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Tidal inlets and embayments constitute navigation routes and they control thestability of adjacent shorelines and the exchanges of water, sediment and dissolvedmaterial between the ocean and back-barrier lagoons. Tidal inlets are thus of critical and growing socio-economical and environmental importance worldwide. They are oftenexceptionally dynamic, due to the combination of tide- and wave-driven processes. Thisintense dynamics drives fast and large morphological changes, which make their behaviorhard to predict and their sustainable management difficult to achieve. To address thisproblem, the development of morphodynamic modeling systems has emerged over thelast decade as the most promising perspective to understand their behavior and predicttheir evolution. Morphodynamic modeling systems, whose development and successfulapplication to tidal inlets has been growing over the last decade, couple a set of modulesto simulate hydrodynamic circulation, wave propagation, sediment transport and bottomevolution.This chapter provides in introduction a synthesis of the existing quantitative methods to investigate tidal inlets and points out the advantages and limitations of morphodynamic modeling systems compared to physical, empirical and analytical models. The next section describes the main principles of morphodynamic modeling systems and explains how the different modules are coupled together. The following section illustrates through three selected applications the capabilities of morphodynamic modeling systems tosimulate morphological changes of tidal inlets at various time scales, but also toinvestigate the mechanisms that control their development. The final section providessome conclusions and perspectives regarding the morphodynamic modeling of tidalinlets.

Although rising global sea levels will affect the estuarine flooded areas over the coming decades, the local and regional-scale processes will also induce important changes in these coastal systems. The main aim of this work is to investigate possible tidal changes in estuarine systems induced by local geomorphologic modifications, analyzing the particular case of Ria de Aveiro which is in risk of inundation. Located in the Portuguese west coast, this tidally driven lagoon has a large area of mostly abandoned salt pans, which are in progressive degradation caused by the lack of maintenance and by the strong currents which erode their protective walls.To explore possible tidal changes the hydrodynamic model ELCIRC was applied to Ria de Aveiro to simulate and analyse the impact in the lagoon hydrodynamics of this degradation which results in the enlargement of the lagoon flooded area. A high-resolution grid (grid spacing of the order of 1 m) was developed in order to represent the narrow channels adjacent to the salt pans. The hydrodynamic model was then successfully calibrated and assessed for skill for the Aveiro lagoon through comparison between measurements and model results and quantification of the numerical accuracy. The model was subsequently used to investigate the effect of the flooded lagoon area enlargement on tidal propagation in Ria de Aveiro. Simulations were performed for three geomorphologic configurations, representing the reference or present situation and two flooded scenarios. Results were compared through the analysis of tidal currents, tidal asymmetry and tidal prism.The increase of the lagoon flooded area results in an intensification of the tidal currents, tidal prism and tidal asymmetry. Results also indicate that the tidal prism further increases when the flooding depth increases. Otherwise, changes in tidal currents and in tidal asymmetry pattern are negligible with the increase of the flooded area depth.These results indicate that modifications of the flooded area of estuarine systems will result in tidal changes, with an intensification of the actual tidal patterns induced by the enlargement of inundation areas.

Among the different types of tidal inlets, wave-dominated inlets have been subjected to few quantitative studies, so that the physical processes controlling their dynamics are not fully understood. This study presents the application of a coastal area morphodynamic modeling system to a wave- dominated inlet (O´ bidos Inlet, western coast of Portugal), in order to investigate the physical processes responsible for channel development during fair weather conditions and shoaling during periods of larger waves. The modeling system was able to reproduce reasonably well morphological changes at the O´ bidos Inlet and subsequent tidal amplitude evolutions inside the lagoon over a period which includes 3 months of fair weather conditions, followed by 2 months representative of winter conditions. The inlet development during fair weather conditions was attributed to the strong ebb-dominance of the main channel without waves, enhanced by the combination of shallow channels and a meso-tidal range. The inlet infilling during the maritime winter was attributed to three main wave-induced mechanisms: (1) the onshore component of wave radiation stresse gradients, which is not fully compensated by the wave-induced setup in front of the inlet; (2) the acceleration and convergence of longshore transport toward the inlet, due to the presence of a strong lateral gradient in free surface elevation on both sides of the inlet, and, to a smaller extent, to wave refraction around the ebb-delta; and (3) the increase in mean water level inside the lagoon, which reduces tidal asymmetry and subsequent ebb-dominance.

