It is important to estimate the quantity of wave run-up and overtopping in seawall design. Previous study on the investigations of run-up is carried out mostly in the laboratories, it seldom perform in field measurements. About previous wave run-up equation can¡¦t accurately estimate run-up elevation. According to run-up data, this study hope that it can make the formula to meet the actual local situation. It can have a better reference by designing coastal structures. This paper study wave run-up during five typhoons by Kalmaegi ,Fung-Wong,Nuri, Hagupit,and Jangmi. It measuring wave height , water level,and topography. These data show that the run-up elevation in bay higher than in breakwater. It shows that wave pass through a submerged breakwater can decay wave height. Analysis of measured data and found that when the wave height is about 1~4 meter with 1/(H0/L0)0.5 has a good correlation. It similar to some past researchers. Experience equations close to measured value when wave height smaller than 4 meter. When wave height more than 4 meter, the empirical prediction value is larger than measured value. Wave run-up doesn¡¦t have good theory, and experience equations different about every field. The empirical equations depends on the scene to investigate the effects of various parameter.

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Over the last few decades, wave run up prediction has gained the interest of numerous researchers and every newly-published paper has aimed to predict wave run up with greater accuracy. Wave run up is defined as the vertical elevation reached by a wave's, front water edge as it runs up a beach, measured relative to the still water line. Wave run up is dependent on the incidental wave height, the wave period, the beach slope and the wave steepness. The majority of publications incorporate all of these factors, but some do not, which has led to numerous debates. The goal of this study is to do a re-assessment of previously published wave run up formulae, to obtain a more informed understanding about wave run up and the available predictive empirical formulae. The study also seeks to evaluate the Mather, Stretch & Garland (2011) formula. The method for undertaking this objective comprised a physical model test series with 10 regular wave conditions on a constant slope, being 1/24, performed with an impermeable floor. Also, a beach study in the field was done on Long Beach, Noordhoek, where run up measurements were taken for 30 minute intervals, resulting in five test conditions. A numerical model was employed in conjunction with the beach study to determine the local offshore wave parameters transformed from a deep water wave rider. This information was used to correlate the run up measurements with known wave parameters. Firstly, the physical model assessment was performed to provide a proper foundation for run up understanding. Plotting empirical normalised run up values (R2/H0 ) versus the Iribarren number for different formulae, a grouping was achieved with upper and lower boundaries. The physical model results plotted on the lower end of this grouping, resulted in prediction differences of more than 10%. These differences may have been caused by the unevenness of the physical model slope or the fact that only one slope had been tested. Despite this, the results fell within a band of wave run up formulae located on the lower end of this grouping. An assessment of the beach measurements in the field gave a better correlation than the physical model results when compared to normalised predicted wave run up formulae. These measurements also plotted on the lower end of the grouping, resulting in prediction differences of less than 10% for some empirical formulae. When comparing these empirical predictions to one another, the results demonstrate that the formulae comparing best with the beach measurements were Holman (1986) and Stockdon, Holman, Howd, & Sallenger Jr. (2006). Extreme over predictions were found by Mase & Iwagaki (1984), Hedges & Mase (2004) and Douglass (1992). Nielsen & Hanslow (1991) only compared best with the beach measurements and De la Pena, Sanchez Gonzalez, Diaz-Sanchez, & Martin Huescar (2012) only compared best to the physical model results. This study supports the formula proposed by Mather, Stretch, & Garland (2011). Applying their formula to the measured results presented a C constant of 3.3 for the physical model and 8.6 for the beach results. Both values are within the range prescribed by the authors. Further reasearch minimized the array of possible „C‟ values by correlating this coefficient to Iribarren numbers. „C‟ values between 3.0~5.0 is prescribed for low Iribarren conditions (0.25-0.4) and values between 7.0~10 for higher Iribarren conditions are 0.75-0.8. However, this formula is still open for operator erros whereby the „C‟ value has a big influence in the final result. The best formulae to use, from results within this thesis, is proposed by Holman (1986) and Stockdon et.al (2006). These formulae are not open to operator erros and uses the significant wave height, deep water wave length and the beach face slope to calculate the wave run up. / AFRIKAANSE OPSOMMING: Gedurende die