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The work contained within this thesis is concerned with a theoretical investigatiop of both laminar and thermally driven types of cavity flow, together with an analysis of their associated mixing processes which find applications to Industrial mixing and also to the environment. The mixing efficiency has been viewed from two perspectives namely the tracking of a selection of fluid particles, and also the simulation of the dispersive mixing of a coloured fluid element as carried along by the flow. This thesis also incorporates features of both Newtonian and a wide range of non-Newtonian fluids.

Les processus de fusion ont joué un rôle clé dans l'évolution de la Terre. Au cours des premiers stades de la formation de la Terre, de grandes quantités de chaleur ont été libérées par(i) l'énergie gravitationnelle lors de la ségrégation noyau-manteau, (ii) la désintégration radioactive et (iii) les collisions entre corps orbitant autour du Soleil (en incluant l'impact géant qui a formé la Lune). Tous ces évènements ont conduit à la fusion du manteau et à des épisodes d'océan magmatique. Ensuite, les processus complexes de cristallisation du manteau ont conduit à la ségrégation chimique entre les différents réservoirs terrestres. Ces phénomènes ont été contrôlés par les propriétés de fusion des matériaux qui constituent le manteau.La fusion partielle se produit encore aujourd'hui dans les différentes régions du manteau. Comme preuves, des zones de vitesses sismiques faibles (LVZ) ont été rapportées dans le manteau supérieur, pour des profondeurs allant de 80 jusqu'à 410 km, grâce à différentes études sismologiques et magnétotelluriques. La diminution de vitesse des ondes sismiques est compatible avec la fusion partielle du manteau. Toutefois, cette question reste la source de vifs débats. Les études expérimentales portant sur la fusion des matériaux du manteau montrent en effet que la température actuelle du manteau est insuffisante pour provoquer la fusion du manteau péridotitique (ou pyrolitique) dans le manteau supérieur. La fusion peut seulement se produire dans certaines conditions, à savoir (i) en présence d'une quantité importante d'éléments volatils, tels que l'eau ou le CO2, car ces éléments diminuent significativement la température de fusion, ou (ii) pour des changements importants de composition chimique, par exemple pour de la croûte océanique subduite dans le manteau.Dans une première partie de cette étude, nous avons effectué des expériences de fusion sur un verre homogène, de composition chondritique, comme analogue du manteau de la Terre primitive après la ségrégation du noyau. Nous avons effectué des études in situ de diffraction de rayons X et de spectroscopie d'impédance pour détecter les premiers stades de fusion. À l'aide d'une presse à multi-enclumes, nous avons reproduit des pressions jusqu'à 25 GPa en vue de déterminer la température de solidus du manteau supérieur primitif. Nos résultats suggèrent que les études précédentes qui utilisaient la méthode de la trempe ont surestimé le solidus d'environ 250 K. Les implications sont multiples. Tout d'abord, cela suggère que la fusion partielle pourrait avoir lieu plus facilement dans le manteau actuel qu'on ne le pensait initialement, en particulier lorsque des éléments volatils, tels que H, sont présents. Nous avons calculé l'effet de l'eau sur la température de solidus en fonction de la teneur en eau, en utilisant la relation cryoscopique. Nos résultats montrent que 500-600 ppm d'eau sont suffisantes pour abaisser la température de solidus jusqu'à la température actuelle du manteau. La présence d'eau dans le manteau pourrait donc expliquer les LVZ observées sismiquement.Une autre implication majeure concerne l'état du manteau supérieur au cours de l'Archéen. Des températures mantelliques 200 à 300 K plus élevées qu'aujourd'hui, comme le suggère la composition d'anciens basaltes et de komatiites, induiraient la fusion partielle à des profondeurs d’environ 200 à 400 km. Ainsi, une couche de matériau partiellement fondu pourrait avoir persisté pendant de longues périodes géologiques au milieu du manteau supérieur. Cette couche aurait entraîné le découplage dynamique entre les parties supérieure et inférieure du manteau, pour éventuellement inhiber la convection globale du manteau. Ensuite,avec le refroidissement séculaire, la disparition de cette zone partiellement fondue aurait pu induire, il y a environ 2.5 milliards d'années, une convection globale et la tectonique des plaques telle que nous l'observons aujourd'hui. (...) / Melting processes play a key role in the Earth’s evolution. In the early stages of theEarth's formation, large amounts of heat were released from (i) gravitational energy from coremantlesegregation, (ii) radiogenic decay and (iii) collisions with large-scale impactors (suchas the Moon-forming impact). This led to extensive mantle melting with eventual formation ofa magma ocean. Then, chemical segregation between the different terrestrial reservoirs resultedfrom the complex processes of mantle crystallization. These mechanisms were primarilycontrolled by thermal evolution of partially molten mantle. Partial melting however may stilloccurs today in different mantle regions. Evidences of low velocities zones (LVZ) in the uppermantle have been reported by different seismological and magneto-telluric studies, at a depthranging from 80 km down to the 410 km seismic discontinuity. The reduction in seismic wavevelocities reported is also consistent with the occurrence of partial melting. However, thismatter remains the source of a vivid debate.The experimental studies addressing melting of mantle materials show that the presentdaytemperature is not sufficient to induce melting of the bulk peridotitic or pyrolitic mantle,at all depths throughout upper mantle, transition zone and lower mantle. Melting can still arisein certain conditions, i.e. (i) in presence of significant amounts of volatile elements, such aswater or CO2, because it can decrease the melting temperature of silicate rocks by hundreds ofdegrees or (ii) for significant compositional changes, e.g. when the oceanic crust is subductedin the mantle.In this study, we performed melting experiment on a homogeneous glass withchondritic composition, a proxy for the primitive Earth’s mantle after core segregation. Weperformed in situ synchrotron X-ray diffraction and in situ impedance spectroscopymeasurements to detect the onset of melting during the experiments in a multi anvil apparatus,at pressures up to 25 GPa, in order to determine the solidus temperature of the primitive uppermantle. Our results show that previous studies overestimated the solidus by approximately 250K. The implication for a lower solidus are manifold. Firstly, partial melting could take place inthe mantle today at lower temperatures than previously believed, especially when volatileelements such as H are present. The variation of the solidus temperature as a function of watercontent was therefore calculated using the cryoscopic relation reported in previous studies. Ourresults show that 500-600 ppm of water are required to depress the solidus temperature enoughto cross the mantle geotherm at depths in which LVL are observed, which is compatible withthe reported maximum water storage capability of the upper mantle.Another major implication concerns the early state of the upper mantle. Mantletemperatures 200-300 K higher than today, as suggested from the composition of ancient nonarcbasalts and komatiites, would induce partial melting at depths from ~200 to ~400 km. Thus,a shell of partially molten material could have persisted in the upper mantle for long geologicaltimes. Such weak layer could have decoupled the convection in upper and lower part of themantle, possibly disabling the establishment of modern tectonic during the Archean. Then,upon secular mantle cooling, the final mantle crystallization at mid upper-mantle depths wouldhave drastically modified the mantle dynamics, inducing global mantle convection.In this work, the melting properties of the basaltic crust subducted in the lower mantleis also presented. Subduction of the oceanic lithosphere is thought to be a major responsiblefor mantle heterogeneities. At shallow depths, slabs undergo dehydration, which induces partialmelting of the mantle wedge and arc magmatism. (...)

