River dynamic behaviour is affected by variations both in the water phase and in the transported sediment phase. A change in the water regime may lead to significant morphological changes in the bed profile, which in turn may strongly influence the flow conditions. Transcritical flows over mobile beds are particularly challenging to model due to the rapid variation in space and time of the solid transport, and to the specific treatment required for boundary conditions. The one-dimensional numerical model presented in this dissertation divides the flow in two fully coupled layers: a water layer and a water-sediment transport layer. This model was initially designed to depict dam-break flows, which does not require a specific treatment of boundary conditions. An extension of the two-layer approach is proposed in order to properly take into account boundary conditions. The treatment of boundary conditions commonly relies on characteristics. Within a two-layer model, which embodies five governing equations, an appropriate eigenstructure analysis is developed based on numerical estimations. This novel approach results in a new characterization of the critical stage by defining a specific two-layer Froude number. The model is compared to the classical Saint-Venant – Exner approach and favourably applied to several typical situations: uniform flow, which allows a straightforward calibration of the model parameters; regressive erosion around a mild-to-steep slope transition; evolution of a mobile bed under a hydraulic jump; and scour hole formation downstream of a fixed bed.

Yes / A potential flow model of the semi-inverse type is proposed to simulate flow over round crested weirs. This technique involves the construction of only streamlines over the weir instead of constructing the entire flow net. A Serre–Green–Naghdi (SGN) equation is employed to determine the initial free-surface profile, which is solved using a combined finite volume-finite difference scheme. The potential flow equations were numerically solved using a five-point central finite difference scheme. The model was applied to define the pressure and velocity fields in channel controls involving transcritical flow, such as the Gaussian weir, parabolic weir, and semicircular weir. The impact of streamline curvature on pressure and velocity distributions was investigated in the study. The curvature of the streamline strongly influenced the rise and drop of the bed pressures along the test section. A semicircular weir experiment was also conducted to validate the pressure and velocity profiles obtained using the proposed 2-D fluid flow model. The computed pressure and flow profiles from the solution of the potential flow equation agree perfectly with the present experiment and similar experiments available in the literature. In conclusion, the SGN equation provides an excellent initial profile to solve a 2-D ideal fluid flow numerically.

A compreensão, monitoramento e simulação da dinâmica da rede de drenagem de um centro urbano, inclusive os rios, podem auxiliar a análise de risco e o desenvolvimento e correção de projetos de rede de drenagem urbana. Entretanto, a simulação de rios urbanos é um grande desafio, devido a rápida variação das condições de escoamento (nível d\'água e velocidade) durante a passagem de onda de cheia, trazendo dificuldades tanto no monitoramento como na modelagem. Por se tratar de escoamentos não permanentes com significativo efeito de histerese da relação nível-vazão, torna-se necessária a utilização de modelos hidrodinâmicos. Além disso, a possível ocorrência de escoamento transcrítico aumenta a complexidade de representação do problema. Neste trabalho, um modelo hidrodinâmico capaz de resolver escoamentos transcríticos foi desenvolvido com o objetivo de simular eventos de passagem de onda de cheia em rios urbanos. O modelo, implementado na linguagem Fortran, foi baseado nas equações unidimensionais completas de Saint-Venant e utiliza o esquema de resolução de Preissmann adaptado por um redutor dos termos de inércia. Isso permitiu a resolução de escoamentos transcríticos, conforme comprovado em problemas teóricos padrões. Na aplicação prática do modelo, eventos de onda de cheia foram monitorados em um trecho do canal do córrego do Gregório na cidade de São Carlos, São Paulo, e simulações foram realizadas considerando apenas dados de níveis. Os resultados obtidos foram satisfatórios (Eficiência de Nash-Sutcliffe acima de 0,7) e permitiram a utilização das vazões estimadas para a proposição de uma curva-chave para o córrego. A metodologia aplicada neste trabalho se mostrou promissora para a definição de curva-chave de rios urbanos que apresentam dificuldades de medição de vazão. / The recognition, monitoring and simulation of the drainage system\'s dynamics of an urban center, including rivers, can assist in the risk assessment and the development and correction of urban drainage network projects. However, the simulation of urban rivers is a great challenge, due to the rapid variation of the flow conditions (water level and velocity) during the passing of flood waves, and poses difficulties for their monitoring and modeling. The use of a hydrodynamic model becomes necessary, as the flow is unsteady and produces a hysteresis effect of stage-discharge relation. Furthermore, the possible occurrence of transcritical flow increases the complexity of the problem representation even more. This manuscript addresses the development of a hydrodynamic model that solves transcritical flows and simulates flood wave events in urban rivers. The model, implemented in the Fortran programming language, was based on the one-dimensional complete equations of Saint Venant and uses the Preissmann scheme of resolution adapted by a reduction factor of the inertial terms. Such features enabled the resolution of transcritical flows, as evidenced in standard theoretical problems. In a practical application of the model, flood wave events were monitored in the Gregório creek in São Carlos, São Paulo, and simulations were performed only with level data. The results were satisfactory (Nash-Sutcliffe efficiency above 0.7) and enabled the use of the flows estimated for the proposal of a rating curve for the creek. The methodology applied has shown promising for the definition of a rating curve for urban rivers of difficult flow measurements.