afgelope paar dekades, het golf-oploop voorspellings die aandag van talle navorsers gelok en elke nuwe geskrewe voorlegging het gepoog om meer akkurate golf-oploop voorspellings te verwesenlik. golf-oploop kan definieer word as die vertikale elevasie bereik deur 'n golf se voorwaterkant soos dit op die strand uitrol, gemeet relatief vanaf die stilwaterlyn. golf-oploop is afhanklik van die invals-golfhoogte, die golfperiode, die strandhelling en die golfsteilheid. Die oorgrote mederheid publikasies uit die literaturr inkorporeer al hierdie faktore, maar sommige nie, wat groot debatvoering tot gevolg het. Die doel met hierdie studie is om vorige gepubliseerde golf- oploop formules te re-evalueer, om 'n meer ingeligte begrip van golf- oploop en beskikbare voorspellende formules te verkry. Die studie poog terselfdertyd ook om golf-opvolg tendense, uniek aan Suid Afrikaanse strande te evalueer deur die huidige formule wat tans hier gebruik word, te assesseer. Om hierdie doelwit te bereik, is gebruik gemaak van 'n fisiese model toets reeks bestaande uit 10 reëlmatige golfstoestande op 'n konstante ondeurlaatbaare strandhelling van 1/24. 'n Veldstudie was ook uitgevoer op Langstrand, Noordhoek, waar golf-oploopmetings met 30 minute tussenposes uitgevoer is, vir vyf toets-toestande. Tesame met die veldstudie, is 'n numeriese model aangewend om die gemete diepsee data nader ann die strand wat bestudeer is te transformeer. Hierdie inligting is benodig om 'n verband tussen tussen oploop-metings en bekende golf parameters te bepaal. Eerstens is die fisiese model assessering uitgevoer om 'n behoorlike basis vir die begrip van golfoploop in die veld te verkry. Deur die emperiese, genormaliseerde oploop waardes (R₂/H₀) vir verkeie formules teenoor die Iribarren getal te plot, is 'n groepering met hoër en laer grense gevind. Daar is gevind dat die fisiese modelwaardes op die laer grens plot, en het verskille met die emperiese waardes van meer as 10% getoon. Hierdie verskille is moontlik veroorsaak as gevolg van 'n oneweredige fisiese model strandhelling of deur die feit dat slegs een helling getoets is. Ten spyte hiervan, het die model oploop waardes binne die bestek van golf- oploop formules geval. Assessering van die veldmetings het 'n beter korrelasie as die fisiese modelresultate getoon, tydens vergelykings met genormaliseerde golf-oploop formules van die emperiese formules. Die oploop waardes van hierdie metings het ook geplot aan die laer grens van die groepering, met verskille van minder as 10% vir die meeste gevalle van die emperiese formules. Wanneer hierdie emperiese voorspellings vergelyk word, is gevind dat die formules wat die beste ooreenstem met die fisiese model, die van Holman (1986) en Stockdon, Howd, & Sallenger Jr. (2006) is. Die emperiese formules van Mase & Iwagake (1984), Hedges & Mase (2004) en Douglas (1992) het die golf-oploop oorvoorspel. Nielsen & Hanslow (1991) het slegs die beste met die strandmetings vergelyk, terwyl De la Pena, Sanchez Gonzalez, Diaz-Sanchez & Martin Huescar (2012) slegs die beste vergelyk het met die fisiese-model resultaat. Hierdie studie ondersteun die formule voorgestel deur Mather, Stretch, & Garland (2011). Deur hul formules op die gemete bevindings toe te pas, is 'n C konstante van 3.3 vir die fisiese model resultate, en 8.0 vir die stranduitlslae bepaal. Beide waardes lê binne die grense wat deur die outeurs voorgestel is. Verdere navorsing het getoon dat moontlike waardes vir die „C‟ konstante tussen 3.0 en 5.0 moet wees vir Iribarren waardes van tussen 0.25 en 0.4. Vir hoër Iribarren waardes, 0.75-0.8, moet die „C‟ kosntante tussen 7.0 en 10 wees; dog is die formule steeds oop vir operateur foute. Die hoofbevindinge van die tesis is gevind dat die beste golf-oploop formules, om tans te gebruik, die van Holman (1986) en Stockdon et.al (2006) is. Hierdie formules kan glad nie beinvloed word deur operateurs foute nie en maak gebruik van die invals golfhoogte, die golfperiode en die strandhelling om die golf-oploop te bepaal.

¡@¡@The research on collection or reflection of solitary waves mainly focus on numerical model and theoretical analytics, there are few study on experiment. due to the process on reaction of solitary waves are very short in times, and the waveform is also hardly to measure quantifiable. ¡@¡@The method present in this paper that we setup a high speed camera at a fixed position, and a grid-point board is located in the water tank and out of the tank after pictured, then we capture the process on reflection of solitary wave at a wall by high speed camera, so that the waveform and the grid surface coincide. finally, we analyze the waveform within the grid by using image techniques. ¡@¡@The results of this paper that present several important parameters in several relative wave height, such as maximal run-up, residual time, phase shift..et.al. the other hand, this paper compare the result of experiment with available evidences likes numerical model and theoretical analytics that found to be in quantitative agreement. ¡@¡@In addition, this paper also present the result of experiment that could compare with the new phenomenon "residual falling jet¡¨, it`s published by Chambarel.et.al (2009) numerical model.

