Cette thèse est une étude expérimentale sur mélange par des écoulements anisotropes turbulents en fluide stratifié. Il s'inscrit dans un projet sur l'étude globale de la structure de l'océan, principalement de sa couche supérieure. Le mélange est étudié en détail, à partir d'expériences réalisées en bicouche de densité dans un dispositif Taylor - Couette. En régime laminaire, le transport dans les zones initialement homogènes est moins intense que le flux de matière arrachée au niveau de l'interface. De multiples interfaces de densité apparaissent et leur action combinée contrôle les flux verticaux de densité. En régime turbulent, on trouve une relation entre flux et gradient de densité qui prédit un flux maximum pour des nombres de Richardson RIO d'environ 10. Un regain d'efficacité est observé pour les très grandes valeurs de RIO. Ces résultats vont dans le sens de la théorie de Balmforth (1998). Pour ces fortes valeurs de RIO, l'observation de l'écoulement par L.I.F., indique une activité intense des ondes et la présence de structures turbulentes de très petites échelles.

Outbreaks of food-born illness associated with the consumption of unpasteurized juice and apple cider have resulted in a rule published by the U.S. Food and Drug Administration (FDA) in order to improve the safety of juice products. The rule (21 CFR120) requires manufacturers of juice products to develop a Hazard Analysis and Critical Control Point (HACCP) plan and to achieve a 5-log reduction in the number of the most resistant pathogens. Ultraviolet (UV) disinfection is one of the promising methods to reach this 5-log reduction of pathogens. The absorption coefficients of juices typically vary from 10 to 40 1/cm and can be even higher depending on brand and processing conditions. Thin film reactors consisting of two concentric cylinders are suitable for inactivating pathogens in juices. When the two concentric cylinders are fixed, the flow pattern in the gap can be laminar Poiseuille flow or turbulent flow depending on flow rates. If the inner cylinder is rotating, and the rotating speed of the inner cylinder exceeds a certain value, the flow pattern can be either laminar or turbulent Taylor-Couette flow. UV disinfection between concentric cylinders in laminar Poiseuille flow, turbulent flow and both laminar and turbulent Taylor-Couette flow was investigated experimentally and numerically. This is the first systematic study done on UV disinfection between concentric cylinders in all three flow patterns. The present work provides new experimental data for pathogen inactivation in each of the three flow patterns. In addition, the present study constitutes the first systematic numerical CFD predictions of expected inactivation levels. Proper operating parameters and optimum gap widths for different flow patterns are suggested. It is concluded that laminar Poiseuille flow provides inferior (small) inactivation levels while laminar Taylor-Couette flow provides superior (large) inactivation levels. The relative inactivation levels are: laminar Poiseuille flow < turbulent flow < laminar Taylor-Couette flow.

Cette thèse porte sur l'étude expérimentale de la réduction de traînée par injection de bulles. Le contexte de l'étude est lié à la propulsion navale. Les bulles peuvent, lorsqu'elles sont injectées dans la couche limite en développement le long des carènes de navires, contribuer à réduire significativement la résistance de frottement, en allégeant d'une part le fluide le long de la coque et d'autre part en interagissant avec les structures turbulentes de proche paroi. La configuration expérimentale retenue pour cette étude est l'écoulement de Taylor-Couette, avec cylindre extérieur fixe et injection de bulles calibrées. Nos investigations portent sur les régimes de transition, de turbulence naissante et turbulent avec persistance des cellules de Taylor (Re=20000). La taille des bulles varie avec le capillaire et le mélange utilisés, entre 0,05 et 0,12 fois la largeur de l'entrefer. Une méthode originale de suivi de la phase dispersée dans un plan méridien, couplée à des mesures de couple global appliqué au cylindre intérieur ont permis de mettre en évidence deux régimes de réduction de traînée et plusieurs types d'arrangements des bulles, en fonction de leur taille et du nombre de Reynolds. Les bulles peuvent avoir une trajectoire glissante, oscillante, être capturées par les cellules de Taylor ou en proche paroi du cylindre intérieur dans les zones de jets sortants. La caractérisation par PIV des vitesses de la phase liquide en monophasique et diphasique a permis d'étudier les modifications induites par les bulles sur la phase liquide et de discuter des mécanismes impliqués dans la modification du couple global par la présence des bulles. Il ressort de cette étude que pour les nombres de Reynolds en deçà de la capture, les bulles contribuent à stabiliser l'écoulement en accord avec une réduction du couple visqueux pouvant atteindre -30% pour des taux de vide très faible (< 1%). Pour des nombres de Reynolds plus élevés, la capture dans les cellules conduit à une réduction de la longueur d'onde axiale et une augmentation de la vorticité des cellules, associée à une augmentation des vitesses rms. Cette configuration est favorable à une augmentation du couple visqueux. A l'inverse, la capture des bulles dans le jet sortant conduit à une augmentation de la longueur d'onde axiale, associée à une diminution de la vorticité. Cette configuration est favorable à une réduction du couple visqueux, moins marquée qu'en absence de capture.

