This thesis proposes an improvement to present near-shore wave prediction models. Using weakly dispersive Boussinesq theory, the shoaling of directionally spread surface gravity waves over a beach with gentle gradients in the cross-shore and alongshore directions is examined. Following Herbers and Burton (1997), the governing fluid flow equations are expanded to third order and depth-integrated over the water column. A resulting amplitude evolution equation for a spectrum of waves is derived, which is the main result of this paper. New terms in the higher order result include effects due to alongshore bottom slope, higher order cross-shore depth variations, and non-linear quartet interactions. The linear terms in this equation are verified by analytical methods using linear finite depth theory. Example computations for a monochromatic wave train over a plane beach quantify some of the improvements of this result over the lower order model. Opportunities for further development and verification of this result are proposed, and recommendations for application of the result in its present form are outlined. / US Navy (USN) author

This dissertation presents the development of a novel hybrid wave model, comprised of the irrotational, 1-D horizontal Boussinesq and 2-D vertical turbulence-closed Reynolds Averaged Navier-Stokes (RANS) wave models. The two constituents are two-way coupled with the interface placed at a location where turbulence is relatively small. Boundary conditions on the interfacing side of each model is provided by its counterpart model through data exchange, requiring certain transformation due to the difference in physical variables employed in both models. The model is intended for large-scale wave simulation, accurate in both the nonbreaking and breaking zones with relatively coarser grid in the former and finer in latter, and yet efficient. Hybrid model tests against idealized solitary and standing wave motions and wave-overtopping on structure exhibit satisfactory to very good agreement. Compared with pure RANS simulations, the hybrid model saves computational time by a factor proportional to the reduction in the size of the RANS domain. Also, a large-scale tsunami simulation is provided for a numerical setup that is practically unapproachable using RANS alone; not only does the hybrid model offer more rapid simulation of relatively small-scale problems, it provides an opportunity to examine very large total domains with the fine resolution typical of RANS simulations. To allow for implementation on even larger domain with affordable CPU time, the hybrid model is parallelized to run on distributed memory machine. This is done by parallelizing the RANS model while leaving the Boussinesq model serial. One of the processors is responsible for both the sub-RANS and Boussinesq calculations. ICCG(0) for solving the pressure equation is parallelized using the nonoverlappingdecomposition technique, requiring more iterations than the serial one. Standing wave and hypothetical tsunami simulations with 960×66 and 1000×100 grids, and using 8 processors confirm model validity and computational efficiency of 82% and 65%. Finally, the 2-D Boussinesq model is parallelized using domain decomposition technique. The solution to the tridiagonal system arising in the model is calculated as the sum of the homogeneous and particular solutions. Parallel model tests using up to 32 processors exhibit model accuracy and efficiency of 80% for simulation with 500×500–2000×2000 grids.

Thesis (M.S. in Meteorology and Physical Oceanography)--Naval Postgraduate School, Sept. 2001. / Thesis advisor, Herbers, Thomas H.C. "September 2001." Includes bibliographical references (p. 47-48). Also available in print.

The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail. First, a fluid layer is placed between rigid boundaries and heated from below to yield the chaotic dynamics of thermal convection rolls (Rayleigh-Bénard convection). Second is a free-surface fluid layer placed on a shaker to yield nonlinear surface waves (Faraday waves). In both cases the full governing partial differential equations are solved using parallel spectral element methods. Rayleigh-Bénard convection is studied in a cylindrical dish with realistic boundaries. The complete flow field is obtained as well as the spectrum of Lyapunov exponents and Lyapunov vectors. The Lyapunov exponents and their corresponding perturbation fields are used to determine when and where events occur that contribute most to the chaotic dynamics. Roll pinch-off and roll mergers are found to be the largest contributors. Two dimensional and three dimensional Faraday waves are studied with periodic boundary conditions. The full Navier-Stokes equations are solved including the complex dynamics of the free surface waves to gain a better understanding of the interplay between the viscous boundary layers, the nonlinear streaming flow, and the bulk flow. The vortices in the bulk flow are weak compared to the flow in the viscous boundary layers. The surface waves are found to be non-sinusoidal and the time evolution of the waves are explored for both large and small amplitude waves. / Master of Science