Made available in DSpace on 2014-06-12T22:58:05Z (GMT). No. of bitstreams: 2 arquivo1446_1.pdf: 4391997 bytes, checksum: cf2f9970dc31e357b9bdb19b4ffdf45b (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O ambiente costeiro é berçário natural para um grande número de espécies marinhas, principalmente onde ocorrem mangues e recifes, que funcionam como abrigo natural para a desova e início de vida de muitas espécies marinhas. A linha de costa está inserida nesse ambiente, pois representa o limite entre o mar e o continente, no alcance máximo das ondas, onde cessa a ação marinha efetiva. Entretanto, a dinâmica de movimentação das marés torna esse limite uma zona de fronteira de difícil demarcação e monitoramento. Além disso, as alterações geomorfológicas, muitas vezes catalisadas pelas interferências antrópicas, diminuem a capacidade de regeneração natural das praias, dificultando o gerenciamento desse ambiente. Em virtude disso, essa tese desenvolveu alguns experimentos para localizar e monitorar linhas de costa nas praias de Sauaçui e Japaratinga, localizadas no Estado de Alagoas Brasil, aplicando tecnologia de posicionamento dos sistemas GNSS (Global Navigation Satellite System), com base em um indicador de linha de costa com representação matemática, correspondente à máxima altura alcançada pelas marés nos últimos 20 anos, acrescida do run-up, correspondente ao espraio das ondas. O GPS (Global Positioning System), que a partir deste ponto será designado apenas GPS, consiste em um sistema de posicionamento por satélite pertencente ao GNSS e pode gerar posicionamentos no modo dinâmico relativo, com precisão de poucos centímetros e suas técnicas já vem sendo aplicadas em programas de gerenciamento costeiro em várias partes do mundo. Entretanto, as alturas geradas pelo GPS são elipsoidais e representam um problema para o uso desse sistema em aplicações que envolvem altitudes, como é o caso das linhas de costa, que são relacionadas com o nível do mar. A técnica proposta nessa tese gera o modelo de elevação digital da praia, com base em perfis de praia, no mesmo referencial de nível das marés e nele identifica a linha de costa. Para isso, os referenciais verticais de maré e do GPS são correlacionados através de um artifício apropriado que requer o conhecimento das alturas de maré e do GPS em um mesmo local. Os perfis de praia aqui referidos são constituídos de pontos coordenados gerados pelo deslocamento de uma antena GPS em ziguezague ao longo da praia. Essa metodologia mostrou-se adequada para localizar e monitorar linhas de costa com precisão sub-métrica e tem como principal vantagem o fato desse modelo facilitar a visualização do comportamento da linha d´água, sendo apropriado para simular o deslocamento do mar sobre o continente. Os resultados mostram a localização geográfica das linhas de costa das praias objeto desse estudo, expressas no Sistema de Projeção Cartográfica Universal Transverso de Mercator (UTM). O monitoramento da linha de costa provém da comparação do seu traçado, superpondo-se os modelos produzidos em diferentes épocas e indica comportamento sazonal das linhas de costas tanto nas praias de Japaratinga (máximo de 6,0 m), como na praia de Sauaçui (máximo de 8,0 m). Além disso, como o referencial do GPS tem grande estabilidade, ele pode ser usado no monitoramento da estabilidade dos marcos de apoio, cujas coordenadas são suscetíveis de alterações, em havendo subsidências do solo e/ou movimentações de placas da crosta terrestre

Tesis para optar al grado de Magíster en Ciencias, Mención Geofísica / En el presente trabajo se analiza la respuesta del agua al proceso temporal de ruptura de terremotos submarinos. Dicho comportamiento es estudiado por medio de la modelación de tsunamis generados por distintos tipos de fuentes sísmicas. Esto construyendo modelos de fallas finitas que permiten aislar los parámetros cinemáticos de las rupturas, para luego ser usados como entrada de la modelación de tsunamis. Los resultados muestran que desde el punto de vista cinemático las grandes amplitudes de tsunamis son una respuesta del agua a las bajas velocidades de ruptura, al tamaño de la columna de agua sobre la fuente y la ubicación del hipocentro en el plano de falla. Este estudio fue hecho considerando dos tipos de escenarios; se utilizó una batimetría simple, compuesta por un fondo plano y un talud que se eleva desde el fondo del mar hasta la costa y una batimetría realista del Norte de Chile, de iguar resolución espacial. Estas dos batimetrías contaron con dos superficies de falla asociadas; para el caso simple, se tuvo una superficie plana rectangular y para el caso del Norte de Chile, se construyeron muchos planos superpuestos sobre el slab en esa zona. Cada superficie de falla utilizó una distribución de slip uniforme y estocástica y para la simulación del terremoto se construyó un modelo cinemático de fuente que permitió controlar la velocidad de ruptura y el Rise Time. Entre los resultados obtenidos se destaca el hecho de que las bajas velocidades de ruptura pueden amplificar hasta 8 veces la altura del Run-Up, con respecto al caso de una fuente instantánea. También se observa que para velocidades lentas, el efecto de la directividad de la fuente controla la distribución espacial de las amplitudes del tsunami, haciendo que las mayores amplitudes del Run-Up se concentren en las costas más cercanas a la proyección horizontal de la dirección de propagación de la ruptura. También se observa que las amplitudes del tsunami dependen de la relación entre la velocidad de ruptura y la profundidad de la batimetría, por lo que se concluye que los terremotos tsunamigénicos de distintas partes del mundo logran excitar tsunamis que se propagan a diferentes velocidades de ruptura, dependiendo de la profundidad de la batimetría sobre la fuente. Finalmente, se observa que los terremotos tsunamigénicos que propagan sus rupturas con cambios abruptos de velocidad, de rápido a lento, logran amplificar la altura de los tsunamis más que las rupturas que se propagan a una velocidad constante.