The environmental and economical consequences of an oil spill near coastal areas lead to an increasing effort by governments and the oil industry to develop tools, such as oil spill modeling systems, that could be used to mitigate these types of catastrophes. Oil spill modeling systems simulate hydrodynamics and the physical, chemical and biological processes that determine the fate of oil slicks. Recent technological developments, such as PC clusters, make these systems extremely attractive for practical applications in support of accident prevention and mitigation measures. This paper introduces a new oil spill modeling system and describes its application to the Prestige disaster (Northeast of the Iberian Peninsula, November 2002). The modeling system includes a flexible oil spill model, which can be used as a 2D surface plume model, or as a sophisticated surface-water column 3D model. Both options include all relevant processes, including the coastal retention and later release of the oil to the water column. The oil spill model is based on Eulerian-Lagrangian formulations, uses unstructured grid discretizations and is coupled with the 3D hydrodynamic model SELFE. A hindcast simulation of the Prestige oil spill disaster between 13 and 19 of November 2002 is presented here, based on the CEDRE information for ship route. The 3D hydrodynamics in the Iberian Atlantic shelf were determined with SELFE, forced by tides, wind and baroclinic gradients, while the 2D surface plume model was used to simulate the surface oil slick trajectory. The boundary and initial conditions for salinity and temperature were obtained from LEVITUS atlas while wind and wave data were retrieved from NCEP and WAVEWATCH III databases (NOAA, US). The oil plume trajectory validation was made against available satellite SAR images. The application shows the good numerical behavior of the model, its ability to predict the plume trajectory, and reveals its potential as a management tool. The application also highlights the importance of the accuracy of the forcings on the plume's pathway.

Erosion of the southern Gold Coast beaches (SE Queensland, Australia) was exacerbated after the extension of the Tweed River training walls in the early 1960s. To achieve the objective of restoring and maintaining beach amenity, significant nourishment works have been undertaken in Coolangatta Bay over the past 30 years. Particularly, under the Tweed River Entrance Sand Bypassing Project (TRESBP) since 1995, a number of nourishment campaigns and the implementation of a permanent sand bypass system in 2001 have resulted in significant changes of Coolangatta Bay morphology. The present case study investigates the influence of both wave climate and nourishment works on the area extending from the updrift Snapper Rocks area to downdrift Kirra Beach. SWAN spectral wave model is implemented at Coolangatta Bay area and forced by the global wave model WW3 to estimate wave forcing and the potential natural longshore drift entering in Coolangatta. Specific transects extracted from accurate bathymetric surveys are used to investigate and quantify Coolangatta Bay sedimentation for the period 1987

Erosion of the southern Gold Coast beaches (SE Queensland, Australia) was exacerbated after the extension of the Tweed River training walls in the early 1960s. To achieve the objective of restoring and maintaining beach amenity, significant nourishment works have been undertaken in Coolangatta Bay over the past 30 years. Particularly, under the Tweed River Entrance Sand Bypassing Project (TRESBP) since 1995, a number of nourishment campaigns and the implementation of a permanent sand bypass system in 2001 have resulted in significant changes of Coolangatta Bay morphology. The present case study investigates the influence of both wave climate and nourishment works on the area extending from the updrift Snapper Rocks area to downdrift Kirra Beach. SWAN spectral wave model is implemented at Coolangatta Bay area and forced by the global wave model WW3 to estimate wave forcing and the potential natural longshore drift entering in Coolangatta. Specific transects extracted from accurate bathymetric surveys are used to investigate and quantify Coolangatta Bay sedimentation for the period 1987

As waves travel and shoal towards a beach, their surface elevation becomes peaky (sharp crests) and asymmetric relative to the vertical. Within a wave period, the corresponding orbital velocity near the bottom shows a similar (time) variation and it is recognized that these nonlinearities are responsible for sediment transport. The resulting wave-induced bottom shear stresses are required for most sediment transport model computations. In this work,simple bottom shear stresses parameterisations for rough seabeds, under nonlinear waves, are analysed. Theeffects of the wave shape on the bottom shear stresses estimates is investigated by analysing a new set of experimental data, under accelerated skewed waves (SILVA et al., 2008). Results indicate a good agreementbetween all the formulations presented.