Ce travail traite du ballottement d'un fluide dans une cuve rectangulaire en mouvement et du couplage avec un corps flottant. Nous exposons premièrement une théorie linéaire basée sur la décomposition des mouvements dans la base des modes propres de la cuve. Pour les mouvements plus importants la théorie linéaire atteint ses limites, nous proposons un modèle de type Boussinesq et un modèle d'équations intégrales avec des conditions de surface libre complètement non-linéaires. Nous considérons également un terme d'amortissement linéarisé. Nous comparons les résultats numériques à des résultats expérimentaux pour une cuve à fond plat et pour un fond légèrement incliné. Le taux de remplissage varie également. Le couplage de la cuve avec une barge rectangulaire est réalisé par développement en série de fonctions propres et par leur raccordement aux frontières des différents sous-domaines. Tous ces résultats, numériques et expérimentaux , sont comparés dans le domaine fréquentiel et temporel. / This work focuses on the sloshing of the fluid in rectangular tanks with forced motions and of the coupling with a floating body. A linear theory is firstly given for the sloshing which is represented by the superposition of natural sloshing modes. Compared with linear theory, the extended Boussinesq-type models are used for the simulations of nonlinear sloshing motions. The fully nonlinear free surface conditions are adopted and linear damping term is considered in the model. The integral equation method with fully nonlinear free surface conditions are also applied. A flat bottom rectangular tank with different filling levels are discussed based on these numerical methods and experiences. The solutions of an inclined bottom tank are studied and compared with experimental results. The sea-keeping of a rectangular barge is modeled by a series of eigen-functions. The coupled computations of the sloshing in the tank and the sea-keeping of floating body are studied in both the frequency domain and time domain. The numerical results are compared with experimental results.

Made available in DSpace on 2016-08-29T15:09:52Z (GMT). No. of bitstreams: 1 tese_7925_Piccoli_2014_TeseDoutorado_ppgea.pdf: 5611548 bytes, checksum: 7d5d9c71acf03a7c8f6afb146cd12dce (MD5) Previous issue date: 2014-04-29 / Modelos de escoamento multifásico são amplamente usados em diversas áreas de pesquisa ambiental, como leitos fluidizados, dispersão de gás em líquidos e vários outros processos que englobam mais de uma propriedade físico-química do meio. Dessa forma, um modelo multifásico foi desenvolvido e adaptado para o estudo do transporte de sedimentos de fundo devido à ação de ondas de gravidade. Neste trabalho, foi elaborado o acoplamento multifásico de um modelo euleriano não-linear de ondas do tipo Boussinesq, baseado na formulação numérica encontrada em Wei et al. (1995), com um modelo lagrangiano de partículas, fundamentado pelo princípio Newtoniano do movimento com o esquema de colisões do tipo esferas rígidas. O modelo de ondas foi testado quanto à sua fonte geradora, representada por uma função gaussiana, pá-pistão e pá-batedor, e quanto à sua interação com a profundidade, através da não-linearidade e de propriedades dispersivas. Nos testes realizados da fonte geradora, foi observado que a fonte gaussiana, conforme Wei et al. (1999), apresentou melhor consistência e estabilidade na geração das ondas, quando comparada à teoria linear para um kh  . A não-linearidade do modelo de ondas de 2ª ordem para a dispersão apresentou resultados satisfatórios quando confrontados com o experimento de ondas sobre um obstáculo trapezoidal, onde a deformação da onda sobre a estrutura submersa está em concordância com os dados experimentais encontrados na literatura. A partir daí, o modelo granular também foi testado em dois experimentos. O primeiro simula uma quebra de barragem em um tanque contendo água e o segundo, a quebra de barragem é simulada com um obstáculo rígido adicionado ao centro do tanque. Nesses experimentos, o algoritmo de colisão foi eficaz no tratamento da interação entre partícula-partícula e partícula-parede, permitindo a evidência de processos físicos que são complicados de serem simulados por modelos de malhas regulares. Para o acoplamento do modelo de ondas e de sedimentos, o algoritmo foi testado com base de dados da literatura quanto à morfologia do leito. Os resultados foram confrontados com dados analíticos e de modelos numéricos, e se mostraram satisfatórios com relação aos pontos de erosão, de sedimentação e na alteração da forma da barra arenosa.