This thesis examines the processes of longshore sediment transport in the swash zone of a mixed sand and gravel shoreline, Lake Coleridge, New Zealand. It focuses on the interactions between waves and currents in the swash zone and the resulting sediment transport. No previous study has attempted to concurrently measure wave and current data and longshore sediment transport rates on a mixed sand and gravel lakeshore beach in New Zealand. Many of these beaches, in both the oceanic and lacustrine environments, are in net long-term erosion. It is recognised that longshore sediment transport is a part of this process, but very little knowledge has existed regarding rates of sediment movement and the relationships between waves, currents and swash activity in the foreshore of these beach types. A field programme was designed to measure a comprehensive range of wind, wave, current and morphological variables concurrently with longshore transport. Four electronic instruments were used to measure both waves and currents simultaneously in the offshore, nearshore and swash zone. In the offshore area, an InterOcean S4ADW wave and current meter was installed to record wave height, period, direction and velocity. A WG-30 capacitance wave gauge measured the total water surface variation. A pair of Marsh-McBirney electromagnetic current meters, measuring current directions and velocities were installed in the nearshore and swash zone. Data were sampled for 18 minutes every hour with a Campbell Scientific CR23x data-logger. The wave gauge data was sampled at a rate of 10 Hz (0.1 s) and the two current meters at a rate of 2 Hz (0.5 s). Longshore sediment transport rates were investigated with the use of two traps placed in the nearshore and swash zone to collect sediment transported under wave and swash action. This occurred concurrently with the wave measurements and together yielded over 500 individual hours of high quality time series data. Important new insights were made into lake wave processes in New Zealand's alpine lakes. Measured wave heights averaged 0.20-0.35 m and ranged up to 0.85 m. Wave height was found to be strongly linked to the wind and grew rapidly to increasing wind strength in an exponential fashion. Wave period responded more slowly and required time and distance for the wave length to develop. Overall, there was a narrow band of wave periods with means ranging from 1.43 to 2.33 s. The wave spectrum was found to be more mixed and complicated than had previously been assumed for lake environments. Spectral band width parameters were large, with 95% of the values between 0.75 and 0.90. The wave regime attained the characteristics of a storm wave spectrum. The waves were characteristically steep and capable of obtaining far greater steepness than oceanic wind-waves. Values ranged from 0.010 to 0.074, with an average of 0.051. Waves were able to progress very close to shore without modification and broke in water less than 0.5 m deep. Wave refraction from deep to shallow water only caused wave angles to be altered in the order of 10%. The two main breaker types were spilling and plunging. However, rapid increases in beach slope near the shoreline often caused the waves to plunge immediately landward of the swash zone, leading to a greater proportion of plunging waves. Wave energy attenuation was found to be severe. Measured velocities were some 10 times less at two thirds the water depth beneath the wave. Mean orbital velocities were 0.30 m s⁻¹ in deep water and 0.15 m s⁻¹ in shallow water. The ratio difference between the measured deep water orbital velocities and the nearshore orbital velocities was just under one half (us/uo = 0.58), almost identical to the predicted phase velocity difference by Linear wave theory. In general Linear wave theory was found to provide good approximations of the wave conditions in a small lake environment. The swash zone is an important area of wave dissipation and it defines the limits of sediment transport. The width of the swash zone was found to be controlled by the wave height, which in turn determined the quantity of sediment transported through the swash zone. It ranged in width from 0.05 m to 6.0 m and widened landward in response to increased wave height and lakeward in response the wave length. Slope was found to be an important secondary control on swash zone width. In low energy conditions, swash zone slopes were typically steep. At the onset of wave activity the swash zone becomes scoured by swash activity and the beach slope grades down. An equation was developed, using the wave height and beach slope that provides close estimates of the swash zone width under a wide range of conditions. Run-up heights were calculated using the swash zone width and slope angle. Run-up elevations ranged from 0.01 m to 0.73 m and were strongly related to the wave height and the beach slope. On average, run-up exceeds the deep water wave height by a factor of 1.16H. The highest run-up elevations were found to occur at intermediate slope angles of between 6-8°. Above 8°, the run-up declined in response to beach porosity and lower wave energy conditions. A generalised run-up equation for lake environments has been developed, that takes into account the negative relationship between beach slope and run-up. Swash velocities averaged 0.30 m s⁻¹ but maximum velocities averaged 0.98 m s⁻¹. After wave breaking, swash velocities quickly reduced through dissipation by approximately one half. Swash velocity was strongly linked to wave height and beach slope. Maximum velocities occurred at beach slopes of 5°, where incident swash dominated. At slopes between 6° and 10°, swash velocities were hindered by turbulence, but the relative differences between the swash and backswash flows were negligible. At slope angles above 10° there was a slight asymmetry to the swash/backswash flow velocities due to beach porosity absorbing water at the limits of the swash zone. Three equations were developed for estimating the mean and maximum swash velocity flows. From an analysis of these interactions, a process-response model was developed that formalises the morphodynamic response of the swash zone to wave activity. Longshore sediment transport occurred exclusively in the swash zone, landward of the breaking wave in bedload. The sediments collected in transit were a heterogeneous mix of coarse sands and fine-large gravels. Hourly trapped rates ranged from 0.02 to 214.88 kg hr⁻¹. Numerical methods were developed to convert trapped mass rates in to volumetric rates that use the density and porosity of the sediment. A sediment transport flux curve was developed from measuring the distribution of longshore sediment transport across the swash zone. Using numerical integration, the area under this curve was calculated and an equation written to accurately estimate the total integrated transport rates in the swash zone. The total transport rates ranged from a minimum of 1.10 x 10-5 m³ hr⁻¹ to a maximum of 1.15 m³ hr⁻¹. The mean rate was 7.36 x 10⁻² m³ hr⁻¹. Sediment transport was found to be most strongly controlled by the wave height, period, wave steepness and mean swash velocity. Transport is initiated when waves break at an oblique angle to the shoreline. No relationships could be found between the grain size and transport rates. Instead, the critical threshold velocities of the sediment sizes were almost always exceed in the turbulent conditions under the breaking wave. The highest transport rates were associated with the lowest beach slopes. It was found that this was linked to swash high velocities and wave heights associated with foreshore scouring. An expression was developed to estimate the longshore sediment transport, termed the LEXSED formula, that divides the cube of the wave height and the wave length and multiplies this by the mean swash velocity and the wave approach angle. The expression performs well across a wide range of conditions and the estimates show very good correlations to the empirical data. LEXSED was used to calculate an accurate annual sediment transport budget for the fieldsite beaches. LEXSED was compared to 16 other longshore sediment transport formulas and performed best overall. The underlying principles of the model make its application to other mixed sand and gravel beaches promising.

