Publicações

A first characterization of greenhouse gases had been carried out to study their role and impact in a productive transitional coastal system of the southern Portugal

Near estuaries and harbours, submerged shoals and defence structures impact the exposure to overtopping. These features may be accounted for in two-dimensional horizontal (2DH) numerical models, either based on phase resolving or phase-average solvers for wave propagation. In between, surfbeat solvers, such as in XBeach, combine an affordable computational cost with the ability to generate and propagate the longer infragravity (IG) waves. However, surfzone wave characteristics and the overtopping exposure modelled with XBeach are sensi tive to settings such as the shape of the forcing wave spectra and the numerical scheme for wave propagation. The present paper explores this sensitivity and assesses the performance of different inundation models built with the 2DH surfbeat solver of XBeach. These models were forced with downscaled water levels and directional wave spectra and the results fuelled a discussion bounded by data collected downdrift of the entrance to the harbour of Figueira da Foz (Portugal). The original second-order upwind scheme, which propagates short-waves with a lower numerical diffusion improved the model performance in terms of long-wave height, and an unconventional breaking criterion better represented the cross-shore distribution of short-wave height near the shore. A cali brated model was validated through the hindcast of an overtopping event observed under moderate swell forcing, and was used to map the overtopping exposure during a hypothetical combination of an energetic swell with a water level having a return period of ~70 years. Compared to the default wave spectra shape and model settings, using an appropriate representation of the short-wave directional spectrum at the open boundary was necessary to reproduce the observed overtopping extent. Refining the cross-shore resolution of the model helped to better represent the observed inundation extents, as also did the reduction of the friction coefficient. Addi tional phase-resolving simulations in 1DH overestimated IG wave energy and produced higher and more frequent overtopping discharges. The differences with the calibrated 2DH surfbeat model increased with the proximity of the inlet and with short-wave height and angle of incidence. Overall, required calibration steps were provided. They aim at making 2DH XBeach surfbeat a credible tool for 1) predicting short and IG wave characteristics up to the shoreline, as well as for 2) providing first estimates of exposure to overtopping in areas with shallow and alongshore-irregular morphologies.

The efects of climate change on the estuarine environment are not fully understood. In temperate regions, droughts are expected to increase in frequency and severity, due to lower precipitation, and the mean sea level is expected to rise. This study aimed to assess how the estuarine environment will be afected by river fow

Mainland Portugal presents an extensive, diversified and complex coastal zone. This diversity gives rise to diverse geomorphologic features which support different densities of human occupancy and a range of land uses and activities. In this sense, the coastal zone becomes an area of great national strategic value, but has also into a multi-hazard zone. To understand this complexity, two statistical techniques, namely Cluster Analysis and Principal Component Analysis, were used to identify and differentiate, between the different coastal typologies, based on a set of variables that express the territorial complexity and the occurrences and impacts of coastal flooding. The chosen methodology enabled a diverse set of coastal typologies to be identified, which contributes towards differentiating local specific characteristics. The holistic and differentiating nature of the applied methodology and the results obtained allows it to contribute to the definition of mitigation strategies and the implementation of adaptation measures. The results enable us to define a set of typologies associated with Coastal Disaster Risk Reduction and Management which are an important contribution to comprehensive coastal flood risk assessment and management.

Ministry of the Sea promoted an expert conference to discuss the currentstate of the Tagus river estuary and adjacent oceanic areas and to promotefuture action. The Tagus river estuary shapes the Lisbon MetropolitanArea, bordering 11 water-facing municipalities across 320 km2(among the largest in Europe and critically positioned along the North-South bird migration corridor of the East Atlantic [1]). It communicateswith the deep North Atlantic through the Tagus submarine prodelta andthe Lisbon/Cascais/Setúbal canyon system (Fig. 1). This proximity allowsinteraction of water masses and biological communities betweenthe estuary and the deep ocean and deserves scientific attention.The conference integrated perspectives on current threats, aftermillennia of human occupation and decades of local efforts to improveenvironmental status and contributed towards an action plan to maintainor improve ecosystem services for this densely populated area,following an ecosystem stewardship framework [2].

