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Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, September 2008. / Thesis Advisor(s): Kwon, Young W. "September 2008." Description based on title screen as viewed on November 3, 2008. Includes bibliographical references (p. 51-52 ). Also available in print.

Thesis (M.Eng.) -- Memorial University of Newfoundland. / Typescript. Bibliography: leaves 73-76. Also available online.

The determination of the mechanisms setting the strength and structure of the large scale circulation is a fundamental and long-standing problem in physical oceanography. In this thesis, we seek to explore the mechanisms contributing to the steady state and variability of the large scale flow, with a focus on better understanding the dynamics of the Atlantic meridional overturning circulation (AMOC). In the first part of this thesis, we explore the linear sensitivity of the monthly mean subtropical AMOC to surface fluxes of buoyancy and momentum. Our approach is to use a numerical adjoint. Key insights are provided into the memory of the AMOC to historic atmospheric forcing. We find that significant memory to wind forcing is confined to timescales of less than a year. In contrast, we identify significant memory to surface buoyancy forcing spanning multi-decadal timescales and characterised by a large scale oscillation in the sign of sensitivity between the eastern and western North Atlantic basin. An important result is that to understand the origins of seasonal variability in the modelled AMOC, we must examine the response to a multidecadal history of atmospheric forcing. In the second part of this thesis, a new tool is presented that enables a clean diagnosis of the force balance controlling the circulation regime for a Boussinesq fluid. Specifically, the tool is based on the development of the "rotational momentum" equations and sets of scalar "velocity potentials" and analogous "force functions". The latter allow the projection of all forces onto the acceleration of the vertical shears and external modes of overturning to be visualised in isolation. The rotational momentum decomposition is applied to the modelled circulation in idealised Atlantic and global configurations of the MITgcm, with a focus on elucidating the dynamics of the simulated AMOC. We discuss the key role played by the rotational buoyancy forcing right on the western boundary.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-07-21T17:04:37Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE ASPSP.pdf: 2001369 bytes, checksum: f6de58de3e0c281db510010c6c904ea9 (MD5) / Made available in DSpace on 2016-07-21T17:04:37Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE ASPSP.pdf: 2001369 bytes, checksum: f6de58de3e0c281db510010c6c904ea9 (MD5) Previous issue date: 2015-11-27 / capes / A área no entorno do arquipélago de São Pedro e São Paulo (ASPSP) (0°55 '10"N e 29º20'33" W) foi investigada, com o objetivo de caracterizar a estrutura da comunidade fitoplanctônica, seus padrões de distribuição horizontal e vertical, especialmente na termoclina que coincide com a profundidade máxima de clorofila (PMC) e identificar os valores de biomassa em carbono orgânico através do biovolume celular. Duas expedições foram realizadas a bordo do navio Hidro-Oceanográfico Cruzeiro do Sul, entre os dias 21 a 23 de julho de 2010 e 29 de setembro a 01 de outubro de 2011, ambas na estação seca da região. Foram estabelecidos dois transectos perpendiculares e opostos no entorno do arquipélago e determinados três pontos de coleta para cada um, em diversas profundidades: superfície, 25 metros, 50 metros, 10 metros acima da PMC, na PMC e 10 metros abaixo da PMC. Foram coletadas amostras no período diurno e noturno. Utilizou-se uma rede cilindro-cônica com malha de 20 μm de abertura para arrastos oblíquos e garrafas de Niskin para as coletas de amostras quali-quantitativas e físico-químicas. Duas massas de água foram identificadas (Água Tropical e Água Central do Atlântico Sul), uma termoclina ficou evidente entre 40 e 100 metros de profundidade. Um total de 128 espécies de organismos fitoplanctônicos foi identificado, pertencentes a quatro filos, sendo 22 espécies consideradas novos registros para a região. A densidade fitoplanctônica total variou de 1 a 183 x103 células.L-1. Trichodesmium thiebautii Gomont ex Gomont, Oxytoxum longiceps Schiller e Protoperidinium minimum (Pavillard) Schiller tiveram correlações significativas com os parâmetros físicos e químicos. A análise de agrupamento evidenciou a formação de cinco grupos em função da profundidade. Trichodesmium thiebautii foi à única considerada constante e dominante no entorno do arquipélago nas duas expedições. Os dados morfológicos encontrados neste estudo estão coerentes com as medidas encontradas por diversos autores na literatura citada. No filo cianobactérias, Trichodesmium hildebrandtii Gomont apresentou os maiores valores de biovolume celular e biomassa de carbono (1.603 μm3 e 254 pgC.