A compreensão, monitoramento e simulação da dinâmica da rede de drenagem de um centro urbano, inclusive os rios, podem auxiliar a análise de risco e o desenvolvimento e correção de projetos de rede de drenagem urbana. Entretanto, a simulação de rios urbanos é um grande desafio, devido a rápida variação das condições de escoamento (nível d\'água e velocidade) durante a passagem de onda de cheia, trazendo dificuldades tanto no monitoramento como na modelagem. Por se tratar de escoamentos não permanentes com significativo efeito de histerese da relação nível-vazão, torna-se necessária a utilização de modelos hidrodinâmicos. Além disso, a possível ocorrência de escoamento transcrítico aumenta a complexidade de representação do problema. Neste trabalho, um modelo hidrodinâmico capaz de resolver escoamentos transcríticos foi desenvolvido com o objetivo de simular eventos de passagem de onda de cheia em rios urbanos. O modelo, implementado na linguagem Fortran, foi baseado nas equações unidimensionais completas de Saint-Venant e utiliza o esquema de resolução de Preissmann adaptado por um redutor dos termos de inércia. Isso permitiu a resolução de escoamentos transcríticos, conforme comprovado em problemas teóricos padrões. Na aplicação prática do modelo, eventos de onda de cheia foram monitorados em um trecho do canal do córrego do Gregório na cidade de São Carlos, São Paulo, e simulações foram realizadas considerando apenas dados de níveis. Os resultados obtidos foram satisfatórios (Eficiência de Nash-Sutcliffe acima de 0,7) e permitiram a utilização das vazões estimadas para a proposição de uma curva-chave para o córrego. A metodologia aplicada neste trabalho se mostrou promissora para a definição de curva-chave de rios urbanos que apresentam dificuldades de medição de vazão. / The recognition, monitoring and simulation of the drainage system\'s dynamics of an urban center, including rivers, can assist in the risk assessment and the development and correction of urban drainage network projects. However, the simulation of urban rivers is a great challenge, due to the rapid variation of the flow conditions (water level and velocity) during the passing of flood waves, and poses difficulties for their monitoring and modeling. The use of a hydrodynamic model becomes necessary, as the flow is unsteady and produces a hysteresis effect of stage-discharge relation. Furthermore, the possible occurrence of transcritical flow increases the complexity of the problem representation even more. This manuscript addresses the development of a hydrodynamic model that solves transcritical flows and simulates flood wave events in urban rivers. The model, implemented in the Fortran programming language, was based on the one-dimensional complete equations of Saint Venant and uses the Preissmann scheme of resolution adapted by a reduction factor of the inertial terms. Such features enabled the resolution of transcritical flows, as evidenced in standard theoretical problems. In a practical application of the model, flood wave events were monitored in the Gregório creek in São Carlos, São Paulo, and simulations were performed only with level data. The results were satisfactory (Nash-Sutcliffe efficiency above 0.7) and enabled the use of the flows estimated for the proposal of a rating curve for the creek. The methodology applied has shown promising for the definition of a rating curve for urban rivers of difficult flow measurements.