The characterization of estuarine hydrodynamics primarily depends on knowledge of the bathymetryand topography. Here, we present the first comprehensive, high-resolution dataset of the topography andbathymetry of the Amazon River estuary, the world

O aprofundamento dos canais de acesso por dragagem, associado ou não à construção de molhes e quebra-mares, tem sido uma característica da evolução dos portos nacionais nos últimos 100 anos. Nesta comunicação, analisa-se a evolução da cota de dragagem dos acessos marítimos aos portos do Continente com base em fontes documentais e levantamentos hidrográficos. No início do século XX verificava-se uma diferença apreciável entre as condições oferecidas pelos portos situados em estuários de maiores dimensões (Lisboa e Setúbal) e artificiais (Leixões), por um lado, e os portos situados em estuários e sistemas lagunares com menor prisma de maré, por outro. Entre 1920 e a atualidade, principalmente desde 1950, todos os portos comerciais em atividade (excetuando Sines) registaram um aumento da profundidade dos canais de acesso entre cerca de 5,5 m e 11,2 m. Considerando os portos no seu conjunto, estima-se que em média, entre 1950 e 2020, se tenha verificado um aumento da profundidade de dragagem na zona da barra de 1,0 m por década.

As inundações costeiras afetam anualmente milhões de pessoas em todo o mundo, com grandes perdas socioeconómicas que irão aumentar face à subida do nível médio do mar e ao aumento dos níveis extremos de água. A extensa linha de costa continental portuguesa, caracterizada por grande diversidade natural e de ocupação, apresenta elevada exposição a fenómenos de galgamento e inundação costeira. Estima-se que o impacto da tempestade Hércules, no início do ano 2014, tenha sido cerca de 16 milhões de euros (Santos et al., 2015). As consequências do impacto de níveis extremos na zona costeira dependem das características do território, pelo que a capacidade de obter e integrar esse conhecimento em ferramentas de previsão que suportem adequadamente as necessidades da gestão do risco deve ser uma prioridade. No âmbito do projeto Mosaic.pt (http://mosaic.lnec.pt) desenvolveram-se ferramentas de avaliação do risco de inundação costeira, integrando a dimensão territorial. A complexidade e a diversidade da costa continental recomendam uma abordagem holística na identificação e diferenciação das características territoriais, que dependem da escala espacial considerada. Assim, a abordagem metodológica do projeto seguiu duas escalas espaciais de análise: a costa continental portuguesa e três observatórios representativos do trecho costeiro Ovar - Marinha Grande, onde se concentra o maior número de ocorrências de inundação costeira (Tavares et al., 2021). Estes observatórios são o setor Barra

The continental coastal zone of Portugal is characterized by its morpho-sedimentary diversity. The high population density and range of land uses, occupation and activities make it an area of great national strategic value, and a multi-hazard zone. In this study, a multidimensional methodology to analyse, evaluate and interpret local vulnerability (Coastal Territorial Vulnerability Index - CTVI) has been developed and applied in three study areas.

Continental Portugal presents an extensive and diversified coastal zone. This diversity gives rise to the existence of different coastal typologies such as sand beaches, rocky, cliffed and artificialized coasts, which support distinct levels of human occupancy. To identify and distinguish the different coastal typologies, cluster analysis was used based on a set of variables, expressing the territorial complexity, as well as the occurrences and impacts resulting from coastal flooding.

As dragagens constituem uma atividade necessária à operação dos portos nacionais, que, todavia, pode ter impactos sobre a dinâmica sedimentar e a evolução costeiras. O presente trabalho reúne informação de base sobre dragagens e gestão dos dragados nos nove portos comerciais do Continente (Viana do Castelo, Leixões, Aveiro, Figueira da Foz, Lisboa, Setúbal, Sines, Portimão e Faro) ao longo de um período de três décadas (1991-2020). Sendo apenas um primeiro contributo para uma avaliação de tendências, a informação recolhida é preliminar e apresenta ainda lacunas significativas. Com esta condicionante, estima-se que na última década se tenha verificado uma diminuição do volume global de dragagem (4,5 x 106 m3 ano-1 em 1991- 2010, excluindo extrações em praias e áreas adjacentes; 3,2 x 106 m3 ano-1 em 2011-2020) e, principalmente, uma alteração do destino dos sedimentos dragados de natureza arenosa, com um forte crescimento da opção de colocação na faixa costeira, em praia emersa ou submarina (13% do volume global de dragagem em 1991-2010; 50% em 2011-2020).

