Publicações

Morphodynamic modeling systems are being subjected to a growing development over the last decade and increasingly appear as valuable tools for understanding and predicting coastal dynamics and morphological changes. The recent improvements of a 2DH unstructured grid morphodynamic modeling system are presented in this paper and include the implementation of an adaptive morphodynamic time step, the integration and full coupling of a wave model and the forcing by large scale wave and tide models. This modeling system was first applied to a dissipative wave-dominated beach located on the French coast, where the availability of field data allowed for a fine calibration and validation of wave-induced flows and longshore transport, and an assessment of the various sediment transport formulae. The modeling system was then applied to a very dynamic Portuguese tidal inlet where numerical tests show the computational efficiency of using an adaptive time step. Morphodynamic simulations of this inlet with real wave and tidal forcings resulted in realistic morphological predictions. The two applications show that the improved modeling system is able to predict hydrodynamics, transport and morphological evolutions in complex coastal environments.

The uncertainty associated with simulations of process-based coastal area morphodynamic models is assessed through numerical experimentation. Appropriate metrics of uncertainty are defined based on thestandard deviation of the model results at each location and each time step. Uncertainty is examined using a set of realistic one year morphodynamic simulations of the evolution of a highly dynamic tidal inlet. Results indicate that uncertainty increases linearly with time, and suggest that its rate grows with increasingsediment fluxes. Hence, the limits of predictability of morphodynamic model applications are higher for slowly varying systems. Attempts to reduce uncertainty by aggregating model results at larger spatial scales met with limited success. Ensemble simulations are suggested as a possible avenue to investigate the longterm evolution of tidal inlets using process-based models.

Thewater and the ecosystem dynamics of the Ria de Aveiro, a shallow, multi-branch lagoon located on the northwest coast of Portugal, are simulated using a newfully coupled 3Dmodeling system. This model couples the hydrodynamic model SELFE (semi-implicit Eulerian-Lagrangian finite element) and an ecological model extended from EcoSim 2.0 to represent zooplankton dynamics. The model application is based on an unstructured grid spatial discretization, which is particularly appropriate for this system given its complex geometry. The baroclinic circulation is calibrated and validated for different environmental conditions, leading to velocity errors smaller than 5 cm/s across the lagoon. Ecological simulations, focused on zooplankton dynamics represented by a site-specific formulation, are then presented and compared against field data for two contrasting environmental conditions: Autumn 2000 and Spring 2001. Results show that the fully coupled model is able to reproduce the dynamics of the ecosystem in the Spring 2001, fitting the model results inside the range of data variation. During this period zooplankton differences between data and model results are of about 0.005mgC/l (60%), while other ecological tracers

The relative impacts of tidal (neap, spring) and river discharge (including a flood event) forcing upon water and sediment circulation have been examined at the rock-bound Guadiana estuary. Near-bed and vertical profiles of current, salinity, turbidity, plus surface suspended sediment concentrations (SSC, at some stations only), were collected at the lower and central/upper estuary during tidal and fortnightly cycles. In addition, vertical salinity and turbidity profiles were collected around high and low water along the estuary. Tidal asymmetry produced faster currents on the ebb than on the flood, especially at the mouth. This pattern of seaward current dominance was enhanced with increasing river flow, due to horizontal advection that was confined within the narrow estuarine channel. The freshwater inputs and, at a degree less, the tidal range controlled the vertical mixing and stratification importance. Well-mixed (spring) and partially stratified (neap) conditions alternated during periods of low river flows, with significant intratidal variations induced by tidal straining (especially at the partially stratified estuary). Highly stratified conditions developed with increasing river discharge. Intratidal variability in the pycnocline depth and thickness resulted from current shear during the ebb. A salt wedge with tidal motion was observed at the lower estuary during the flood event. Depending on the intensity of turbulent mixing, the residual water circulation was dominantly controlled either by tidal asymmetry or gravitational circulation. The SSC was governed by cyclical local processes (resuspension, deposition, mixing, advection) driven by the neap-spring fluctuations in tidal current velocities. More, intratidal variability in stratification indicated the significance of tidal pumping at the partially and highly stratified estuary. The estuary turbidity maximum (ETM) was enhanced with increasing current velocities, and displaced downstream during periods of high river discharge. During the flood event, the ETM was expelled out of the estuary, and the SSC along the estuary was controlled by the sediment load from the drainage basin. Under these highly variable river flow conditions, our observations suggest that sand is exported to the nearshore over the long-term (>years).