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abstract: The mineralogy of the deep mantle is one of the key factors for the chemical evolution of the Earth. The constituent minerals of the mantle rock control the physical properties of the mantle, which have significant impacts on the large-scale processes occurring in the Earth's interior. In my PhD research, I adopted experimental approaches to investigate the mineralogy and the physical properties of the Earth's materials in the deep mantle by using the diamond anvil cells (DACs) combined with in-situ X-ray diffraction techniques. First, I found that Ca-bearing bridgmanite can be stable in the deeper part of the Earth's lower mantle where temperature is sufficiently high. The dissolution of calcium into bridgmanite can change the physical properties of the mantle, such as compressibility and viscosity. This study suggests a new mineralogical model for the lower mantle, which is composed of the two layers depending on whether calcium dissolves in bridgmanite or forms CaSiO3 perovskite as a separate phase. Second, I investigated the mineralogy and density of the subducting materials in the Archean at the P-T conditions near 670 km-depth. The experiments suggest that the major phases of Archean volcanic crust is majoritic garnet and ringwoodite in the P-T conditions of the deep transition zone, which become bridgmanite with increasing pressure. The density model showed that Archean volcanic crust would have been denser than the surrounding mantle, promoting sinking into the lower mantle regardless of the style of the transportation in the Archean. Lastly, I further investigated the mineralogies and densities of the ancient volcanic crusts for the Archean and Proterozoic at the P-T conditions of the lower mantle. The experiments suggest that the mineralogy of the ancient volcanic crusts is composed mostly of bridgmanite, which is systemically denser than the surrounding lower mantle. This implies that the ancient volcanic crusts would have accumulated at the base of the mantle because of their large density and thickness. Therefore, the distinctive chemistry of the ancient volcanic crusts from the surrounding mantle would have given a rise to the chemical heterogeneities in the region for billions of years. / Dissertation/Thesis / Doctoral Dissertation Geological Sciences 2020

Aim of this work is a systematic investigation of the modes of thermal convection (onset of convection, stationary solutions, periodic solutions, chaotic states) in a material whose properties vary with depth like the material of Earth mantle; the problem was solved in Cartesian geometry. The Stokes equation set was consistently formulated in the spectral region not only horizontally but also vertically, and thus in the model consisting of layers with a constant viscosity but with general course of velocity and temperature in each layer. This equation set was solved with matrix method for each wave vector. Thermal equation was solved in the spatial domain and the transition of velocity and temperature between spectral and spatial domains was performed using the fast Fourier transform. This procedure allows a straightforward parallelization, thereby opening the possibility of not only two-dimensional but also three-dimensional modeling and modeling of chaotic regimes. On the basis of the numerical difficulties of method presented here an model investigated in finite elemens was used. The basic modes of thermal convection were then investigated using model assembled in the software Comsol. Powered by TCPDF (www.tcpdf.org)

Title: Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics Author: Hana Šustková Department: Department of Geophysics Supervisor: doc. RNDr. Ctirad Matyska, DrSc. Abstract: This thesis concerns the study of convection in Cartesian models in two and three dimensions. Specifically, it deals with the systematic monitoring of critical Rayleigh numbers based on the geometry model, on the functional dependence of the viscosity or of other parameters. Models has been created with layered viscosity and constant or temperature- and depth- dependent parameters (thermal expansion and conductivity). The system has been described by conventional dimensionless Boussinesq approximation. Part of the work is devoted to the application of matrix method for solving the appropriate Stokes flow and use of Euler's method for solving the thermal equation. The actual calculations were then performed in an environment of commercial software Comsol and thus by using the finite element method. It was shown that the dominant influence on the critical Rayleigh numbers has a viscosity model (with increasing viscosity the critical Rayleigh numbers increase), other important parameter is system's geometry (larger size and dimension of the geometry reduce the critical Rayleigh number). The...