Made available in DSpace on 2016-08-29T15:09:39Z (GMT). No. of bitstreams: 1 tese_2708_Dissertação_FABIO.pdf: 18277781 bytes, checksum: 568c5e5cc458b065a66491fbb865419a (MD5) Previous issue date: 2008-08-27 / Ondas propagando-se em direção à costa sofrem importantes transformações, que são de fundamental importância para o entendimento das mudanças da linha de costa e dos processos que ocorrem nas proximidades da linha de costa. Os modelos numéricos são instrumentos utilizados por engenheiros e oceanógrafos como um método de estudos desses processos dentro de uma pequena margem de erro. Neste trabalho de pesquisa são realizadas simulações numéricas para avaliar dois tipos de interação onda-corpo. No primeiro caso foram consideradas ondas monocromáticas incidentes interagindo com uma região costeira complexa e no segundo caso ondas interagindo com um recife artificial multifuncional. A região costeira escolhida é a Curva da Jurema e o recife artificial multifuncional é colocado em um trecho da praia de Camburi, ambas as regiões estão localizadas na Baia do Espírito Santo e vêm sofrendo processos de erosão. As simulações foram realizadas usando o modelo numérico FUNWAVE 2.0, fundamentado nas equações do tipo Boussinesq de Wei et al. (1995). A grade computacional não-uniforme utilizada tem comprimento típico de 5m para a região da Curva da Jurema e de 1m para a região do Recife Artificial. Na região da Curva da Jurema os resultados de simulações de ondas incidentes do quadrante de Nordeste e de Sudeste mostraram que as amplitudes das ondas são quase que totalmente dissipadas dentro do embaiamento e se aproxima de zero junto à praia. Os processos de refração, de difração e de reflexão da onda incidente com a profundidade e os contornos da costa são evidenciados, no campo de onda, e estes podem ser responsáveis pelo aparecimento de um super-harmônico no espectro de onda proveniente de Sudeste. Em um trecho de praia de Camburi, onde foi colocado o recife artificial, as ondas de Nordeste e de Sudeste incidem perpendicularmente a praia. Sem o recife, o comportamento das ondas neste domínio se mostrou influenciado pelos gradientes batimétricos, gerando fluxos de retorno e grande concentração de energia próxima à linha de costa. Com instalação do recife artificial multifuncional verifico-se uma diminuição da intensidade de energia de onda na linha de costa. O recife foi projetado com uma declividade e ângulos internos propícios para geração de ondas surfáveis. Os resultados das simulações realizadas com a inclusão do recife mostraram que as ondas que se propagam sobre recife são intensificadas em altura até quebrarem, a uma distância de aproximadamente 200m da linha de costa. Ao quebrarem, as ondas se propagam em direção a linha de costa com uma energia menor que aquela sem o recife. Assim, os resultados das simulações numéricas realizadas com o modelo de ondas FUNWAVE mostraram que o modelo é capaz de reproduzir os principais processos que ocorrem em regiões costeiras podendo ser usando como ferramenta para o gerenciamento costeiro.

We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation. / Ph. D.