Ocean surface gravity waves play a major role in many engineering and environmental problems, both in the open ocean and in coastal zones. Therefore, it is essential to improve our knowledge on spatial and temporal variability of wave climate. This study aims at investigating this variability in the North-East Atlantic Ocean (25º W

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A ocorrência de condições hidrodinâmicas extremas em zonas ribeirinhas de estuários e lagunas, ambientes privilegiadospara a ocupação humana, pode conduzir a avultados prejuízos materiais e humanos. Revela-se prioritário o desenvolvimentode ferramentas de avaliação da vulnerabilidade destas regiões para apoio ao seu planeamento.Neste estudo é proposta uma metodologia de base para a previsão de níveis extremos de inundação das zonas ribeirinhasde ambientes estuarinos resultantes da acção combinada de vários fenómenos hidrodinâmicos. Esta metodologia é aplicadaao estuário interno do Tejo, numa área cuja morfologia se tem mantido estável à mesoescala (década) e à escala anual: arestinga do Alfeite, na margem Sul do estuário. Os resultados desta aplicação foram integrados num MDT (ModeloDigital de Terreno), para facilitar a análise de vulnerabilidade da área em estudo aos fenómenos simulados. A metodologiaproposta tem em conta os fenómenos indutores de inundação em zonas estuarinas e costeiras: i) elevados níveis de maré,ii) sobreelevação meteorológica, iii) sobreelevação associada a cheia, iv) subida do NMM (nível médio do mar) e v)agitação marítima em situação de tempestade. Trata-se de uma metodologia robusta que integra modelos amplamentedivulgados e aplicados para estes fenómenos: modelo hidrodinâmico de ondas longas, modelo de geração

Apresenta-se uma panorâmica geral sobre os principais problemas relacionados com a fisiografia costeira e as principaistécnicas de protecção da orla costeira. Referem-se os processos físicos responsáveis pela dinâmica sedimentar, e os principaisproblemas a ela associados que afectam praias e embocaduras de estuários e lagunas. As soluções mais comuns para estetipo de problemas são depois revistas de forma crítica. Finalmente, três casos de estudo são utilizados para exemplificarproblemas e soluções, e, simultaneamente, ilustrar abordagens seguidas em estudos de engenharia: uma praia encaixadaem erosão (praia de Hac-Sá, República Popular da China), um sistema no Rio de Janeiro, Brasil, composto por uma praiaarqueada (praias de Leblon, Ipanema e Arpoador), um canal e uma laguna com problemas simultâneos de erosão eassoreamento e uma embocadura lagunar com problemas de assoreamento e de estabilidade (Lagoa de Óbidos, Portugal).

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This study investigates the annual and inter-annual longshore transport at a high-energy dissipative beach (St. Trojan, SW Ole´ron Island, France), over the period 1997

The Barbarie spit (Langue de Barbarie) is a 100

ShorelineS is a recent coastline evolution model allowing for extreme coastline curvatures and spit formation at high-angle wave incidence. This paper investigates ShorelineS

The XBeach modelling system was used to hindcast the morphological evolution of an ephemeral tidal inlet during Hurricane Leslie (2018). Simulations of morphological evolution were compared against daily observations from topographic surveys conducted at the Albufeira Lagoon during this event. On the one hand, numerical simulations successfully reproduced the observed accumulation pattern at the flood delta. On the other hand, numerical simulations displayed a slight tendency to overestimate the sediment erosion that took place at the transitional channel.

During storm conditions, infragravity (IG) waves with periods between 25 s and 300 s can dominate the seasurfaceoscillations near the shoreline. Through processes like wave run-up, overwash and wave overtopping,IG waves can hence become major drivers of coastal hazards. Although IG dynamics are relatively wellunderstood in open beaches, their contribution of the hydro-sedimentary dynamics of more complex coastalsettings, such as tidal inlets characterized by their ebb and flood deltas connected through a transitional channel, is not well understood. Here, we assess the performance of the widely used XBeach numerical model to predict IG wave dynamics through a comparison against field observations collected on an ephemeral tidal inlet (Albufeira Lagoon) during storm Leslie (2018). XBeach accurately predicted the observed IG significant wave heights reaching up to 1 m over a 2-day period. This performance is assessed at both the nearby beaches and the flood-delta.

The inlet of the Óbidos Lagoon is a wave-dominated tidal inlet located on the Portuguese coast. It is known for its unstable behaviour, which often leads to erosion issues on its margin or to its complete closure. Over twenty years of satellite data were compiled to document this behaviour. The reconstructed behaviour was compared to the contemporary offshore wave climate. The comparison showed that the inlet

The geometric characteristics of sand waves in the main channel of the outer Tagus estuary are investigated, using high-resolution surveys conducted in 2019 and 2020. The relationship between bedform height and spacing over a 1400 m transect, at ca. 20 m depth, is in good agreement with the global mean trend equation proposed by Flemming (1988). The consistent ebb-oriented asymmetry suggests that the direction of net sediment transport is seaward. The apparent direction of sand wave migration obtained from the comparison between surveys is more variable, but on average also ebb-oriented.

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.

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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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