Étude des instabilités de l'écoulement engendré par un disque tournant en présence de surface libre : Confrontation expérimentale et numérique

Les instabilités se formant dans une cavité cylindrique fixe à fond tournant et en présence de surface libre sont étudiées à la fois au moyen de simulations numériques mais aussi à l'aide d'un montage expérimental. Les motifs obtenus dans l'expérience au passage de la première bifurcation qui brise l'axisymétrie sont généralement bien reproduits numériquement. Cependant les écarts constatés entre les valeurs des paramètres critiques trouvés par les approches numérique et expérimentale sont parfois surprenants. Nous cherchons à expliquer les raisons des écarts et comparer nos travaux avec d'autres expériences similaires

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

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

Effet de la rotation sur les instabilités thermocapillaires dans un pont liquide chauffé latéralement

Dans les procédés de croissance cristalline, la rotation est souvent utilisée comme moyen pour éliminer les défauts d'axisymétrie du chauffage. La rotation du système de chauffage étant en général difficile à mettre en {\oe}uvre, une solution consiste à faire tourner à la fois le cristal et le polycristal soit dans le même sens soit dans des directions opposées. Les vitesses optimales de rotation du cristal et du polycristal sont souvent déterminées empiriquement. A l'aide d'une étude numérique de stabilité linéaire tridimensionnelle puis d'un bilan d'énergie, nous avons cherché à comprendre les effets de rotation sur l'instabilité thermocapillaire en zone flottante. Nous présentons des résultats où nous montrons que la rotation peut avoir des effets surprenants de stabilisation ou de déstabilisation et proposons des pistes pour l'interprétation

Seuils de stabilité pour un écoulement engendré dans une cavité cylindrique avec surface libre et fond tournant

Par une étude de stabilité linéaire nous nous proposons d'analyser un écoulement dans une cavité cylindrique fixe remplie de fluide, dont le fond tourne. Le rayon de la cavité est grand devant la hauteur de fluide. Ce travail s'inspire d'une étude expérimentale récente, réalisée à Marseille, (Poncet & Chauve 2007) qui a mis en évidence une instabilité aux motifs particulièrement intéressants. La rotation et la présence d'une surface libre rendent difficile la simulation numérique car la déformation de cette dernière impose d'utiliser des codes de calculs permettant de prendre en compte des géométries complexes. Dans une première approche, nous avons utilisé une modélisation de la surface libre plane (conditions de symétrie) afin de comparer les résultats expérimentaux et notre étude de stabilité linéaire. Nous discuterons de la pertinence de cette modélisation c'est à dire de la nécessité de prendre en compte la déformation de la surface

Free surface flow driven by a rotating end wall in a stationary cylinder: Structure of the axisymmetric base flow

We study the steady free-surface flow of a viscous liquid layer contained in a cylinder with a rotating bottom and a fixed lateral wall. When the disk rotates at large speed, the free surface deforms strongly and three-dimensional instability patterns (rotating polygons) or sloshing motions can arise. In order to get some insight on their formation mechanisms, a study of the axisymmetric base flow is carried out numerically. The flow structure consists of a well-known central fluid column entrained in a motion of solid-body rotation at the disk angular velocity. The fluid region situated at the periphery reveals a complex structure as it is found to be surrounded by four boundary layers. This leads us to discuss the relevance of existing base-flow models used for instability studies of this flow configuration

Identification of genetic variants associated with Huntington's disease progression: a genome-wide association study

Background Huntington's disease is caused by a CAG repeat expansion in the huntingtin gene, HTT. Age at onset has been used as a quantitative phenotype in genetic analysis looking for Huntington's disease modifiers, but is hard to define and not always available. Therefore, we aimed to generate a novel measure of disease progression and to identify genetic markers associated with this progression measure. Methods We generated a progression score on the basis of principal component analysis of prospectively acquired longitudinal changes in motor, cognitive, and imaging measures in the 218 indivduals in the TRACK-HD cohort of Huntington's disease gene mutation carriers (data collected 2008–11). We generated a parallel progression score using data from 1773 previously genotyped participants from the European Huntington's Disease Network REGISTRY study of Huntington's disease mutation carriers (data collected 2003–13). We did a genome-wide association analyses in terms of progression for 216 TRACK-HD participants and 1773 REGISTRY participants, then a meta-analysis of these results was undertaken. Findings Longitudinal motor, cognitive, and imaging scores were correlated with each other in TRACK-HD participants, justifying use of a single, cross-domain measure of disease progression in both studies. The TRACK-HD and REGISTRY progression measures were correlated with each other (r=0·674), and with age at onset (TRACK-HD, r=0·315; REGISTRY, r=0·234). The meta-analysis of progression in TRACK-HD and REGISTRY gave a genome-wide significant signal (p=1·12 × 10−10) on chromosome 5 spanning three genes: MSH3, DHFR, and MTRNR2L2. The genes in this locus were associated with progression in TRACK-HD (MSH3 p=2·94 × 10−8 DHFR p=8·37 × 10−7 MTRNR2L2 p=2·15 × 10−9) and to a lesser extent in REGISTRY (MSH3 p=9·36 × 10−4 DHFR p=8·45 × 10−4 MTRNR2L2 p=1·20 × 10−3). The lead single nucleotide polymorphism (SNP) in TRACK-HD (rs557874766) was genome-wide significant in the meta-analysis (p=1·58 × 10−8), and encodes an aminoacid change (Pro67Ala) in MSH3. In TRACK-HD, each copy of the minor allele at this SNP was associated with a 0·4 units per year (95% CI 0·16–0·66) reduction in the rate of change of the Unified Huntington's Disease Rating Scale (UHDRS) Total Motor Score, and a reduction of 0·12 units per year (95% CI 0·06–0·18) in the rate of change of UHDRS Total Functional Capacity score. These associations remained significant after adjusting for age of onset. Interpretation The multidomain progression measure in TRACK-HD was associated with a functional variant that was genome-wide significant in our meta-analysis. The association in only 216 participants implies that the progression measure is a sensitive reflection of disease burden, that the effect size at this locus is large, or both. Knockout of Msh3 reduces somatic expansion in Huntington's disease mouse models, suggesting this mechanism as an area for future therapeutic investigation