An objective of the project MOSAIC.pt is to develop an operational forecasting system for coastal flooding capable of accounting for storm driven morphodynamics. The developed system relies on the OPENCoastS architecture for downscaling North-Atlantic metocean conditions at any local beach or waterfront (Oliveira et al., 2021). The downscaled conditions then serve to force local applications of XBeach (Roelvink et al., 2018), in 2DH and using its surfbeat hydrodynamic solver. Based on hydro- and geomorphological data collected within the project (Freire et al., 2020), an application was setup and validated for the waterfront of Cova-Gala, south of the entrance to the Figueira da Foz harbour. The system runs for now with or without morphological evolution over 48-hour periods. So it is important to quantify the errors induced by geomorphological changes over longer timescales.

The exposure to wave overtopping is growing worldwide which forces coastal communities toadopt methodologies for anticipating the risks associated with it. In areas with shallow foreshores,like those created by extended ebb-tidal deltas, at the entrance of estuaries or harbours forinstance, infragravity waves play an important, if not dominant, role. Therefore, hydrodynamic andtopographic data collected on the downdrift side of the entrance to Figueira da Foz harbour, alongthe wave exposed western coast of Portugal, were used to calibrate a local XBbeach 2DH-surfbeatmodel to (1) investigate the role of infragravity waves and (2) the ability of a phase average modelto account for the main drivers of coastal overtopping in similar locations. The local model wasforced on its open boundary by water levels and 2D wave spectra dynamically downscaled usingan operational model workflow developed for providing near real-time forecasts. The localdissipation of short-waves in the surf zone was calibrated based on the hydrodynamic data. Thisdata, collected under a moderate swell, was also used to ensure the model

Extending for more than 900 km with diverse geomorphologies and land-use occupations, the Portuguese coastal zone is highly vulnerable to overtopping and flooding. The project Mosaic.pt developed a flood risk framework to support management in coastal zones taking the territorial diversity into account. The framework delivers improved hazard prediction strategies and guidelines for spatial planning and increased coastal community resilience.

The morphological response of the S. João da Caparica beach, Almada, to the maritime stormHercules that occurred in January/2014, was studied through mathematical modelling, for three oftwelve topo-bathymetric configurations surveyed between 2008 and 2017: the two with the lowest andthe one with the highest volume of sediment in the topographic part. This study aimed to quantifyindicators of beach vulnerability, such as sand volume above three reference vertical levels, averageand maximum retreat of two reference isobaths and maximum topo-bathymetric lowering, in order toprovide guidance for future nourishment interventions. Hydrodynamic models at regional andintermediate scales were used to determine the forcing of the morphodynamic local model applied,XBeach. Besides the beach vulnerability indicators, the results revealed that the morphologicalconfiguration of the submerged zone plays an important role in the beach response when submitted toa storm with the characteristics of Hercules.

A baía de Nacala é um sistema costeiro semi-confinado que acolhe o principal porto do nortede Moçambique. As marés, as correntes, as ondas e o transporte de sedimentos no sistema foramestudados com recurso a modelos hidrodinâmicos e morfodinâmicos. Estima-se que as correntes demaré atinjam velocidades máximas de 0,5 m s-1 à entrada da baía e de 0,2 m s-1 no seu interior. Aondulação do largo quase não se propaga para o interior da baía, onde a agitação é essencialmente degeração local. Estima-se que o transporte de sedimentos arenosos seja significativo apenas para eventosextremos (ciclones tropicais) e circunscrito a uma faixa marginal (acima da batimétrica dos 10 m). Estesresultados parecem consistentes com a distribuição dos sedimentos superficiais da baía, areias e areiassiltosas nas zonas pouco profundas e materiais mais finos nas zonas de maior profundidade.