μm-3, respectivamente). Em relação ao filo Dinophyta, Pyrocystis fusiformis Thomson apresentou os maiores valores de biovolume celular e biomassa em carbono (1.660,269 μm3 e 149.693 pgC.μm-3, respectivamente) e Prorocentrum balticum Loeblich apresentou os menores valores (1.145 μm3 e 161 pgC.μm-3, respectivamente). Para o filo Ochrophyta, Planktoniella sol (C.G.Wallich) Schutt, foi a única espécie analisada do grupo, com 63.107 μm3 de biovolume celular e 2.250 pgC.μm-3 de biomassa em carbono. Os dados de clorofila a e nutrientes foram considerados baixos em ambas as expedições, confirmando a oligotrofia da área. Estes dados indicam que ASPSP pode ser associado a um efeito ilha na circulação oceânica e que a distribuição horizontal e vertical dos dados hidrológicos, demonstra tratar-se de um ambiente estável em relação à temperatura, salinidade e oxigênio dissolvido. Em relação aos nutrientes, entretanto, ficou comprovado que estes interferem diretamente na composição das cianobactérias, mesmo com a dominância de T. thiebautii. / The area surrounding the São Pedro and São Paulo Archipelago (ASPSP) (0°55 '10"N and 29º20'33" W) was investigated to characterize the structure of the phytoplankton community and its patterns of horizontal and vertical distribution in the water column, especially in the thermocline that coincides with the maximum depth of chlorophyll (DCM). This area was also investigated to identify organic carbon biomass values according to cell biovolume. Samples were collected during two expeditions aboard the hydro-oceanographic ship Cruzeiro do Sul, between July 21 and 23, 2010 and between September 29 and October 1, 2011. This expedition occurred during the dry season. We established two opposite, perpendicular transects and selected three collection points in each transect at varying depths, as follows: surface, 25 meters, 50 meters, 10 meters above the DCM, DCM and 10 meters below the DCM. Samples were collected during the day and night. We used a cylindrical-conical net and Niskin bottles to collect the samples for qualitative, quantitative and physio-chemical analysis. Two water masses were identified (Tropical Water and Central Water of the South Atlantic), and a thermocline was detected between depths of 40 and 100 meters. A total of 128 species of phytoplankton organisms were identified, belonging to four phyla. Of these species, 22 were considered new records for the region. Total phytoplankton density ranged from 1 to 183 x103 cells. L-1. Trichodesmium thiebautii Gomont ex Gomont, Oxytoxum longiceps Schiller and Protoperidinium minimum (Pavillard) Schiller showed a significant correlation with the physical and chemical parameters. Cluster analysis revealed the formation of five groups by depths. Trichodesmium thiebautii was the only species considered constant and dominant in the area surrounding the archipelago for both expeditions. The morphological data found in this study are consistent with the measurements found by various authors in the cited literature. For the phylum cyanobacteria, Trichodesmium hildebrandtii Gomont presented the highest values of cell biovolume and biomass in carbon (1603 μm3 and 254 pgC.μm-3, respectively). In relation to the phylum Dinophyta, Pyrocystis fusiformis Thomson presented the highest values of cell biovolume and biomass in carbon (1.660,269 μm3 and 149,693 pgC.μm-3, respectively) and Prorocentrum balticum (Lohmann) Loeblich presented the lowest values (1145 μm3 and 161 pgC.μm-3, respectively). For the phylum Ochrophyta, Planktoniella sol (C.G.Wallich) Schütt was the only species of the group that was examined, with 63,107 μm3 of cell biovolume and 2250 pgC.μm-3 of biomass in carbon. The data of chlorophyll a and nutrients were considered low in both expeditions, which confirm the oligotrophy of the area. These data indicate that ASPSP can be associated to the island mass effect in the oceanic circulation. Moreover, the horizontal and vertical distribution of the hydrological data in the ASPS shows that this environment is stable in relation to temperature, salinity and dissolved oxygen. However, the results also show that the nutrients interfere directly in the composition of cyanobacteria, even with the dominance of T. thiebautii.

