Dans cette thèse, nous présentons un modèle granulaire décrivant la dynamique d'un assemblage de floes rigides de tailles et de formes diverses, soumis aux forces de traînée dues aux courants atmosphérique et océanique. Ce modèle est basé sur les équations des moments linéaire et angulaire pour décrire la dynamique régulière des floes et sur la résolution de problèmes linéaires de complémentarité pour traiter les collisions entre les floes. Entre les collisions, le mouvement d'un floe isolé satisfait la conservation des équations des moments linéaire et angulaire écrites à partir des formulations classiques des traînées dues au vent et à l'océan. Nous décrivons les collisions entre les floes comme des événements instantanés et les traitons avant qu'elles n'entraînent une interpénétration. Cela implique la notion d'impulsion de contact et la mise sous la forme de problèmes linéaires de complémentarité basés sur la condition de Signorini pour la non interpénétration et la loi de Coulomb. La nature du contact est représentée à travers un coefficient de friction et un coefficient de restitution décrivant la perte d'énergie cinétique durant la collision. Dans cette présente version du modèle, le coefficient de restitution est fixé. Le modèle a été validé en utilisant des données obtenues du mouvement de disques de bois évoluant en bassin de test aussi bien qu'en comparant le comportement des floes simulés avec un comportement attendu dans des scénarios classiques de dérive de glace et de collisions entre des solides rigides. Les résultats de simulations comprenant différents assemblages contenant des floes de tailles et de formes variées, soumis à différents scénarios de forçage, sont aussi discutés. Ils montrent tout le potentiel de notre approche sans qu'une analyse détaillée et complète n'ait encore été proposée. / In this thesis, we present a model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag. The granular model presented is based on simplified momentum equations for ice floe motion between collisions and on the resolution of linear complementarity problems to deal with ice floe collisions. Between collisions, the motion of an individual ice floe satisfies the linear and angular momentum conservation equations, with classical formula applied to account for atmospheric and oceanic skin drag. To deal with collisions, before they lead to interpenetration, we included a linear complementarity problem based on the Signorini condition and Coulombs law. The nature of the contact is described through a constant coefficient of friction, as well as a coefficient of restitution describing the loss of kinetic energy during the collision. In the present version of our model, this coefficient is fixed. The model was validated using data obtained from the motion of interacting artificial wood floes in a test basin. The results of simulations comprising few hundreds of ice floes of various shapes and sizes, exposed to different forcing scenarios, and under different configurations, are also discussed. They show that the progressive clustering of ice floes as the result of kinetic energy dissipation during collisions is well captured, and suggest a collisional regimes of floe dispersion at small scales, different from a large-scale regime essentially driven by wind forcing.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:48:38Z No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:49:04Z (GMT) No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-11-16T09:49:04Z (GMT). No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-09-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In a society dependent on electric energy for the execution of various daily activities, it is normal that its use is increasingly increasing over time. In order to carry out the transportation of all electric energy, it is essential to use transmission lines, which with increasing energy demand inevitably have tended to multiply throughout the world, and especially in Brazil, given its continental dimensions. Considering the function of the transmission lines for the electrical system, its importance in the context of the electric power supply is remarkable. However, the lines constitute one of the great emitting sources of electric and magnetic fields of low frequency, which has caused concern and has been motivating fact of several studies, like the realized in this work. Therefore, in view of the scenario presented in the previous paragraph, it is necessary to establish ways of calculating the fields more and more precisely. For the calculation of the electric field is used the Image Method, the Maxwell Potential Coefficients Method and the Coulomb Law, and for the magnetic field the Biot-Savart's Law is used. The results obtained for the electric and magnetic fields were for infinite rectilinear geometries, finite rectilinear and for the conductors taking the form of a catenary, the latter geometry being the most real model for the arrangement of the conductors in a line. In all cases treated, an analytical and numerical approach was performed, in order to allow the calculation of the three geometries with accuracy. Taking advantage of the methodology of calculation of the fields, in addition this work proposes a method of support to the monitoring of transmission lines. The method consists of using the Genetic Algorithm associated to the values of the electric and magnetic fields measured to determine the parameters of the line, such as: phase spacing, cable-soil height, equivalent conductor diameter, current and operating voltage. Given the simplicity of implementation when compared to other methods, the achievement of satisfactory results and the need for a single measuring device to monitor the transmission line, the proposed method proves to be viable and promising to carry out the line monitoring process. / Em uma sociedade dependente da energia elétrica para a execução de diversas atividades do cotidiano, é normal que a sua utilização seja cada vez mais crescente no decorrer do tempo. Para realizar o transporte de toda energia elétrica é imprescindível o uso de linhas de transmissão, que com o aumento da demanda de energia inevitavelmente tenderam a se multiplicar pelo mundo e em especial pelo território brasileiro, dadas as suas dimensões continentais. Tendo em vista a função das linhas de transmissão para o sistema elétrico, é notável a sua importância no contexto do fornecimento de energia elétrica. No entanto, as linhas constituem uma das grandes fontes emissoras de campos elétricos e magnéticos de baixa frequência, o que tem causado preocupação e tem sido fato motivador de diversos estudos, como o realizado neste trabalho. Portanto, diante do cenário apresentado no parágrafo anterior, se faz necessário estabelecer formas de calcular os campos de maneira cada vez mais precisa. Para o cálculo do campo elétrico utiliza-se o Método das Imagens, o Método dos Coeficientes de Potencial de Maxwell e a Lei de Coulomb, já para o campo magnético a Lei de Biot-Savart é empregada. Os resultados obtidos para os campos elétricos e magnéticos foram para as geometrias retilíneas infinitas, retilíneas finitas e para os condutores assumindo a forma de uma catenária, sendo que essa última geometria constitui o modelo mais real quanto à disposição dos condutores em uma linha. Em todos os casos tratados foram realizadas uma abordagem analítica e numérica, de maneira a possibilitar o cálculo das três geometrias com exatidão. Aproveitando-se da metodologia de cálculo dos campos, adicionalmente este trabalho propõe um método de apoio ao monitoramento de linhas de transmissão. O método consiste em utilizar o Algoritmo Genético associado aos valores dos campos elétrico e magnético medidos para determinar os parâmetros da linha, como: espaçamento entre fases, altura cabo-solo, diâmetro equivalente dos condutores, corrente e tensão de operação. Dada a simplicidade de implementação quando comparado a outros métodos, a obtenção de resultados satisfatórios e a necessidade de um único aparelho de medição para monitorar a linha de transmissão, o método proposto mostra-se viável e promissor para realizar o processo de monitoramento de linhas.