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The hydrodynamics and sediment dynamics of a low energy estuarine beach was analysed. The beach is subjected to local wind waves generated in an area of restricted fetch, wake waves generated by catamarans and a semi diurnal meso-tidal regime. Only storm events of short duration modify the beach profile, which, once the normal hydrodynamic conditions are restored, naturally recovers its initial shape. The beach is characterised by having a steep upper slope until mean sea level, followed, seaward, by a low gradient terrace, and a bimodal sediment distribution. To investigate the hydro sedimentologic beach behaviour, wind, topo-hydrographic and sedimentologic data were used as input and validation of process based numerical modelling. Wave generation and transformation in an area of restricted fetch, nearshore circulation, sediment transport and morphological evolution were simulated for average annual conditions and storm conditions. The statistical analysis of a six-year wind data series allowed to derive the average wind regime, based on which, the average annual wave regime and the average annual longshore sediment budget, 14.5x103 m3year-1, were calculated. The contribution of the individual components of the representative wave regime, discretised by directional sector and height class of incidence, was evaluated as well as the spatial distribution of the longshore sediment transport in the active part of the beach profile. The characteristics of the wave groups generated by the passage of catamarans at different speeds were estimated and their action on the beach morphology was simulated. Although when the catamarans travel at 20 knots speed the average annual wake wave energy dissipated at the beach is 2.5 times higher than the average annual wind wave energy, the erosion effect on the beach profile is still not relevant for the present traffic. In opposition, short duration storm events generate the formation of an erosion scarp at the upper part of the beach face. The numerical modelling of this phenomenon allowed to acknowledge on the protective effect that the low gradient terrace has on the beach face.

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A two-dimensional model of wind-driven circulation in a closed basin was developed using a finite-volume technique for generalized curvilinear grids and applying some of the recent developments in hydrodynamic modeling. The terms in the Navier¬Stokes equations were treated separately according to the fractional step method and the propagation step, including the continuity equation and the pressure and stress terms in the momentum equations, was solved using a conjugate gradient method.The model was then applied to a number of test cases to examine the feasibility of the approach used by comparing with results obtained with the two-dimensional version of the three-dimensional model CH3D. These included a square basin with constant slope and with a V-shaped bottom and Lake Okeechobee, in South Florida. To evaluate the long-term numerical stability of the model, a ten-day model simu¬lation with varying wind was also run for Lake Okeechobee.

An examination of the causes for generation and dynamics of turbidity maxima in estuaries reveals the critical role of sediment tidal pumping phenomenon and, to a lesser extent, of the well-known effect of residual gravitational circulation due to salt water penetration. Both phenomena depend on the vertical sediment concentration profile and, consequently, on the magnitude of the vertical mass transport fluxes. Where high concentration suspensions occur regularly, the erosion/deposition fluxes can be drastically modified by sediment stratification, consequently influencing sus¬pended sediment response to currents and wave action. This influence is inherent in flow-sediment hysteresis, which therefore reflects the role of vertical mass transport in the estuarine and coastal suspended fine sediment regime.A vertical transport numerical model was used to investigate the influence of several key parameters describing sediment settling, bed properties and stabilized diffusion on the concentration profile. The model was also applied to simulate the influence of the same parameters on the time-lagged sediment response to flow variations, reflected in the characteristics of flow-sediment hysteresis loops.Field data obtained in Hangzhou Bay (People´s Republic of China), a high concentration environment, showed typical features of flow-sediment hysteresis and confirmed the importance of the vertical mass fluxes in contributing to sediment transport in the bay. A qualitative simulation provided by the numerical model, using settling parameters corresponding to local sediment, while confirming the importance of the hysteresis phenomenon, also revealed the critical need to use algorithms describing adequately stabilized diffusion and bed fluxes.Additional evidence of hysteresis was obtained through analysis of microscale variables, such as the Reynolds stresses and the variances of the velocity components resulting from combined effects of wave action and turbulence. Spectral analysis of the measured random variations did not support the commonly accepted hypothesis of similarity between the responses to turbulent flow of sediment concentration and temperature. The normalized turbulent intensities for all the measured veloc¬ity components showed their highest values during the period of lowest sediment concentration; this result is consistent with the hypothesis of turbulent intensity damping by suspended sediment.

