Subcritical axisymmetric solutions in rotor-stator flow

Rotor-stator cavity flows are known to exhibit unsteady flow structures in the form of circular and spiral rolls. While the origin of the spirals is well understood, that of the circular rolls is not. In the present study the axisymmetric flow in an aspect ratio $R/H=10$ cavity is revisited {numerically using recent concepts and tools from bifurcation theory}. It is confirmed that a linear instability takes place at a finite critical Reynolds number $Re=Re_c$, and that there exists a subcritical branch of large amplitude chaotic solutions. This motivates the search for subcritical finite-amplitude solutions. The branch of periodic states born in a Hopf bifurcation at $Re=Re_c$, identified using a Self-Consistent Method (SCM) and arclength continuation, is found to be supercritical. The associated solutions only exist, however, in a very narrow range of $Re$ and do not explain the subcritical chaotic rolls. Another subcritical branch of periodic solutions is found using the Harmonic Balance Method with an initial guess obtained by SCM. In addition, edge states separating the steady laminar and chaotic regimes are identified using a bisection algorithm. These edge states are bi-periodic in time for most values of $Re$, {where} their dynamics is {analysed in detail}. Both solution branches fold around at approximately the same value of $Re$, which is lower than $Re_c$ yet still larger than the values reported in experiments. This suggests that, at least in the absence of external forcing, sustained chaotic rolls have their origin in the bifurcations from these unstable solutions

On the origin of circular rolls in rotor-stator flow

Rotor-stator flows are known to exhibit instabilities in the form of circular and spiral rolls. While the spirals are known to emanate from a supercritical Hopf bifurcation, the origin of the circular rolls is still unclear. In the present work we suggest a quantitative scenario for the circular rolls as a response of the system to external forcing. We consider two types of axisymmetric forcing: bulk forcing (based on the resolvent analysis) and boundary forcing using direct numerical simulation. Using the singular value decomposition of the resolvent operator the optimal response is shown to take the form of circular rolls. The linear gain curve shows strong amplification at non-zero frequencies following a pseudo-resonance mechanism. The optimal energy gain is found to grow rapidly with the Reynolds number (based on the rotation rate and interdisc spacing $H$) in connection with huge levels of non-normality. The results for both types of forcing are compared with former experimental works and previous numerical studies. Our findings suggest that the circular rolls observed experimentally are the combined effect of the high forcing gain and the roll-like form of the leading response of the linearised operator. For high enough Reynolds number it is possible to delineate between linear and nonlinear response. For sufficiently strong forcing amplitudes, the nonlinear response is consistent with the self-sustained states found recently for the unforced problem. The onset of such non-trivial dynamics is shown to correspond in state space to a deterministic leaky attractor, as in other subcritical wall-bounded shear flows

Glucose- and pH-responsive Nanogels Crosslinked by Functional Superparamagnetic Maghemite Nanoparticles as Innovative Drug Delivery Systems

peer reviewe

Administrative internment in Provence‐Côte d’Azur during the liberation

Le sujet de cette thèse traite des seize camps d’internement administratif implantés dans les six départements de la région Provence Côte‐d’Azur entre la Libération et décembre 1945. Dans cette région libérée, mais économiquement exsangue et encore en guerre dans sa partie orientale jusqu’en mai 1945, nous nous demanderons si l’internement administratif, un outil de l’épuration quasiment absent de l’historiographie régionale, est déconnecté des tensions propresà ce territoire ou si, au contraire, il les cristallise. Dans un premier temps, nous nous interrogerons sur la mise en pratique des textes normatifs qui donnent lieu à la création et à l’aménagement des centres de séjour surveillé dans la région R2 au cours des premières semaines chaotiques de la Libération. Une seconde partie porte sur l’organisation des campsdans tous ses aspects : les recherches de financement, le quotidien des internés, le ravitaillement et le transport, l‘état sanitaire, le recrutement du personnel et la sécurité des camps. La troisième partie propose une étude des populations internées ainsi qu’une approche sociologique constituée à partir d’un échantillon de 624 internés des centres de séjour surveillé de Saint‐Mitre (Bouches‐du‐Rhône), de Sorgues (Vaucluse) et de Saint‐Vincent‐les‐Forts (Basses‐Alpes). Avec lafin de la Seconde Guerre mondiale, cette thèse explore enfin la dissolution des camps et les nouvelles affectations de ces lieux, tout en abordant la question du risque mémoriel.The subject of this thesis deals with 16 administrative internment camps planted in the six departments of the Provence Côte d’Azur region between the liberation and December 1945. In this liberated, but economically sapped region that was still at war in its eastern parts until May 1945, we ask ourselves if administrative internment, as a tool for purification practically absent in the region’s historiography, is it disconnected from the real tensions of this territory or if, on the contrary, it crystallized them. First of all we ask ourselves about how the various texts for creating and transforming the guarded centers in the region R2 during the chaotic days of the liberation came about. In the second part there is the examination of the organization of the camps in all their aspects: looking for finance, daily life for the internees, the transport, state of health, the recruiting of the personal, and the security of the camps. In the third part a study is proposed of the population of internees as well as a sociological approach made up from a sample of 624 internees from guarded centers in Saint‐Mitre (Bouches‐du‐Rhône), in Sorgues (Vaucluse) and in Saint‐Vincent‐les‐Forts (Basses‐Alpes). With the end of the second world war, this thesis explores the dismantling of the camps and the new uses of these sites, addressing thequestion of the risks of memorials