Prior to the announcement of a merger or acquisition, the stock price of the target company often experiences a price run-up prior to the announcement of the transaction. This price run-up can be attributed to information leakage and insider trading. This paper examines how changes in the SEC’s budget effects the pre-announcement price run-up of mergers and acquisitions. Furthermore, this paper explores the political processes surrounding SEC budgeting, as well as flaws in the current system. This paper finds that with a $10 million increase in the SEC’s budget, the average pre-announcement run-up ratio decreases by 0.3%. The findings of this paper suggest a concrete means of reducing insider trading, dependent on an increase in SEC budget.

Cette thèse est divisée en quatre parties. Dans la première, je vais présenter notre travail sur le run-up des vagues longues et sur les phénomènes d’amplification par résonance. Grâce à des simulations numériques basées sur les équations en eau peu profonde non-linéaires, nous montrons que dans le cas des vagues monochromatiques d’incidence normale sur une plage inclinée, une amplification résonante du run-up se produit lorsque la longueur de la vague d’entrée est 5.2 fois plus grande que la longueur de la plage. Nous montrons également que cette amplification résonante de run-up peut être observée à partir de plusieurs profils de vagues. Cependant, l’amplification résonante du run-up n’est pas limitée aux plages inclinées infinies. En faisant varier le profil bathymétrique, la résonance est également présente dans le cas de bathymétries linéaires par morceaux et pour des bathymétries réalistes. Dans la deuxième partie, je présente une nouvelle solution analytique pour étudier la propagation des tsunamis générés par une source non ponctuelle sur une profondeur constante en utilisant la théorie des vagues en eau peu profonde linéaires. La solution, qui repose sur la séparation des variables et sur une double transformée de Fourier dans l’espace, est exacte, facile à mettre en œuvre et permet l’étude d’ondes de formes réalistes comme les ondes en forme de N (N–waves). Dans la troisième partie, j'étudie l’effet de protubérances localisées sur la génération de vagues longues. Même lorsque le déplacement final est connu grâce à l’analyse sismique, le plancher océanique qui se déforme peut avoir du relief comme des montagnes et des failles. On étudie analytiquement l’effet de la bathymétrie sur la génération des vagues de surface, en résolvant les équations en eau peu profonde linéaires avec for. Nous constatons que quand la hauteur du rebord augmente, le piégeage partiel de la vague permet de réduire la hauteur des vagues dans le champ lointain, tout en l’amplifiant au-dessus du rebord. Je vais aussi présenter brièvement une solution de la même équation forcée au-dessus d’un cône. Enfin, dans la dernière partie, nous verrons si les petites îles peuvent protéger les côtes proches de tsunamis comme il est largement admis par les communautés locales. Des découvertes récentes sur le tsunami des îles Mentawai en 2010 montrent un run-up amplifié sur les zones côtières derrière de petites îles, par rapport au run-up sur les lieux adjacents, qui ne sont pas influencés par la présence des îles. Nous allons étudier les conditions de cette amplification du run-up en résolvant numériquement les équations en eau peu profonde non-linaires. Le dispositif expérimental est régi par cinq paramètres physiques. L’objectif est double: Trouver l’amplification maximale du run-up avec un nombre minimum de simulations. Nous présentons un plan d’expériences actif, récemment mis au point et basé sur les processus Gaussiens, qui réduit considérablement le coût de calcul. Après exécution de deux cents simulations, nous constatons que dans aucun des cas considérés l’île n’offre une protection à la zone côtière derrière elle. Au contraire, nous avons mesuré une amplification du run-up sur la plage derrière elle par rapport à une position latérale sur la plage non directement affectée par la présence de l’île. Cette amplification a atteint un facteur maximal de 1.7. Ainsi, les petites îles à proximité du territoire continental agissent comme des amplificateurs des vagues longues dans la région directement derrière elles et non comme des obstacles naturels comme il était communément admis jusqu’ici. / This thesis is divided in four parts. In the first one I will present our work on long wave run-up and some resonant amplification phenomena. With the use of numerical simulations for the nonlinear shallow water equations, we show that in the case of monochromatic waves normally incident on a plane beach, resonant run-up amplification occurs when the incoming wavelength is 5.2 times larger the beach length. We also show that this resonant run-up amplification can be observed for several wave profiles such as bichromatic, polychromatic and cnoidal. However, resonant run-up amplification is not restricted to infinitely sloping beaches. We varied the bathymetric profile, and we saw that resonance is present in the case of piecewise linear and real bathymetries. In the second part I will present a new analytical solution to study the propagation of tsunamis from a finite strip source over constant depth using linear shallow-water wave theory. The solution, which is based on separation of variables and a double Fourier transform in