La matière molle se consacre à l'étude des propriétés de fluides complexes. Ces fluides diffèrent des fluides simples à cause de l'existence d'une microstructure qui provient de l'arrangement particulier des éléments mésoscopiques constitutifs du matériau (agrégats de particules de noir de carbone, enchevêtrements de polymères, micelles de molécules tensioactives). C'est le couplage entre microstructure et déformation qui confère aux fluides complexes des comportements singuliers et qui engendre des écoulements hétérogènes. Comprendre ces états hors-équilibre et les dynamiques associées présente un intérêt à la fois industriel et fondamental. La rhéologie en cellule de Taylor-Couette est une technique très répandue pour l'étude de la déformation et de l'écoulement de fluides complexes. Cependant, cette méthode n'est pas adaptée à l'étude des écoulements hétérogènes car elle ne fournit qu'une description globale de l'écoulement. Pour pallier ce problème, une technique de vélocimétrie ultrasonore à deux dimensions a été couplée à la rhéologie classique. Cette visualisation locale nous a permis d'étudier l'instabilité inertielle de Taylor-Couette dans les fluides newtoniens, les instabilités élastiques de fluides viscoélastiques (polymères et solutions micellaires), la fluidification de fluides à seuil (gels de noir de carbone, microgels de carbopol et émulsions) et enfin la rupture de gels de protéine soumis à une contrainte de cisaillement. Tous ces exemples montrent des coexistences entre différents états induits par l'écoulement et permettent de revisiter les approches rhéologiques à partir de caractérisations locales des champs de déformation et de vitesse.

A high resolution spectrally accurate three-dimensional flow solver is developed in order to simulate convection dominated fluid flows. The governing incompressible Navier Stokes equations along with the energy equation for temperature are discretized using a second-order accurate projection method which utilizes Adams Bashforth and Backward Differentiation formula for temporal discretization of the non-linear convective and linear viscous terms, respectively. Spatial discretization is performed using a Fourier/Chebyshev spectral method. Extensive tests on three-dimensional Taylor Couette flow are performed and it is shown that the method successfully captures the different states ranging from formation of Taylor vortices to wavy vortex regime. Next, the code is validated for convection dominated flows through a comprehensive comparison of the results for two dimensional Rayleigh Benard convection with the theoretical and experimental results from the literature. Finally, fully parallel simulations, with efficient utilization of computational resources and memory, are performed on a model three-dimensional axially homogeneous Rayleigh Benard convection problem in order to explore the high Rayleigh number flows and to test the scaling of global properties.