A contribution to increased use and development of the method of artificial nourishment of beaches is the main objective of this thesis. It also aims at being a guide for the design of the reconsctrution or outright creation of beaches.In the first chapter, the subject is introduced and the objectives of the thesis are outlined. The second chapter cover´s some general considerations on littoral dynamics, beach equilibrium and sediment budget.Since the theoretical foundations of the artificial nourishment of beaches still leave much to be desired, a description of this method and its principles are presented in the third chapter. Important technical and economic aspects are included, such as: sampling, analysis and characterization of native and borrow material; selection Of nourishment sources; extraction and transport of borrow sand; and characteristics of the theoretical final beach profile. Such problems as the integration of ecological aspects, and cost-benefit analysis are also treated.in the fourth chapter, the Portuguese experience in this domain is described. The experience of such countries as France and the U.S., where this method has frequently been used is also mentioned. In this way a considerable amount of hitherto scattered information is presented in a unified way.The fifth chapter, treats briefly the problem of coastal model similitude, both as a support for the experimental work: which was carried out and to help engineers in the design of a coastal physical model or in merely assessing the possibilities of such a model.In the sixth chapter, an experimental study is described of the influence of both the grain size of borrow material and the nourishment method on the redistribution of sediments after the nourishment. The obtained results are compared with existing theoretical methods and some prototype results.Finally, in the last chapter the main conclusions and recomendations of the thesis are presented.

We provide a systematic analysis of the consistency, stability, convergence and accuracy of the numerical solution of the transport equation by a general Eulerian-Lagrangian Method (ELM). The method involvesthree basic steps: the backwards tracking of characteristic lines following the flow, the interpolation of concentrations at the feet of these lines, and the solution of dispersion taking such concentrations as initial conditions. The first two steps constitute the Backwards Method of Characteristics (BMC); the third step involves a time-discretization along the characteristic lines, and a spatial discretization of the dispersion operator, both based on conventional techniques (e.g.. Euler or Crank¬Nicholson for time; finite-elements or finite-differences for space).The choice of the spatial interpolator is shown to impact the consistency, stability and convergence, as well as the accuracy of the BMC. Most interpolators ensure consistency, but only a few ensure stability, hence convergence; stability criteria are derived from a newly developed generalized Fourier analysis, which can account for non-linearities introduced by quadratic grids. The comparison of formally derived propagation and truncation errors, complemented by numerical experimentation, provides a reference for the choice of the interpolator, given a specific transport problem characterized by prevailing concentration gradients.The BMC potentiates the use of large time-steps, well above Courant number of order one. In the limiting case of pure advection, optimal accuracy would be obtained for a At close to the total time of interest; the presence of dispersion constrains, however, the size of At, especially in the case of non-uniform flows. The comparison of the truncation errors for the three basic steps of ELM provides a reference to select At. as a function of Ax, of the spatial interpolators and time-discretization schemes, and of the gradients of flow and concentrations.