space, is exact, easy to implement and allows the study of realistic waveforms such as N-waves. In the third part I will explore the effect of localized bathymetric features on long wave generation. Even when the final displacement is known from seismic analysis, the deforming seafloor includes relief features such as mounts and trenches. We investigate analytically the effect of bathymetry on the surface wave generation, by solving the forced linear shallow water equation. Our model for bathymetry consists of a cylindrical sill on a flat bottom, to help understand the effect of seamounts on tsunami generation. We derive the same solution by applying both the Laplace and the Fourier transforms in time. We find that as the sill height increases, partial wave trapping reduces the wave height in the far field, while amplifying it above the sill. Finally, in the last part I will try to explore whether small islands can protect nearby coasts from tsunamis as it is widely believed by local communities. Recent findings for the 2010 Mentawai Islands tsunami show amplified run-up on coastal areas behind small islands, compared with the run-up on adjacent locations, not influenced by the presence of the islands. We will investigate the conditions for this run-up amplification by numerically solving the nonlinear shallow water equations. Our bathymetric setup consists of a conical island sitting on a flat bed in front of a plane beach and we send normally incident single waves. The experimental setup is governed by five physical parameters. The objective is twofold: Find the maximum run-up amplification with the least number of simulations. Given that our input space is five-dimensional and a normal grid approach would be prohibitively computationally expensive, we present a recently developed active experimental design strategy, based on Gaussian Processes, which significantly reduces the computational cost. After running two hundred simulations, we find that in none of the cases considered the island did offer protection to the coastal area behind it. On the contrary, we have measured run-up amplification on the beach behind it compared to a lateral location on the beach, not directly affected by the presence of the island, which reached a maximum factor of 1.7. Thus, small islands in the vicinity of the mainland will act as amplifiers of long wave severity at the region directly behind them and not as natural barriers as it was commonly believed so far.

This thesis examines the processes of longshore sediment transport in the swash zone of a mixed sand and gravel shoreline, Lake Coleridge, New Zealand. It focuses on the interactions between waves and currents in the swash zone and the resulting sediment transport. No previous study has attempted to concurrently measure wave and current data and longshore sediment transport rates on a mixed sand and gravel lakeshore beach in New Zealand. Many of these beaches, in both the oceanic and lacustrine environments, are in net long-term erosion. It is recognised that longshore sediment transport is a part of this process, but very little knowledge has existed regarding rates of sediment movement and the relationships between waves, currents and swash activity in the foreshore of these beach types. A field programme was designed to measure a comprehensive range of wind, wave, current and morphological variables concurrently with longshore transport. Four electronic instruments were used to measure both waves and currents simultaneously in the offshore, nearshore and swash zone. In the offshore area, an InterOcean S4ADW wave and current meter was installed to record wave height, period, direction and velocity. A WG-30 capacitance wave gauge measured the total water surface variation. A pair of Marsh-McBirney electromagnetic current meters, measuring current directions and velocities were installed in the nearshore and swash zone. Data were sampled for 18 minutes every hour with a Campbell Scientific CR23x data-logger. The wave gauge data was sampled at a rate of 10 Hz (0.1 s) and the two current meters at a rate of 2 Hz (0.5 s). Longshore sediment transport rates were investigated with the use of two traps placed in the nearshore and swash zone to collect sediment transported under wave and swash action. This occurred concurrently with the wave measurements and together yielded over 500 individual hours of high quality time series data. Important new insights were made into lake wave processes in New Zealand's alpine lakes. Measured wave heights averaged 0.20-0.35 m and ranged up to 0.85 m. Wave height was found to be strongly linked to the wind and grew rapidly to increasing wind strength in an exponential fashion. Wave period responded more slowly and required time and distance for the wave length to develop. Overall, there was a narrow band of wave periods with means ranging from 1.43 to 2.33 s. The wave spectrum was found to be more mixed and complicated than had previously been assumed for lake environments. Spectral band width parameters were large, with 95% of the values between 0.75 and 0.90. The wave regime attained the characteristics of a storm wave spectrum. The waves were characteristically steep and capable of obtaining far greater steepness than oceanic wind-waves. Values ranged from 0.010 to 0.074, with an average of 0.051. Waves were able to progress very close to shore without modification