Cette thèse est consacrée à la vérification de l'analogie entre l'instabilité viscoélastique (VEI) et l'instabilité magnéto-rotationnel (MRI) dans un écoulement képlérien, afin de mieux comprendre le transport du moment dans les disques d'accrétion. Le discriminant de Rayleigh élasto-rotationnel est établi pour clarifier le rôle de l'élasticité dans le VEI. L'analyse de stabilité linéaire (LSA) avec le modèle d’Oldroyd-B est effectuée pour prédire les paramètres critiques des modes viscoélastiques. Il fait apparaître également l'influence de l'élasticité, la viscosité polymérique et d'autres paramètres de contrôle pour le VEI. Des expériences bien contrôlées avec des solutions aqueuses de polyoxyéthylène (POE) et de polyéthylène glycol (PEG) sont effectuées. Nous avons observé le mode stationnaire axisymétrique supercritique avec des solutions de faible élasticité et modes désordonnés sous-critiques avec des solutions de grande élasticité. Les formes et les valeurs critiques de ces modes sont en bon accord avec les prédictions théoriques de LSA. Selon l'analogie, le mode axisymétrique stationnaire est probablement l'analogue de MRI standard, tandis que le mode désordonné est probable que l'analogue de MRI hélicoïdale. La thèse contient aussi des résultats théoriques expérimentaux sur quatre autres régimes de rotation et un cas de limite d'élasticité infinie. / This thesis is devoted to the verification of the analogy between the viscoelastic instability (VEI) and the magnetorotational instability (MRI) in a Keplerian flow, in order to get better understanding of the momentum transportation in accretion disks.The elasto-rotational Rayleigh discriminant is deduced to clarify the role of the elasticity in the VEI. The linear stability analysis (LSA) with Oldroyd-B model is performed to predict critical parameters of viscoelastic modes, and it reveals the influence of the elasticity, polymer viscosity on the VEI. Experiments with well controlled aqueous solutions of polyoxyethylene (POE) and polyethylene glycol (PEG) are conducted. We have observed supercritical stationary axisymmetric mode with solutions of small elasticity and subcritical disordered modes with solutions of large elasticity. Both the flow patterns and the critical values of these modes are in good agreement with the LSA predictions. According to the analogy, the stationary axisymmetric mode is likely the analog of the standard MRI while the disordered mode is likely the analog of the helical MRI. The thesis contains also theoretical and experimental results with four other rotation regimes and the limit case of infinite elasticity.

Accretion disks are ubiquitous in astrophysics. They are found in active galactic nuclei, around newly formed stars, around compact stellar objects, like black holes, neutron stars etc. When the ambient matter with sufficient initial angular momentum falls towards a central massive object, forming a disk shaped astrophysical structure, it is called an accretion disk. There are both ionized and neutral disks depending on their temperatures. Generally, in accretion disks, Gravitational force is balanced by the centrifugal force (due to the presence of angular momentum of the matter) and the forces due to gas pressure, radiation pressure and advection. Now, the matter to be accreted needs to lose angular momentum. For most of the accretion disks, the mass of the central object is much higher than the mass of the disk, giving rise to a dynamics governed by a central force. Therefore we can neglect the effect of self-gravity of the disk. Balancing the Newtonian gravitational force and centrifugal force leads to a Keplerian rotation profile of the accreting matter with the angular velocity ∼ r−3/2, where r is the distance from the central object. The Keplerian disk model is extremely useful to explain several flow classes (e.g. emission of soft X-ray in disks around stellar mass black holes). Due to the presence of differential rotation and hence shear viscosity, the matter can slowly lose its angular momentum and falls towards the central object. In this way, the accreting matter in the disk releases its gravitational potential energy and gives rise to luminosity that we observe. However, the molecular viscosity originated from the microscopic physics (due to the collisions between molecules) of the disk matter is not sufficient to explain the observed luminosity or accretion rate. For example, it can be shown that the temperature arisen from the dissipation of energy due to molecular viscosity (which is around 50000K for optical depth τ = 100) is much less than the temperature observed in these systems (around 107K). In my thesis, I have addressed the famous problem of infall of matter in astrophysical accretion disks. In general, the emphasis is given on the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, which are extensively seen in astrophysics, are Rayleigh-stable, but must be turbulent in order to explain observed data (observed temperature, as described above). Since the molecular viscosity is negligible in these systems, for a very large astrophysical length scale, Shakura and Sunyaev argued for turbulent viscosity for energy dissipation and hence to explain the infall of matter towards the central object. This idea is particularly attractive because of its high Reynolds number (Re ∼ 1014). However, the Keplerian disks, which are relevant to many astrophysical applications, are