in this case trapped close to the boundaries and Doppler shifted, allowing two counter propagating waves to become stationary and mutually resonant. More generally this wave interaction process identiﬁes a class of instability which is characteristic of shear ﬂows (e.g. [6]) as discovered for instance in the unstratiﬁed plane Couette ﬂow in the shallow water approximation [7], or more recently in the stratiﬁed plane Couette [8] or in the stratiﬁed plane Poiseuille [9, 10]. Finally, it will be shown how the application of a magnetic ﬁeld can create Alfven waves in a rotating electrically conducting ﬂuid and in which conditions, the magneto-rotational instability (MRI) can grow [11]. This instability is believed to destabilize proto-planetary accretion disks.

[1] M. Le Bars, D. Cebron, P. Le Gal, Flows Driven by Libration, Precession, and Tides, Annual Review of Fluid Mechanics, 47:1, 163-193, 2015.

[2] L. Lacaze, P. Le Gal, S. Le Dizes, Elliptical instability in a rotating spheroid Journal of Fluid Mechanics 505, 1-22, 2004.

[3] C. Eloy, P. Le Gal, S. Le Dizes, Experimental Study of the Multipolar Vortex Instability Phys. Rev. Lett. 85, 3400, 2000.

[4] M. Le Bars, P. Le Gal, Experimental analysis of the stratorotational instability in a cylindrical Couette

flow Phys. Rev. Lett. 99 (6), 064502, 2007.

[5] I. Yavneh, J.C. McWilliams, J. C. Molemaker, M. Jeroen, Non-axisymmetric instability of centrifugally stable stratied Taylor-Couette flow, Journal of Fluid Mechanics 448, 1-21, 2001.

[6] P. G. Baines, H. Mitsudera, On the mechanism of shear flow instabilities, Journal of Fluid Mechanics 276, 327342, 1994.

[7] T. Satomura, An investigation of shear instability in a shallow water, Journal of the Meteorological Society of Japan. Ser. II 59 (1), 148-167, 1981.

[8] G. Facchini, B. Favier, P. Le Gal, M. Wang, M. Le Bars, The linear instability of the stratied plane Couette flow, arXiv preprint arXiv:1711.11312, 2018.

[9] J. Chen, Stabilite d'un ecoulement stratie sur une paroi et dans un canal. PhD thesis, Ecole Centrale Marseille, 2016.

[10] P. Le Gal, U. Harlander, I. Borcia, Experiments on stratied Poiseuille flow in Cottbus, 18 - 27 April, 2018, Note interne IRPHE, 2018.

[11] S.A. Balbus, J.F. Hawley, Instability, turbulence, and enhanced transport in accretion disks, Rev. Mod. Phys. 70, 153, 1998.

Jean-Philippe Matas

Department of mechanics

Université Claude Bernard, Lyon