The hydrodynamics and alongshore sediment dynamics were evaluated on a meso-tidal estuarine beach, submitted to wind and vessel waves generated in an area of restricted fetch, not affected by oceanic waves. The beach morphology is characterised by two main features, a steep upper beach followed, seaward, by a low gradient terrace, both engaged in the surf zone depending on the tidal level. Sedimentologic surveys revealed the presence of coarser sand grains at the steep upper beach, finer sand grains at the low gradient terrace and a large geometrical spreading at the base of the beach face. The characterisation, based on a six-year wind data series, of the average annual wave climate in front of the beach, indicates a low energy environment where the estimated longshore transport is 14.5x103 m3.year-1, equally distributed in both directions. This study also concluded on the cross-shore distribution of the longshore sediment transport in the active part of the beach and on the contribution of each wind wave component to the longshore transport. Despite the important impact that the catamarans can have on cross-shore beach dynamics, their effect on the longshore transport is irrelevant

In this work, a video-monitoring system applicable to the study of beach morphodynamics was developed and applied to the DTM extraction of the intertidal zone of a fetch limited beach (Alfeite, Portugal). This low-cost system, intended to complement standard survey tools, has the additional benefit of enabling the continuousmonitoring of beach meso-scale process (spatial/temporal scales in the order of kilometers and years, respectively). The development of this system, based on terrestrial photogrammetric techniques, involved three main steps: i) camera calibration, where the internal camera parameters were determined in the laboratory using open-source software; ii) the development of image correction subroutines, which aimed to correct the relativelylarge image distortions induced by camera optics; this procedure revealed to be essential as the system was builtupon standard non-metric surveillance cameras; iii) the development of image rectification subroutines totransform oblique images into vertically equivalent images; this transformation was based on external camera orientation parameters obtained in the field through the surveying of ground control points. Alfeite beach DTM extraction was performed through the shoreline digitalization, in geo-referenced rectified images acquired every 10 min, during the flood. The overlapped set of shoreline curves, properly referred to a vertical datum by meansof tide measurements, characterized the intertidal beach morphology. The obtained results were compared with the ones acquired with classic survey techniques revealing very encouraging results; the overall vertical rms was 0.08 m with a maximum value of 0.15 m at 390 m of the camera.

This paper describes a site specific study of a low energy estuarine beach sheltered from oceanic waves which presents a medium term (decade) geomorphologic stability. However, extreme meteorological events, characterized by strong winds, generate episodes of retreat of the beach face, which, under restored wave conditions, recovers in the short term. Three process-based models (a wind wave generation propagation model, a 2D-V littoral drift model and a 2D-V cross-shore morphodynamics model), frequently applied in open coastal areas but never in such low energy environments, were applied. The longshore transport was difficult to measure in the field and thus the numerical estimate was not validated. However, its uncertainty (9.6-16.1 x103 m3.year-1) was tested based on a sensitivity analysis of three influential parameters. Field measurements of meteo-oceanographic data and profile changes during a storm episode allowed the simulation of the hydrodynamics and sediment transport, and finally the verification of the numerical profile. Despite the volume of sediment extracted from the beach face being in good agreement with the observations, about 10m3.m-1, the profile geometry was not: the numerical profile exhibits an erosion scarp located bellow the retreat observed and a bar, at the beach face base, which was not observed in the field (probably flattened by the uprush and downrush flows). The effect of the passage of a catamaran was also evaluated: it generates an erosion of sediment up to 0.04m3.m-1 (depending on the catamaran velocity). Due to the beach geomorphologic characteristics the sediment transport is higher at higher tidal levels.

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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