Boundary condition influence on instabilities in a low Reynolds free surface rotating flow

International audienceThe study of a rotating flow in one its most simple configuration (fixed cylindrical cavity, rotating bottom disk, free top surface) reveals a much more complicated physic than expected. While we tried to validate our experimental setup with both publica- tion 1 and numerical result, we were able to obtain the right unstable modes, but at much lower Reynolds. After several investigation on possibles issue in our experience, we finally suspected free condition surface to deeply influence both base flow and instabilities.We first used a condition introduced in 2, that we call “Frozen condition”, and that consists in setting the surface radial velocity to 0. But if this condition lowered the critical Reynolds, Stability analysis was no more able to predict the right mode. So we built a new top boundary condition as an α weighted sum of free and frozen conditions.A search for critical Reynolds depending on α reveals a second unstable branch, with a lower critical Reynolds, and better visualization agreement 1(c) with instabil- ities that are experimentally observed 1(b)

Boundary condition influence on instabilities in a low Reynolds free surface rotating flow

International audienceThe study of a rotating flow in one its most simple configuration (fixed cylindrical cavity, rotating bottom disk, free top surface) reveals a much more complicated physic than expected. While we tried to validate our experimental setup with both publica- tion 1 and numerical result, we were able to obtain the right unstable modes, but at much lower Reynolds. After several investigation on possibles issue in our experience, we finally suspected free condition surface to deeply influence both base flow and instabilities.We first used a condition introduced in 2, that we call “Frozen condition”, and that consists in setting the surface radial velocity to 0. But if this condition lowered the critical Reynolds, Stability analysis was no more able to predict the right mode. So we built a new top boundary condition as an α weighted sum of free and frozen conditions.A search for critical Reynolds depending on α reveals a second unstable branch, with a lower critical Reynolds, and better visualization agreement 1(c) with instabil- ities that are experimentally observed 1(b)

A simple model for arbitrary pollution effects on swirling free-surface flows

International audienceAmbient pollution acts like surfactants on free-surface flows and can hence strongly affect their nonlinear dynamics. A cylindrical free-surface flow driven by a slow rotating bottom is considered here as a generic example for such effects and is investigated both experimentally and numerically. We suggest here a simple numerical model without superficial transport of the surfactants, adaptable into any code for single-phase flows. The model does not possess any free parameter and is independent on the closure model for surfactants. For the stationary axisymmetric base flow, the radial velocity at the interface is set to zero whereas the usual stress-free boundary conditions are retained for the perturbations. For a geometrical aspect ratio of 1/4, known to display ambiguous behaviour regarding stability thresholds, the modal selection as well as a nonlinear stability island found in the experiments are well reproduced by the model, both qualitatively and quantitatively

Influence of boundary conditions on instabilities in free surface rotating flows

International audienceThe study of rotating flows in one of its most simple configurations (fixed cylindrical vessel, rotating disk at the bottom, free surface at the top) reveals much more complicated physics than expected. This flow, for low aspect ratios, is known to develop travelling instabilities as the angular velocity of the disk exceeds a finite threshold [1]. We revisit this flow case using distilled water experiments, direct numerical simulation and linear stability analysis. The comparison reveals a robust discrepancy in the instability thresholds. After a critical assessment of the possible issues in the experimental set-up, we eventually question the modelling of the free surface in the presence of water contaminants [2].The influence of this numerical boundary condition was first tested by considering a new ’frozen’ boundary condition where the radial velocity vanishes at the liquid interface [3]. In a second stage we generalise this new boundary condition into a linear combina- tion of both ’free’ and ’frozen’ conditions, thereby introducing an additional free parameter α.The search for the critical Reynolds number, parametrized by α, reveals a second branch of unstable modes with a lower critical threshold. The visual and quantitative agreeement between this new instability mode and the experimentally observed structures (cf Fig. 2) is very encouraging