and broke in water less than 0.5 m deep. Wave refraction from deep to shallow water only caused wave angles to be altered in the order of 10%. The two main breaker types were spilling and plunging. However, rapid increases in beach slope near the shoreline often caused the waves to plunge immediately landward of the swash zone, leading to a greater proportion of plunging waves. Wave energy attenuation was found to be severe. Measured velocities were some 10 times less at two thirds the water depth beneath the wave. Mean orbital velocities were 0.30 m s⁻¹ in deep water and 0.15 m s⁻¹ in shallow water. The ratio difference between the measured deep water orbital velocities and the nearshore orbital velocities was just under one half (us/uo = 0.58), almost identical to the predicted phase velocity difference by Linear wave theory. In general Linear wave theory was found to provide good approximations of the wave conditions in a small lake environment. The swash zone is an important area of wave dissipation and it defines the limits of sediment transport. The width of the swash zone was found to be controlled by the wave height, which in turn determined the quantity of sediment transported through the swash zone. It ranged in width from 0.05 m to 6.0 m and widened landward in response to increased wave height and lakeward in response the wave length. Slope was found to be an important secondary control on swash zone width. In low energy conditions, swash zone slopes were typically steep. At the onset of wave activity the swash zone becomes scoured by swash activity and the beach slope grades down. An equation was developed, using the wave height and beach slope that provides close estimates of the swash zone width under a wide range of conditions. Run-up heights were calculated using the swash zone width and slope angle. Run-up elevations ranged from 0.01 m to 0.73 m and were strongly related to the wave height and the beach slope. On average, run-up exceeds the deep water wave height by a factor of 1.16H. The highest run-up elevations were found to occur at intermediate slope angles of between 6-8°. Above 8°, the run-up declined in response to beach porosity and lower wave energy conditions. A generalised run-up equation for lake environments has been developed, that takes into account the negative relationship between beach slope and run-up. Swash velocities averaged 0.30 m s⁻¹ but maximum velocities averaged 0.98 m s⁻¹. After wave breaking, swash velocities quickly reduced through dissipation by approximately one half. Swash velocity was strongly linked to wave height and beach slope. Maximum velocities occurred at beach slopes of 5°, where incident swash dominated. At slopes between 6° and 10°, swash velocities were hindered by turbulence, but the relative differences between the swash and backswash flows were negligible. At slope angles above 10° there was a slight asymmetry to the swash/backswash flow velocities due to beach porosity absorbing water at the limits of the swash zone. Three equations were developed for estimating the mean and maximum swash velocity flows. From an analysis of these interactions, a process-response model was developed that formalises the morphodynamic response of the swash zone to wave activity. Longshore sediment transport occurred exclusively in the swash zone, landward of the breaking wave in bedload. The sediments collected in transit were a heterogeneous mix of coarse sands and fine-large gravels. Hourly trapped rates ranged from 0.02 to 214.88 kg hr⁻¹. Numerical methods were developed to convert trapped mass rates in to volumetric rates that use the density and porosity of the sediment. A sediment transport flux curve was developed from measuring the distribution of longshore sediment transport across the swash zone. Using numerical integration, the area under this curve was calculated and an equation written to accurately estimate the total integrated transport rates in the swash zone. The total transport rates ranged from a minimum of 1.10 x 10-5 m³ hr⁻¹ to a maximum of 1.15 m³ hr⁻¹. The mean rate was 7.36 x 10⁻² m³ hr⁻¹. Sediment transport was found to be most strongly controlled by the wave height, period, wave steepness and mean swash velocity. Transport is initiated when waves break at an oblique angle to the shoreline. No relationships could be found between the grain size and transport rates. Instead, the critical threshold velocities of the sediment sizes were almost always exceed in the turbulent conditions under the breaking wave. The highest transport rates were associated with the lowest beach slopes. It was found that this was linked to swash high velocities and wave heights associated with foreshore scouring. An expression was developed to estimate the longshore sediment transport, termed the LEXSED formula, that divides the cube of the wave height and the wave length and multiplies this by the mean swash velocity and the wave approach angle. The expression performs well across a wide range of conditions and the estimates show very good correlations to the empirical data. LEXSED was used to calculate an accurate annual sediment transport budget for the fieldsite beaches. LEXSED was compared to 16 other longshore sediment transport formulas and performed best overall. The underlying principles of the model make its application to other mixed sand and gravel beaches promising.