Lors d'événements météorologiques extrêmes, cyclones ou tempêtes, les états de mer exceptionnels avec un déferlement important provoquent une montée du niveau de l'eau sur le littoral (surcote) et un envahissement des terres émergées amplifié par l'effet du vent. Cela peut causer d'énormes dégâts humains et matériels (Xynthia, février 2010).Dans un premier temps, le but de ce travail était de comprendre les mécanismes hydrodynamiques mis en jeu lors des tempêtes. Pour cela, nous avons mis en place une campagne de mesures dans la grande soufflerie air-eau de l'IRPHE à Luminy. L'objectif était de quantifier le runup des vagues en fonction d'un vent onshore (jusqu'à 15m/s) pour différentes conditions de houle (régulière, irrégulière ou vent seul) mais aussi de connaître les effets du vent sur les caractéristiques de la houle et sur les courants moyens près du rivage.Dans un deuxième temps, un modèle numérique de type Boussinesq dans le domaine temporel a ensuite été développé en tenant compte des effets combinés vagues/vent/déferlement. Ce modèle est basé sur l'approche de Bingham et al. (2009). Il intègre une bathymétrie variable pour modéliser la propagation d'ondes à l'abord du rivage. Un terme d'amplification des vagues par le vent, Jeffreys (1925, 1926), Miles (1957) ainsi qu'un terme de dissipation pour tenir compte du déferlement ont été introduit, Madsen et al. (1997a), Muscari et Di Mascio (2002). Enfin un modèle simple de runup a été implémenté, Hibberd et Peregrine (1979), Lynett et al. (2002). Afin d'être validé le modèle est confronté à diverses expériences de la littérature, ou à des expériences déjà réalisées au sein du laboratoire. / During extreme weather events like cyclones and storms, the extreme states sea withimportant breaking cause a level setup and coastal flooding magnified by strong wind and can cause human and material damage (Xynthia, february 2010).Initially, the aim of this work is to understand the hydrodynamics mechanisms when storms. To understand this, a measurement campaign was carried out in large air/sea facility at Marseille Luminy. The objective was to quantify maximum runup due to the wind and waves during onshore wind (up to 15m/s) for different conditions of waves (regular, irregular or only wind) and also to know the effect of wind on the waves characteristics and currents near the shore.A Boussinesq-type model in time domain has been developed taking into account the combined effects of wave/wind/breaking. The model that we use is based on the model developed by Bingham et al. (2009). It incorporates a variable bathymetry to simulate the propagation of the waves from offshore to the coastal environment. Amplification of waves by wind is added in two different ways. Jeffreys (1925, 1926), Miles (1957) and to take into account the dissipation of wave, we included a dissipation term, Madsen et al. (1997a), Muscari and Di Mascio (2002). Finally, we introduced the simple runup model of Hibberd et Peregrine (1979), Lynett et al. (2002). In order to validate the model, we have compared our results with differents experiments.

Made available in DSpace on 2015-05-15T11:46:03Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 876230 bytes, checksum: 3a204615891ef1a7232794e0c75afdc8 (MD5) Previous issue date: 2010-09-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation is devoted to prove the local exact controllability to the trajectories for a coupled system, of the Boussinesq kind. In the state system, the unknowns are the velocity field and pressure of the uid (y; p), the temperature (-) and an additional variable c that can be viewed as the concentration of a contaminant solute. We prove several results, that essentially show that it is sufficient to act locally in space on the equations satisfied by (-) and c. The controllability property of this system will be obtained by means of a Carleman inequality for apropriate system and of a inverse function theorem. / Esta dissertação é dedicada a provar a controlabilidade exata local ás trajetórias para um sistema acoplado do tipo Boussinesq. No sistema estado, as variáveis desconhecidas são o campo velocidade e pressão do fluido (y; p), a temperatura - e uma variável adicional c que pode ser vista como uma concentração de um soluto contaminante. A propriedade de controlabilidade nula desse sistema será obtida por meio de uma desigualdade de Carleman para um sistema apropriado e de um teorema de função inversa.