[Truncated abstract] Observations are presented from Lake Biwa (Japan) and Lake Kinneret (Israel) showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode one solitary waves with wavelength ˜100-500 m and frequency near 103 Hz and (2) sinusoidal vertical mode one waves with wavelength ˜5-30 m and frequency just below the local maximum buoyancy frequency near 102 Hz. The sinusoidal waves were associated with shear instability and were shown to dissipate their energy sporadically within the lake interior. Conversely, the solitary waves were found to be capable of propagating to the lake perimeter where they may break upon sloping topography, each releasing ˜1% of the total basin-scale internal wave energy to the benthic boundary layer.

Department of Civil, Surveying and Environmental Engineering. Bibliography: leaves 246-255

Dans ce travail nous nous intéressons aux comportement de vagues soumises à l’action d’une pression atmosphérique non constante, un fond mobile et la force de Coriolis. Une première partie est dédiée à l’étude de la résonance de Proudman. Nous proposons une approche mathématique rigoureuse pour étudier ce phénomène. Nous commençons par démontrer un résultat d’existence locale dans un cadre irrotationnel sur les équations des vagues (appelées aussi formulation de Zakharov/Craig-Sulem). Puis, nous justifions différents modèles asymptotiques pour généraliser cette résonance dans diverses situations physiques. Nous proposons en particulier une étude détaillée dans des eaux profondes dans un régime linéaire. Nous étudions aussi la propagation de vagues dans des eaux profondes dans un régime faiblement non-linéaire grâce aux équations de Saut-Xu et nous proposons un schéma numérique pour résoudre ces équations. Dans une deuxième partie, nous étudions l’effet de la force de Coriolis sur les vagues. Nous démontrons un résultat d’existence locale sur les équations Castro-Lannes, équations qui généralisent la formulation de Zakharov/Craig-Sulem dans un cadre rotationnel. Nous justifions ensuite différents modèles asymptotiques dans des eaux peu profondes en présence de la force de Coriolis. En particulier, nous proposons une généralisation des équations de Boussinesq (modèle asymptotique dans un régime faiblement linéaire) lorsque la force de Coriolis n’est pas négligeable. Ces équations nous permettent ensuite de justifier mathématiquement les ondes de Poincaré puis l’équation d’Ostrovsky qui généralise l’équation de Korteweg-De-Vries en présence de la force de Coriolis. / In this work, we are interested in the evolution of water waves under the influence of a non constant atmospheric pressure, a moving bottom and a Coriolis forcing. In a first part, we study the Proudman resonance. We propose a mathematical approach to understand this phenomenon. First, we prove a local wellposedness result in a irrotational framework on the water waves equations (also called the Zakharov/Craig-Sulem formulation). Then, we fully justify different asymptotic models. In particular, we carefully study the Proudman resonance in deep water in the linear regime. Finally, we study the propagation of water waves in a weakly nonlinear regime thanks to the Saut-Xu equations and we propose a numerical scheme in order to solve these equations. In a second part, we study the influence of a Coriolis forcing on water waves. We prove a local wellposedness result on the Castro-Lannes equations, which generalize the Zakharov/Craig-Sulem formulation in the rotational framework. Then, we fully justify different asymptotic models when we take into account a Coriolis forcing. In particular, we generalize the Boussinesq equations (asymptotic model in a weakly nonlinear regime) in this setting. Thanks to these equations, we justify the Poincaré waves and then the Ostrovsky equation, which generalize the Korteweg-De- Vries equation when a Coriolis forcing is taking into account.

Low-frequency, long-range sound propagation over a seasurface has been calculated using a wide-angel Cranck-NicholsonParabolic Equation method. The model is developed toinvestigate noise from off-shore wind turbines. Thecalculations are made using normal meteorological conditions ofthe Baltic Sea. Special consideration has been made to a windphenomenon called low level jet with strong winds on rather lowaltitude. The effects of water waves on sound propagation have beenincorporated in the ground boundary condition using a bossmodel. This way of including roughness in sound propagationmodels is valid for water wave heights that are small comparedto the wave length of the sound. Nevertheless, since only lowfrequency sound is considered, waves up to the mean wave heightof the Baltic Sea can be included in this manner. The calculation model has been tested against benchmarkcases and agrees well with measurements. The calculations showthat channelling of sound occurs at downwind conditions andthat the sound propagation tends towards cylindrical spreading.The effects of the water waves are found to be fairlysmall. Keywords:wind turbine noise, off-shore wind power,long-range sound propagation, parabolic equation, scattering,water waves / QC 20110617