Este trabalho apresenta o cálculo da cota de inundação para a Enseada do Itapocorói e para a praia de Morro dos Conventos, litoral do Estado de Santa Catarina. Para atingir os objetivos desse trabalho, a cota de inundação foi calculada através da soma das marés meteorológica e astronômica e do wave run-up. Foi utilizada uma base de 60 anos (horária) de dados de marés e ondas, além de dados de batimetria e topografia das praias. Com o intuito de se obter dados mais realistas do wave run-up, os parâmetros ondulatórios da base de dados foram transferidos de águas profundas para próximo da costa com a utilização do modelo SWAN (Simulating Waves Nearshore). A Enseada do Itapocorói foi dividida em quatro setores (exposto, semiexposto, semiprotegido e protegido) em função dos diferentes graus de exposição à ação de ondas, sendo as equações calibradas para cada setor. A partir dos resultados para Enseada do Itapocorói, notou-se que quanto mais exposta a praia, melhor as equações existentes representavam o wave run-up, assim, para a praia de Morro dos Conventos foi utilizada a equação mais aceita na literatura sem calibração. A cota de inundação instantânea foi calculada para cada hora da série de 60 anos somando-se o wave run-up às marés astronômicas e meteorológicas. Sobre a série de cota de inundação instantânea, para ambas as áreas, foi calculada a cota atingida durante 50% do tempo e por eventos extremos com recorrência de 50, 100 e 200 anos. A estas foi adicionada a previsão de elevação do nível do mar de longo prazo para o mesmo período. A cota atingida durante 50% do tempo na Enseada do Itapocorói foi de 1,35 m no setor exposto, enquanto nos setores semiexposto, semiprotegido e protegido foi de 1 m, 0,9 m e 0,7 m respectivamente. Também, o setor exposto foi o que apresentou as maiores cotas atingidas, sendo 3,45 m, 3,85 m e 4,45 m com tempo de recorrência de 50,100 e 200 anos respectivamente. No setor semiexposto, os valores calculados foram de 2,85 m (50 anos), 3,25 m (100 anos) e 3,9 m (200 anos). No setor semiprotegido, as cotas com tempo de recorrência de 50, 100 e 200 anos foram de 2,65 m, 3,05 m, 3,75 m respectivamente. Já o setor protegido apresentou as menores cotas entre os setores, 2,4 m, 2,85 m e 3,5 m para 50, 100 e 200 anos de tempo de recorrência. Considerando a extensão da área costeira que possui um levantamento de topografia do terreno, 2,4 % da área é inundada durante 50% do tempo, subindo para 26%, 29% e 33% nos casos de recorrência com 50, 100 e 200 anos. A cota atingida na praia de Morro dos Conventos durante 50% do tempo é de 1,1 m, já as cotas calculadas para os tempos de recorrência de 50, 100 e 200 anos foram de 4,2 m, 4,6 m e 5,35 m respectivamente. E, da mesma forma, a área costeira com levantamento topográfico teve 15% de superfície é inundada em 50% do tempo, passando para 85%, 91% e 96% da área total analisada com 50, 100 e 200 anos de tempo de recorrência. A metodologia proposta neste trabalho contribui para o planejamento de zonas costeiras, à medida que indica áreas afetadas por inundação aos eventos extremos. A apresentação de cartas contendo esse tipo de informação em ambiente de SIG facilita a tomada de decisão e o entendimento da área por determinado evento extremo. / The goal of this study is to determine the inundation levels at Ensenada do Itapocorói and Morro dos Conventos beaches, located in Santa Catarina State. This was accomplished through the calculation of the inundation level as the sum of astronomical and meteorological tides and wave run-up. The database for this study included -60 years of hourly waves and tides, bathymetric and topographic data. The instantaneous sea level has been defined for each hour of the data series through the summation of astronomical and meteorological tides. To determine more realistic wave run-up data, the wave parameters have been propagated to shallower water using the SWAN (Simulating WAves Nearshore) model. Published equations were used and results were compared with measured data at a headland bay beach (Enseada do Itapocorói); furthermore, the equations have been calibrated for four sectors of the bay (exposed, semi-exposed, semi-protected and protected). Morro dos Conventos is an exposed beach, comparable to those for which the equations have been developed, so the raw, un-calibrated equations were applied for this site. The inundation level was calculated for each hour of the 60 year-long series by summing the run-up values to obtain the instantaneous level. Over the series of inundation levels, the area inundated during 50% of the time, and the return period for this inundation, have been calculated for 50, 100 and 200 years. The sea-level rise prediction for each calculated period has also been incorporated in order estimate the area likely to be inundated by future events. For Enseada do Itapocorói, the inundation level reached 50% of the time was 1,35 m in the exposed sector, 1 m in the semi-exposed sector, 0,9 m in the semi-protected sector and 0,7 in the protected sector. The exposed sector demonstrated the highest values of inundation, 3,45, 3,85 and 4,5 m for 50, 100 and 200 years of return period respectively. At the semi-exposed sector, the values calculated were 2,85 (50 years), 3,25 (100 years) and 3,9 (200 years) m. At semi-protected sector, inundation levels for the 50-, 100- and 200-year return period intervals were 2,65, 3,05 and 3,75 m, respectively. At the protected sector the lowest levels were reached: 2,4, 2,85 and 3,5 m for 50-, 100- and 200-year return period intervals. 2,4% of the total area for which topographic data is available would be inundated during 50% of the time, increasing to 26%, 29% and 33% for 50-, 100- and 200-year return periods. At Morro dos Conventos, the level of inundation reaches 1,1 m 50% of the time;, for 50,100 and 200 years the level rises to 4,2, 4,6 and 5,36 m respectively. Approximately 15% of the area for which topographic data is available would be area is inundated during 50% of the time, 85% with a 50 year return period, 91% with a 100-year period and 96% with a 200 year period.