Ocean submesoscales are the subject of increasing focus in the oceanographic literature; with instrumentation now more capable of observing them in situ and numerical models now able to reach the resolution required to more fully capture them. Submesoscales are typified by horizontal spatial scales of O(1 − 10) km, vertical scales O(100) m and time-scales of O(1) day and are known to be associated with regions of high vertical velocity and vorticity. Occurring most commonly at density fronts at the ocean surface they can control mixed layer restratification and provide an important control on fluxes between the atmosphere and the deep ocean. This thesis sets out to better understand the fundamental physical processes underpinning submesoscale instabilities using a number of idealised process models. Linear stability analysis complemented by non-linear, high-resolution simulations will be used initially to explore the ways in which submesoscale instabilities in the mixed layer may compete and interact with one another. In particular, we will investigate the way in which symmetric and ageostrophic baroclinic instabilities interact when simultaneously present in a flow, with focus on the growth rates and energetic pathways of previously unexplored dynamic instabilities that arise in this paradigm; three-dimensional, mixed symmetric-baroclinic instabilities. Further, these non-linear simulations will allow us to investigate the transition to dissipative scales that can occur in the classical Eady model via a multitude of small-scale secondary instabilities that result from primary submesoscale instabilities. Finally, observational data, taken aboard the SMILES project cruise to the Southern Ocean, helps to motivate the consideration of a new dynamical paradigm; the Eady model with superimposed high amplitude barotropic jet. Non-linear simulations investigate the extent to which the addition of such a jet is capable of damping submesoscale growth. The causes of this damping are then investigated using linear analysis. With this approach eventually demonstrated as being unable to fully explain growth rate reductions, we introduce a new framework combining potential vorticity mixing by submesoscale instabilities with geostrophic adjustment, which relaxes the flow back to a geostrophic balanced state. This framework will help to explain, conceptually, how non-linear eddies control the linear stability of the flow.

Au cours des dernières années, la disponibilité toujours croissante de données de télédétection multi-source de l'océan a été un facteur clé pour améliorer notre compréhension des dynamiques de la surface de l'océan. A cet égard, il est essentiel de mettre au point des approches efficaces pour exploiter ces ensembles de données. En particulier, la décomposition des processus géophysiques en modes pertinents est une question clé pour les problèmes de caractérisation, de prédiction et de reconstruction. Inspirés par des progrès récents en séparation aveugle des sources, nous visons, dans la première partie de cette thèse, à étendre les modèles de séparation aveugle de sources sous contraintes de non-négativité au problème de la caractérisation et décomposition d'opérateurs ou fonctions de transfert entre variables d'intérêt. Nous développons des schémas computationnels efficaces reposant sur des fondations mathématiques solides. Nous illustrons la pertinence des modèles de décomposition proposés dans différentes applications impliquant l'analyse et la prédiction de dynamiques géophysiques. Par la suite, étant donné que la disponibilité toujours croissante d'ensembles de données multi-sources supporte l'exploration des approches pilotées par les données en tant qu'alternative aux formulations classiques basées sur des modèles, nous explorons des approches basées sur les données récemment introduits pour l'interpolation des champs géophysiques à partir d'observations satellitaires irrégulièrement échantillonnées. De plus, en vue de la future mission SWOT, la première mission satellitaire à produire des observations d'altimétrie par satellite complètement bidimensionnelles et à large fauchée, nous nous intéressons à évaluer dans quelle mesure les données SWOT permettraient une meilleure reconstruction des champs altimétriques. / In the last few decades, the ever-growing availability of multi-source ocean remote sensing data has been a key factor for improving our understanding of upper ocean dynamics. In this regard, developing efficient approaches to exploit these datasets is of major importance. Particularly, the decomposition of geophysical processes into relevant modes is a key issue for characterization, forecasting and reconstruction problems. Inspired by recent advances in blind source separation, we aim, in the first part of this thesis dissertation, at extending non-negative blind source separation models to the problem of the observation-based characterization and decomposition of linear operators or transfer functions between variables of interest. We develop mathematically sound and computationally efficient schemes. We illustrate the relevance of the proposed decomposition models in different applications involving the analysis and forecasting of geophysical dynamics. Subsequently, given that the ever-increasing availability of multi-source datasets supports the exploration of data-driven alternatives to classical model-driven formulations, we explore recently introduced data-driven models for the interpolation of geophysical fields from irregularly sampled satellite-derived observations. Importantly, with a view towards the future SWOT mission, the first satellite mission to produce complete two-dimensional wide-swath satellite altimetry observations, we focus on assessing the extent to which SWOT data may lead to an improved reconstruction of altimetry fields.