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Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: When a sailing ship passes a moored ship the moored ship experiences forces and moments. These forces and moments cause the moored ship to move. The resulting ship motions due to the passing ship can sometimes be more severe than the ship motions due to ocean waves and can cause serious accidents at moorings such as the failing of mooring lines or even the total break away of the ship from the berth. Since bulk carriers and tankers were traditionally the largest seafaring ships, passing ship studies have focused mainly on these vessels, but recently container ships have grown to a comparable size. In this study an existing numerical model “Passcat” is validated with physical model measurements for a Post Panamax container ship passing a Panamax bulk carrier. Other existing mathematical formulae are also evaluated by comparison with these model tests. In the physical model tests the passing speed (V), passing distance (G), depth draft ratio (d/D) and the presence of walls and channels were varied. It was found that the passing ship forces are proportional to the passing speed to the power of 2.32. This is slightly higher than the generally accepted quadratic relationship for passing ship induced forces. Similar relationships were found for the other variables. The numerical model results were compared to the physical model measurements by determining agreement ratios. A perfect agreement between the numerical and physical models would result in an agreement ratio of 1. Agreement ratio boundaries, wherein agreement would be regarded as good, were drawn between 0.7 and 1.3. The numerical model, Passcat, was found to under predict the passing ship forces. It was found that Passcat is valid for a wide range of sensitivities and remains within the agreement ratio limits as long as passing speed is limited to 10 knots (kt), depth draft ratio to more than 1.164, passing distance to less than four times the moored ship beam (Bm) for surge and sway estimation and passing distance to less than three times the moored ship beam for yaw estimations. These limits are true for no structures in the water. For structures in the water only the passing speed limits are different. When quay walls are present, the surge and sway forces will only provide acceptable answers at passing speeds below 9kt. When 9Bm or 12Bm channels are present, the sway force will only provide acceptable answers at passing speeds below 7kt. When a 6Bm channel is present, the yaw moments will only provide acceptable answers at passing speeds below 6kt. From the mathematical model evaluation study it was found that empirical or semi empirical methods can not provide answers with good agreement to the physical model when walls or channels are present. For the open water case, it is only the Flory method that can provide answers with good agreement to the physical model for surge, sway and yaw forces. The Flory method can provide answers with acceptable agreement within narrow boundaries of passing distance (1 to 2 times the beam of the moored ship), passing speed (4 kt to 14 kt) and depth draft ratio (less than 1.7). The numerical model, Passcat can be used with little effort to provide answers with better agreement to the physical model for a larger range of variables. / AFRIKAANSE OPSOMMING: Wanneer ’n skip verby ‘n vasgemeerde skip vaar, ondervind die vasgemeerde skip kragte en momente. Hierdie kragte induseer beweging van die vasgemeerde skip. Die beweging kan soms groter wees as die effek van wind of golwe. Indien die bewegings groot genoeg is kan dit van die vasmeer lyne van die skip laat breek, of al die lyne laat breek sodat die skip vry in die hawe ronddryf. Aangesien erts skepe en tenk skepe vir jare die grootste skepe in the wêreld was, het die meeste van die skip interaksie studies op daardie skepe gefokus. Die grootte van behouering skepe het egter in die onlangse tye gegroei om dimensies soortgelyk aan die van erts en tenk skepe te hê. In hierdie studie word ’n bestaande numeriese model “Passcat” gestaaf met fisiese model metings op ’n Post Panamax behoueringskip wat verby ‘n Panamax erts skip vaar. Bestaande wiskundige formules is ook getoets deur dit met dieselfde fisiese model metings te vergelyk. In die fisiese model studie is die spoed van die skip (V), tussenafstand (G), diepte diepgang verhouding (d/D) en die teenwoordigheid van kaai mure en kanale in die water getoets. Daar is gevind dat die kragte op die vasgemeerde skip direk eweredig is aan die spoed van die skip tot die mag 2.32. Dit is effens meer as die algemeen aanvaarde kwadratiese verhouding tussen vloeistof sleurkrag en vloeisnelheid asook tussen skip interaksie kragte en vaar snelheid. Soortgelyke verhoudings is vir al die veranderlikes bereken. Numeriese model resultate is vergelyk met die fisiese model om die verhouding van ooreenstemming te bepaal. ’n Perfekte ooreenstemming word voorgestel deur ’n verhouding van ooreenstemming van 1. Grense waarbinne die verhouding van ooreenstemming as goed beskou word is getrek tussen 0.7 en 1.3. Daar is gevind dat die numeriese model, Passcat, kragte oor die algemeen onderskat. Passcat is geldig vir 'n breë reeks van veranderlikes en sal geldig bly solank die skip spoed tot 10 knope, diepte diepgang verhouding tot meer as 1.164, tussenafstand tot minder as vier skipwydtes (Bm) vir 'surge' en 'sway' kragte en tot minder as drie skipwydtes vir 'yaw' momente beperk word. Hierdie grense is opgestel vir geen strukture in die water. Vir strukture in die water word slegs die skip spoed aangepas. Wanneer daar mure in die water is sal 'surge' en 'sway' slegs geskikte antwoorde gee as die skip spoed tot 9 knope beperk word. Vir 9Bm of 12Bm kanale sal geskikte antwoorde vir 'sway' kragte slegs voorkom met 'n skip spoed minder as 7 knope. Vir 6Bm kanale sal geskikte antwoorde vir 'yaw' momente slegs voorkom met 'n skip spoed van minder as 6 knope. Van die wiskundige model evaluasie studie is gevind dat empiriese of semi empiriese metodes nie resultate met goeie ooreenstemming tot the fisiese model metings kan gee, wanneer daar kaai of kanaal mure in die water is nie. Vir die oopwater geval is dit slegs die Flory metode wat antwoorde kan voorsien wat goed ooreenstem met die fisiese model vir 'surge', 'sway', en 'yaw' kragte. Die Flory metode voorsien hierdie resultate binne noue grense vir tussenafstand (1 tot 2 wydtes van die vasgemeerde skip), verbyvaar spoed (4 knope tot 14 knope) en diepte diepgang verhouding (minder as 1.7). Die numeriese model, Passcat, kan met min moeite antwoorde bereken wat beter ooreenstemming vir 'n groter reeks veranderlikes gee.