Apresenta-se um estudo sistemático, baseado simultaneamente em análises formais e em experimentação numérica, da precisão e estabilidade da solução da equação de transporte por um método Euleriana-Lagrangeana (MEL). 0 método decompõe a equação de transporte em equações separadas de advecção e de difusão, resolvendo a primeira pelo método das características regressivas no tempo (MCR), e a segundo por um método de elementos finitos, do tipo Galerkin.Mostra-se que as interpolações no espaço requeridas pelo MCR são um factor limitativo da precisão global do MEL, e comparam-se diversas técnicas alternativas de interpolação, algumas das quais originais. A combinação de esquemas compactos e não-compactos de interpolação, baseados em polinómios de Lagrange, é apontada como uma potencial solução óptima.Demonstra-se que, para uma adequada escolha do esquema de interpolação, o MCR é consistente, estável e convergente e tem boas características de precisão. Escolhas inadequadas do esquema de interpolação podem, no entanto, causar instabilidade e inconsistência.Estabelece-se a dependência da precisão do MCR no passo de cálculo, mostrando-se que essa precisão aumenta, em geral (para um tempo total fixo), quando se reduz o número de passos de cálculo, isto é, quando se aumenta o passo de cálculo (uma propriedade simultaneamente pouco habitual e muito conveniente). No entanto, na gama de valores muito pequenos do Número de Courant, a precisão é praticamente independente do passo de cálculo, o que evita que o método se torne divergente.Analisa-se brevemente o efeito de malhas irregulares e pluridimensionais sobre a aplicabilidade e precisão do MCR. Apesar de sensível à irregularidade da malha, o método mantém boas características de precisão desde que as distorções geométricas não sejam excessivas. Malhas pluri-dimensionais, quando simultaneamente irregulares, levantam problemas específicos de aplicabilidade de esquemas não-compactos de interpolação; esses problemas poderão se resolvidos através da utilização conjugada de esquemas compactos e não-compactos, para um mesmo problema. Investigação adicional a ainda requerida nestas áreas.Mostra-se ainda que a presença de mecanismos físicos de difusão beneficia tanta a precisão da solução da equação de advecção como a precisão global do MEL.Finalmente, demonstra-se a eficácia da aplicação do MEL (numa forma particular, restricta a esquemas de interpolação compactos) à simulação do transporte de poluentes em águas costeiras. 0 método permite, em particular, realizar simulações longas (várias marés) a custos moderados, mesma para malhas irregulares com elevado número de nós, e, também, evitar a necessidade do uso de difusividades artificiais como garante de estabilidade; em geral, e nestes dois aspectos em particular, o método revela-se superior a métodos Eulerianos, mais convencionais (por exemplo, métodos de elementos finitos, do tipo Galrkin ou Petrov-Galerkin, aplicados à equação de transporte indivisa).

No âmbito de um projecto de investigação intitulado caracterizarão de Formações Estuárias e do Meio Marítimo Litoral Por Técnicas de Detecção Remota , insere-se o estu¬do da avaliação de suspensões na água do mar com recurso à aplicação de técnicas de detecção remota como meio de caracterização de parâmetros de qualidade de água. 0 trabalho que se apresenta foi desenvolvido com os seguintes objectivos:1- Desenvolvimento de metodologias de análise e quantificação de suspensões na água do mar a partir de dados de satélite;2- Implementação sob forma de programas para computador de modelos de quantificação de suspensões orgânicas e inorgânicas na água do mar, a aplicar aos dados do radiómetro CZCS do satélite NIMBUS-7;3- Aplicação e verificação do modelo ao litoral português.Corn vista à consecussão destes objectivos, começa-se por apresentar uma extensa análise das formas de abordagem do problema, enumerando-se os diversos métodos actualmente seguidos, nomeadamente o Empírico, o Teórico e, neste, os métodos microscópico e macroscópico.Com base nesta análise, propõe-se um modelo numérico de quantificção das suspensões a partir dos dados do radiómetro CZCS do satélite NIMBUS-7, o qual, embora empírico na sua formulação como a maioria dos actualmente existentes, se apoia no comportamento radiomótrico da água do mar e dos seus constituintes típicos, cujas características se apresentam também.A implementação prática do modelo exige a filtragem da componente atmosférica presente nos dados rediométricos. Com este objectivo, apresenta-se um modelo baseado na metodo¬logia correntemente utilizada. Consiste na consideração da difusão simples, causada pelos constituintes básicos da atmosfera (moléculas gasosas, aerosóis e ozono) na gama de comprimentos de onda considerada (440, 520, 550 e 670nm). Esta metodologia conduz, porém, a um sistema de equações indeterminado e que é resolvido pela consideração de uma equação ´exterior´ ao processo de transferência radiativa que tem lugar na atmasfera. Para este efeito, utilizou-se a equação de Smith e Wilson por ser a mais divulgada, ressalvando-se, contudo, a necessidade de verificação da sua efectiva aplicação às águas do litoral português, o oqe não foi possível concretizar dada a inexistência de dados.