Variable resolution method helps to study the local scale phenomenon of interest within the context of global scale atmosphere/ocean dynamics. Global spectral methods based on spherical harmonics as basis functions are known to resolve a given function defined on the sphere, in an uniform manner. Though known for its mathematical elegance and higher order accuracy, global spectral methods are considered to be restrictive for developing mesh-refinement strategies. The only mesh refinement strategy available until now is due to the pioneering work of F. Schmidt. Schmidt transformation can study only one region with higher resolution. The study of tropical dynamics is an interesting theme due to the presence of teleconnections between various phenomena, especially Indian Monsoon and the El-Nino. The Inter-Tropical Convergence Zone (ITCZ)is a continental scale phenamenon. It is in the ITCZ, many monsoon systems and tropical cyclones do occur. To study such phenomena under variable resolution method, high resolution is required in the entire tropical belt. Hitherto such a kind of mesh refinement strategies were not available in global spectral models. In this work, a new variable resolution method is developed that can help to study the tropical sub-scale phenomena with high resolution, in global spectral models. A new conformal coordinate transformation named ’High resolution Tropical Belt Transformation(HTBT)’ is developed to generate high resolution in the entire tropical belt. Mathematical demonstrations are given to show the existence of additional conformal transformations available on the sphere, indicating additional degrees of freedom available to create variable resolution global spectral method. Variable resolution global spectral method with high resolution over tropics is created through HTBT. The restriction imposed by Schmidt’s framework that the map-ping factor of the transformation need to have a finite-decomposition in the spectral space of the transformed domain is relaxed, by introduction of a new framework. The new framework uses transformed spherical harmonics Bnm as basis for spectral computations. With the use of FFT algorithm and Gaussian quadrature, the efficiency of the traditional spectral method is retained with the variable resolution global spectral method. The newly defined basis functions Bnm are the eigenvalues of the transformed Laplacian operator . This property of Bnm provide an elegant direct solver for the transformed Helmholtz operator on the sphere. The transformed Helmholtz equations are solved accurately with the variable resolution method. Advection experiments conducted with variable resolution spectral transport scheme on the HTBT variable grid produces near-dispersion free advection on the tropical belt. Transport across homogeneous resolution regions produce very less dispersion errors. Transport of a feature over the poles result in severe grid representation errors. It is shown that an increase in resolution around the poles greatly reduces this error. Transport of a feature from a point close to poles but not over it, does not produce such representation errors. Fourth-order Runge-Kutta scheme improves the accuracy of the transport scheme. The second order Magazenkov time-scheme proves to be better accurate than the leap-frog scheme with Asselin filter. The non-divergent barotropic vorticity equation is tested with two exact solutions namely Rochas solution and Rossby-Haurwitz wave solutions. Each of the solution tests certain unique and contrasting characteristic of the system. The numerical behaviour of the solutions show non-linear interactions in them. The singularity at the poles, arising due to the unbounded nature of the latitudinal derivative of the map factor of HTBT, triggers Gibbs phenomena for certain functions. However the recent advances in spectral methods, especially spectral viscosity method and Boyd-Vandeven filtering strategy provide ways to control the Gibbs oscillation and recover higher accuracy; make the variable resolution global spectral method viable for accurate meteorological computations.