When traditional linearised theory is used to study free-surface flows past a surface-piercing object or over an obstruction in a stream, the geometry of the object is usually lost, having been assumed small in one or several of its dimensions. In order to preserve the nonlinear nature of the geometry, asymptotic expansions in the low-Froude or low-Bond limits can be derived, but here, the solution invariably predicts a waveless free-surface at every order. This is because the waves are in fact, exponentially small, and thus beyond-all-orders of regular asymptotics; their formation is a consequence of the divergence of the asymptotic series and the associated Stokes Phenomenon. In this thesis, we will apply exponential asymptotics to the study of two new problems involving nonlinear geometries. In the first, we examine the case of free-surface flow over a step including the effects of both gravity and surface tension. Here, we shall see that the availability of multiple singularities in the geometry, coupled with the interplay of gravitational and cohesive effects, leads to the discovery of a remarkable new set of solutions. In the second problem, we study the waves produced by bluff-bodied ships in low-Froude flows. We will derive the analytical form of the exponentially small waves for a wide range of hull geometries, including single-cornered and multi-cornered ships, and then provide comparisons with numerical computations. A particularly significant result is our confirmation of the thirty-year old conjecture by Vanden-Broeck & Tuck (1977) regarding the impossibility of waveless single-cornered ships.

O conhecimento de zonas potencialmente instáveis no fundo do mar é de fundamental importância para o desenvolvimento das estruturas marinhas, pois permite posicionar estruturas offshore em áreas mais seguras, reduzindo-se possíveis danos, custos e eventual poluição ambiental. Nesse contexto, o objetivo do presente trabalho é investigar, através de uma abordagem analítico-numérica, a estabilidade de maciços submarinos submetidos ao carregamento cíclico da onda. O efeito das ondas de água sobre o leito submerso é descrito pela propagação de uma onda de pressão ao longo de sua superfície, empregando-se a teoria linear de Stokes. São considerados maciços com superfície superior horizontal e inclinada, constituídos por material coesivo (argilas) e material granular (areias). Em maciços constituídos por solos finos, a capacidade resistente do material é modelada pelo critério de Tresca não-homogêneo e a análise da estabilidade é desenvolvida em condição não drenada. Por outro lado, em leitos granulares, a resistência do meio depende explicitamente do valor da poropressão, sendo descrita classicamente pelo critério de Coulomb sem coesão. A análise de estabilidade é então desenvolvida em tensões efetivas e o gradiente de poropressão atua como uma força volumétrica sobre o esqueleto, caracterizando o modo de carregamento principal deste material. Em razão da tendência a se densificar quando submetido a um estado de tensões desviadoras cíclicas, ocorre, em geral, a acumulação de excesso de poropressão no maciço granular. Consequentemente, o acoplamento entre o comportamento do material e o carregamento cíclico tem fundamental importância sobre o cálculo do excesso de poropressão desenvolvido. Para determinação das forças de percolação, considera-se uma abordagem simplificada baseada na partição das deformações em contribuições reversível e irreversível, que permite desacoplar o cálculo da pressão intersticial induzida pela onda. Aplicando-se conceitos da teoria da Análise Limite é possível formular limites inferiores e superiores da máxima amplitude segura do carregamento da onda. Finalmente, os efeitos da declividade da superfície do leito e da espessura de camada de solo sobre a estabilidade são analisados. / The knowledge of potentially unstable areas on the seabed is of fundamental importance to the development of marine structures, because it allows to install offshore structures in safer areas, reducing possible damages, costs and eventual environmental pollution. In this context, the objective of the present work is to investigate the stability of submarine soil masses subjected to the wave cyclic loading through analytical-numerical approaches. The effect of water waves on the submerged bed is described by the propagation of a pressure wave along its surface, using the Stokes’s linear theory. Soil masses with horizontal and sloped upper surface, composed of cohesive material (clays) and granular materiais (sands) are considered in this study. In soil masses constituted of fine soil, the material strength capacity is modeled by the non-homogeneous Tresca criterion and the stability analysis is carried out in undrained condition. On the other hand, in granular beds, the strength explicitly depends on the pore pressure value, being classically described by the Coulomb criterion without cohesion. Then, the stability analysis is developed in effective stress and the pore pressure gradient acts as a volumetric force on the skeleton, characterizing the main charging mode of this material. Due to the tendency to densify when subjected to a cyclic deviatoric stress state occurs, in general, the build-up of pore pressure excess in the granular mass. Consequently, the coupling between the material behavior and the cyclic loading has fundamental importance in the calculation of the pore pressure excess generated. In order to define the seepage forces, a simplified approach based on the partition of deformations in reversible and irreversible contributions is considered, which allows to decouple the wave-induced pore pressure calculation. Applying the concepts of the limit analysis theory it is possible to formulate upper and lower boundaries of the maximum safe amplitude of the wave loading. Finally, the effects of the seabed surface steepness and of the soil layer thickness on the stability are analyzed.

Since 2004 there have been multiple devastating tsunamis around the globe triggered by large magnitude earthquakes; with the most recent being the Tohoku, Japan tsunami in March 2011. These tsunamis have caused significant loss of life and damage to the coastal communities impacted by these powerful waves. The resulting devastation has raised awareness of the dangers of tsunamis and the Network for Earthquake Engineering Simulation (NEES) housesmash project (NEEShousesmash), was started to investigate several different areas of tsunami inundation. The work presented in the following two manuscripts was performed at the O.H. Hinsdale Wave Lab and Gene D. Knudson Wood Engineering Lab, which are located at Oregon State University. This work represents a small portion of the total NEEShousesmash project, and is focused on improving the knowledge and predictability of tsunami loading and structural performance. The first manuscript investigates tsunami wave impact on full scale light-frame wood walls, and compares the measured forces to calculated values using the linear momentum equation, previously evaluated by Cross (1967). The results show for each wave height tested a peak transient force followed by a sustained quasi-static force, with a ratio of transient force to quasi-static force of 2.2. The results also show that the linear momentum equation did an acceptable job of predicting the measured transient forces on the walls to within ±10%, and that increased wall flexibility, 2x4 vs. 2x6 dimensional lumber, resulted in lower measured transient forces when subjected to similar tsunami wave heights. These results are important for practical use because the linear momentum equation is a simple equation to use, that only requires a couple of site specific input variables. The second manuscript is a continuation of the work done in the wave lab for the first manuscript. These experiments provide a starting point for expanding the testing of the structural response and performance of larger scale structures subjected to tsunami wave loads. By simulating tsunami loading in a traditional structures laboratory, the inherent limits of testing structural performance in small scale tsunami laboratory facilities is removed. The results show that a light-frame wood shear wall, built to current standards, is susceptible to premature failures from concentrated impact loads at intermediate heights compared to the design strength at full height. It is also shown that the out-of-plane walls subjected to both elastic and inelastic loads behave like a one way slab with minimal load sharing between adjacent studs. The failures observed during the hydrodynamic wave testing of the nailed connection between the bottom plate and studs was successfully reproduced, and shows that current construction standards are not fully utilizing the available capacity of each stud when subjected to tsunami waves. The reinforcement of this connection with traditional metal brackets would help increase the capacity of the out-of-plane wall to resist tsunami wave loads. / Graduation date: 2012