remarkably Rayleigh stable. Therefore, linear perturbation apparently cannot induce the onset of turbulence, and consequently cannot provide enough viscosity to transport matter inwards. The primary theme of my thesis is, how these accretion disks can be made turbulent in the first place to give rise to turbulent viscosity. With the application of Magnetorotational Instability (MRI) to Keplerian disks, Balbus and Hawley showed that initial seed, weak magnetic fields can lead to the velocity and magnetic field perturbations growing exponentially. Within a few rotation times, such exponential growth could reveal the onset of turbulence. Since then, MRI has been a widely accepted mechanism to explain origin of instability and hence transport of matter in accretion disks. Note that for flows having strong magnetic fields, where the magnetic field is tightly coupled with the flow, MRI is not expected to work. Hence, it is very clear that the MRI is bounded in a small regime of parameter values when the field is also weak. It has been well established by several works that transient growth (TG) can reveal nonlinearity and transition to turbulence at a sub-critical Re. Such a sub-critical transition to turbulence was invoked to explain colder, purely hydrodynamic accretion flows, e.g. quiescent cataclysmic variables, proto-planetary and star-forming disks, the outer region of the disks in active galactic nuclei etc. Baroclinic instability is another plausible source for vigorous turbulence in colder accretion disks. Note that while hotter flows are expected to be ionized enough to produce weak magnetic fields therein and subsequent MRI, colder flows may remain to be practically neutral in charge and hence any instability and turbulence therein must be hydrodynamic. However, in the absence of magnetic effects, the Coriolis force does not allow any significant TG in accretion disks in three dimensions, independent of Re, while in pure two dimensions, TG could be large at large Re. However, a pure two-dimensional flow is a very idealistic case. Nevertheless, in the presence of magnetic field, even in three dimensions, TG could be very large (Coriolis effects could not suppress the growth). Hence, in a real three-dimensional flow, it is very important to explore magnetic TG. However, as mentioned above, the charge neutral Rayleigh-stable astrophysical flows have hardly any magnetic field (e.g. protoplanetary disks, quiescent cataclysmic variables etc.). Also, the hydrodynamic Rayleigh-stable Taylor-Couette flows and plane Couette flows in the laboratory experiments are seen to be turbulent without the presence of any magnetic field, while they are shown to be stable in linear stability analysis. It is a century old unsolved problem to explain hydrodynamically, the linear instability of Couette flows and other Rayleigh-stable Flows, which are observed to be turbulent, starting from laboratory experiments to astrophysical observations. Therefore, as in one hand, the hydrodynamic instability of the astrophysical accretion flows and laboratory shear flows (e.g. Rayleighstable Taylor-Couette flow, plane Couette flow etc.) has to be understood, on the other hand, the magnetohydrodynamic (MHD) instability of the hotter flows has also to be investigated to understand the nature of MHD instability clearly, whether it arises due to MRI or TG. I have investigated the effect of stochastic noise (which is generated by the shearing motion of the disk layers) on the hydrodynamics and magnetohydrodynamics of accretion disks and explain how stochastic noise can make accretion Disks turbulent. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbations, and hence large energy dissipations of perturbation with time, which presumably generates instability and turbulence. I have also given in my thesis, a plausible resolution of the hydrodynamic turbulence problem of the accretion flows and laboratory shear flows (as discussed above) from pure hydrodynamics, invoking the idea of Brownian motion of particles. I have shown that in any shear flow, very likely, the stochastic noise is generated due to thermal fluctuations. Therefore, the shear flows must be studied including the effect of stochastically driving force and hence the governing equations should not be deterministic. Incorporating the effects of noise in the study of the above mentioned shear flows, I have shown in my thesis that hydrodynamic Rayleigh-stable flows and plane Couette flows can be linearly unstable. I have also investigated the importance of transient growth over magnetorotational instability (MRI) to produce turbulence in accretion disks. Balbus and Hawley asserted that the MRI is the fastest weak field instability in accretion disks. However, they used only the plane wave perturbations to study the instability problem. I have shown that for the flows with high Reynolds number, which are indeed the case for astrophysical accretion disks, transient growth can make the system nonlinear much faster than MRI and can be a plausible primary source of turbulence, using the shearing mode perturbations. Therefore, this thesis provides a plausible resolution of hydrodynamic turbulence observed in astrophysical accretion disks and some laboratory shear flows, such as, Rayleigh-stable Taylor-Couette flows and plane Couette flows. Moreover, this thesis also provides a clear understanding of MHD turbulence for astrophysical accretion disks.