Depuis la fermeture du passage qui reliait la proto-Méditerranée à l’océan indien, il y a environ 14 Ma, celle-ci devient une mer semi fermée avec une seule connexion à l’océan mondial par Gibraltar. C’est dans ce contexte que se produisent des crises anoxiques régulières, les sapropèles. La forte concentration de matière organique caractérisant les dépôts de sapropèle, suggère une réduction drastique de la ventilation océanique profonde, ainsi qu'une activité biologique accrue permettant l’accumulation de la matière organique pendant plusieurs milliers d’années. Depuis leur découverte, il a été admis que l'amplification de la mousson africaine, associée aux changements d’insolation par la variation de la précession orbitale, permettait de déclencher les sapropèles. En effet de fortes précipitations sur le bassin versant du Nil, auraient permis au fleuve de déverser une importante quantité d'eau douce dans la Méditerranée orientale. Cette apport en eau douce, dans une mer très salée, aurait augmenté la stratification verticale, empêchant la convection et menant à une anoxie des eaux de fonds. Cependant, même si cette explication semble robuste, notamment par la corrélation entre la fréquence des sapropèles et celle de l'indice de précession, ces épisodes se produisent dans des contextes climatiques très différents, du Miocène à nos jours. Même en se limitant à ceux des derniers cycles glaciaires, ils laissent une empreinte sédimentaire variable que l'amplification du Nil seule ne peut expliquer. C'est particulièrement le cas du dernier sapropèle, le « S1 », le plus étudié, intervenu entre 10.5 et 7 ka BP, se produisant à la fin du dernier épisode glaciaire. De récents travaux, notamment de modélisation, ont montré que la chronologie des enregistrements entre la variation de la précession et l’amplification de la mousson Africaine, ne concordait pas avec celui du dépôt du S1. Ainsi d’autres facteurs, notamment la montée du niveau marin et les perturbations hydrologiques associées à la fonte non linéaire des calottes glaciaires, auraient favorisé la crise anoxique des eaux profondes du bassin Est méditerranéen. Dans cette thèse nous nous proposons, avec l’outil de la modélisation numérique, de revisiter le rôle de la contribution du Nil pendant le S1 mais aussi d’autres facteurs potentiellement plus déterminants. D’une part nous avons tiré avantage des récentes recherches effectuées sur l’εNd pendant la période du S1. Nous avons modélisé ce traceur (adapté à l’enregistrement des changements de la circulation océanique passé), dans un modèle couplé océan-atmosphère à haute résolution (1/8°) en Méditerranée, afin de représenter au mieux les changements de convection. D’autre part, afin d’inclure le plus de mécanismes contributeurs au S1, nous avons développé une plateforme de modélisation globale-régionale pour représenter le climat du bassin Méditerranéen, ainsi que sa circulation océanique pendant le début de l’Holocène, période du dépôt du S1. Enfin, grâce à cette plateforme, nous avons évalué la contribution de la fonte de la calotte glaciaire eurasiatique via la mer Noire, et son impact sur le bassin Méditerranéen oriental. Les résultats de cette thèse montrent premièrement comment la modélisation de l’εNd est un indicateur approprié des changements de circulation initiés par le Nil, et dont le signal simulé est corroboré par les données existantes. Notre plateforme de modèle a permis la simulation et l’identification, à un coût numérique moins important que le couplage océan-atmosphère, des changements hydrologiques majeurs du bassin Méditerranéen pendant le début de l’Holocène. Enfin, le sapropèle S1 est directement affecté par les perturbations hydrologiques associées à la fonte de la calotte eurasiatique préalablement à l’augmentation des moussons. Nous avons quantifié leur rôle respectif dans la déstabilisation de la ventilation profonde, et permis l’installation de conditions favorables au développement du sapropèle S1. / Sapropel events are anoxic crisis occurring quasi-periodically (21000 years) since the Mediterranean Sea became semi enclosed around 14 Ma ago, with only one connection to the global ocean through the Gibraltar strait. The high level of organic content found in sapropels suggests the shutdown of the deep ventilation, and an enhanced biological activity leading to the accumulation of organic material in sediments for thousands of years. Numerous studies highlighted the role of African monsoon enhancement, linked to precession variation, as the trigger of sapropels. The increased precipitation over the Nile catchment provided a huge amount of freshwater through the Nile River into the salty Eastern Mediterranean, leading to a strong stratification of the water column, the reduction of intermediate and deep convection and ultimately to the development of anoxic environment. This hypothesis was robust enough to explain the sapropels due to the correlation between their frequency and precession variation. However, the diversity of these events in strength, duration and cyclicality cannot be entirely explained with this sole hypothesis. This is the case, for instance, of the