A numerical method for the solution of the two-dimensional, unsteady, transport equation is formulated, and its accuracy is tested.The method uses a Eulerian-Lagrangian approach, in which the transport equation is divided into a diffusion equation (solved by a finite element method) and a convection equation (solved by the method of characteristics). This approach leads to results that are free of spurious oscillations and excessive numerical damping, even in the case where advection strongly dominates diffusion. For pure diffusion problems, optimal accuracy is approached as the time-step, At, goes to zero; conversely, for pure-convection problems, accuracy improves with increasing At; for convection-diffusion problems the At leading to optimal accuracy depends on the characteristics of the spatial discretization and on the relative importance of convection and diffusion.The method is cost-effective in modeling pollutant transport in coastal waters, as demonstrated by an illustrative application to a case study (sludge dumping in Massachusetts Bay). Numerical diffusion is eliminated or greatly reduced, raising the need for realistic estimation of dispersion coefficients. Costs (based on CPU time) should not exceed those of conventional Eulerian methods and, in some cases (e.g., problems involving predictions over several tidal cycles), considerable savings may even be achieved.

0 principal objectivo desta tese é mostrar a habilidade do métodos dos elementos finitos e do método dos elementos de fronteira na modelação das ondas gravíticas de superfície.Na análise linear, as equações reduzidas do movimento ondulatório são resolvidas pelo método dos elementos finitos, levando em linha de conta a reflexão parcial, a radiação e o atrito de fundo. A modelação da radiação é feita com elementos infinitos ou com elementos de radiação, sendo estes encarados como um caso particular dos elementos de reflexão. 0 atrito de fundo é introduzido após a discretização e é levado a efeito através de um coeficiente empírico que se pode relacionar com o coeficiente de Chezy.Quer o modelo determinístico quer o modelo estocástico, obtido do primeiro com base na noção do estimador natural, permitem a realização de ensaios de ressonância ou de agitação. Nos ensaios de ressonância de uma bacia portuária tem particular interesse o conhecimento do espectro de resposta ao ruído bran¬co de banda limitada.A título de exemplo de aplicação mostram-se alguns aspectos do estudo das condições de ressonância do porto de Leixões.Logo que não sejam válidas as hipóteses simplificativas que permitem uma abordagem linear das ondas gravíticas de superfície, são resolvidas as equações não lineares do movimento ondulatório com superfície livre, pelo método dos elementos de fronteira. As suas peculiaridades permitem, sem qualquer dúvida, considerar o método dos elementos de fronteira como o mais vocacionado para este tipo de análise.Os programas de cálculo automático para o estudo da análise não linear estão ainda em fase de teste, pelo que não se apresentam exemplos de aplicação.

Este trabalho é dirigido principalmente para o uso da simulação numérica dos escoamentos em estuários como uma ferramenta pa¬ra estudos de engenharia. Fazem-se algumas considerações gerais sobre a definição e classificação de estuários seguidas por uma descrição sumária da hidrodinâmica dos estuários. Descrevem-se e comparam-se as várias técnicas utilizadas na solução de problemas de hidradinâmica de stuários.Faz-se a dedução formal de um modelo matemático do escoamento em estuários homogéneos e integram-se verticalmente as suas e¬quações, obtendo-se as conhecidas equações do escoamento em águas pouco profundas ("shallow water equations"). Estas equações são discretizadas utilizando os métodos dos elementos finitos e das diferenças finitas, respectivamente no espaço e no tempo.Faz-se a descrição de um sistema de cálculo para determinar a solução do modelo matemático discretizado e tecem-se várias considerações acerca do seu desenvolvimento e uso.Finalmente apresentam-se os resultados de alguns testes utilizados para verificar o funcionamento do sistema de cálculo.

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