last sapropel event, “S1”, which occurred between 10.5 and 7 ka BP, at the end of the last glacial episode. Recent works depicted the non-synchronous timing of the precession, monsoon enhancement and S1 deposition, and invoked other factors, such as sea level rise and climate variation to drive the establishment of anoxic environment in Mediterranean Sea. In this thesis, we investigate, with the help of climate modeling, the contribution of the Nile River during S1 but also other factors potentially more important. First, we took advantage of recent εNd data investigation during S1 to include this tracer, which is appropriate to assess the paleo-oceanic circulation, in a coupled ocean-atmosphere model at 1/8° to represent properly the changes in convection. In a second part, to account for other hydrological changes linked with the Early Holocene climate, we developed a global-regional model architecture to represent the Mediterranean region climate and its oceanic circulation. Finally, we use this model to evaluate the deglaciation of the Eurasian ice-sheet through the Black Sea toward the Eastern Mediterranean Sea. The main results show the capability of simulated εNd to capture the convection changes in response to high freshwater input, validated by data. Our model architecture allows the simulation of the Mediterranean Early Holocene climate and associated hydrological changes with a numerical cost lower than the coupled configuration. Finally, the continental deglaciation would be complementary to the sea level rise to destabilize the deep ventilation and lead to favorable condition to the development of S1. In summary, we developed three different approaches and dedicated tools to investigate the hydrological perturbations occurring prior to Early Holocene over the Mediterranean basin, which drastically modified the ocean dynamics to favor anoxia crisis.

Dans les premiers instants de l'histoire des planètes telluriques, la chaleur d'accrétion, le chauffage radioactif et la différenciation noyau-manteau apparaissent comme des sources d'énergie capables de fondre le manteau terrestre significativement. L'évolution d'un océan de magma suite à ces évènements catastrophiques dépend des propriétés physiques des matériaux silicatés en conditions mantelliques et de la dynamique convective complexe d'un manteau en cristallisation. Actuellement, certains auteurs proposent que la structure actuelle du manteau profond pourrait être associée à des reliques de la cristallisation d'un océan de magma primitif. Nous avons développé un modèle thermodynamique capable de modéliser de façon auto cohérente des séquences de cristallisation dans les conditions du manteau profond. A partir de ce modèle, nous avons montré que le magma s'enrichit progressivement en fer au cours de la cristallisation. Le liquide résiduel devient ainsi plus dense que la phase solide. Ce modèle thermodynamique suggère un scénario de cristallisation de l'océan de magma similaire à celui proposé par (Labrosse et al., 2007). Celui-ci prédit que la structure actuelle de la base du manteau hériterait de la cristallisation d'un océan de magma primitif. Afin d'étudier l'influence de ce contraste de densité et des profils de liquidus sur la dynamique syn- cristallisation d'un océan de magma, nous avons développé un code de convection multiphasique intégrant changement phase, percolation / compaction et cristallisation fractionnée. Dans ce mémoire, nous présentons des modèles dynamiques préliminaires de cristallisation dans le cas univariant / Early in the history of terrestrial planet, heat of accreation, radioactive deacay and core-mantle segratation may have melted the silicate mantle significantly. Magma ocean evolution depends on both physical properties of materials at relevant P-T conditions and the complex dynamics of a convecting cristallizing mantle. Present deep Earth mantle structures might be direclty linked to the crystallization of a potential magma ocean. We propose a complete thermodynamic model of the solid-liquid equilibrium in the MgO-FeO-SiO2 system which allows to compute self-consistenltly crystallization sequence at deep mantle conditions. The present study shows that, at thermodynamic equilibrium, the first solids that crystallize in the deep mantle are lighter than the liquid as they are more Mg-rich. This further enriches the melt in iron and this residual melt becomes much denser than the solid phase. Both the anti-freeze effect of iron and its high density suggest a mantle crystallization scenario similar to that described in Labrosse et al. (2007) where the ULVZ are iron rich and very fusible remnants of a primordial basal magma ocean. In addition, we have developped a multiphase convection code accounting for solid-liquid phase change, compaction and fractionnal cristallization. This mechanical model is dedicated to the investigation of the effects of various temperature profile and solid liquid density cross-overs on the dynamics of a cristallizing mantle. In this thesis, we show preliminary models illustrating the effect of chemical density contrasts between melt and solid in the case of univariant crystallization