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This dissertation presents results of the study on symplectic and multisymplectic numerical methods for solving linear and nonlinear Hamiltonian wave equations. The emphasis is put on the second order space and time discretizations of the linear wave, the Klein-Gordon and the sine-Gordon equations. For those equations we develop two multisymplectic (MS) integrators and compare their performance to other popular symplectic and non-symplectic numerical methods. Tools used in the linear analysis are related to the Fourier transform and consist of the dispersion relationship and the power spectrum of the numerical solution. Nonlinear analysis, in turn, is closely connected to the temporal evolution of the total energy (Hamiltonian) and can be viewed from the topological perspective as preservation of the phase space structures. Using both linear and nonlinear diagnostics we find qualitative differences between MS and non-MS methods. The first difference can be noted in simulations of the linear wave equation solved for broad spectrum Gaussian initial data. Initial wave profiles of this type immediately split into an oscillatory wave-train with the high modes traveling faster (MS schemes), or slower (non-MS methods), than the analytic group velocity. This result is confirmed by an analysis of the dispersion relationship, which also indicates improved qualitative agreement of the dispersive curves for MS methods over non-MS ones. Moreover, observations of the convergence patterns in the wave profile obtained for the sine-Gordon equation for the initial data corresponding to the double-pole soliton and the temporal evolution of the Hamiltonian functional computed for solutions obtained from different discretizations suggest a change of the geometry of the phase space. Finally, we present some theoretical considerations concerning wave action. Lagrangian formulation of linear partial differential equations (PDEs) with slowly varying solutions is capable of linking the wave action conservation law with the dispersion relationship thus suggesting the possibility to extend this connection to multisymplectic PDEs.

Yes / Laboratory experiments are presented to investigate the effect of different piggyback pipeline configurations on the morphology of local scour under wave conditions. Scour depth and width around the pipelines under regular and irregular waves are measured and analyzed for a range of pipeline and wave conditions; such as the spacing between two pipes (G), gap between the main pipe and seabed (e), pipe diameter (D), wave height (H) and period (T). Experimental results reveal that both the scour depth and width around piggyback pipeline is much larger than those around single pipe under the same wave conditions. Scour depth increases with the increase of the Keulegan-Carpenter (KC) number and decreases with increase of G and e. When e exceeds 0.5D, scour depth tends to approach 0.When spacing G is greater than 0.4D, the destabilization from small pipe to large one is greatly reduced, resulting in scour depth around piggyback pipeline being close to that around single pipe. Similar to scour depth, scour width broadens with the increase of KC number increasing and decreases with the increase of G. Experiments also show that the effect of e on scour depth is greater than that of G under the same test conditions, while their impact on scour width is opposite. Furthermore, scour width under irregular waves is extended slightly compared with regular wave for otherwise the identical conditions. / National Natural Science Foundation (No. 51279189).

It has long been known that ship wakes are observable by synthetic aperture radar. However, incomplete physical understanding has prevented the development of simulation tools that can predict both the structure and persistence of wakes in the ocean environment. It is the focus of this work to develop an end-to-end multi-scale modeling-and-simulation methodology that captures the known physics between the source of disturbance and the sensor. This includes turbulent hydrodynamics, free-surface effects, environmental forcing through Langmuir-type circulations, generation of surface currents and redistribution of surface-active substances, surface-roughness modification, and simulation of the signature generated by reflection and scattering of electromagnetic waves from the ocean surface. The end-to-end methodology is based upon several customized computational fluid dynamics solvers and empirical models which are linked together. The unsteady Reynolds-averaged Navier-Stokes equations, including models for the Craik-Leibovich vortex force and near surface Reynolds-stress anisotropy, are solved at full-scale Reynolds and Froude numbers on domains that extend tens of kilometers behind the ship. A parametric study is undertaken to explore the effects of ship heading, ship propulsion, ocean-wave amplitude and wavelength, and the relative importance of Langmuir-type circulations vs. near-surface Reynolds-stress anisotropy on the generation of surface currents that are transverse to the wake centerline. Due to the vortex force, the structure of the persistent wake is shown to be a function of the relative angle between the ambient long-wavelength swell and the ship heading. Ships operating in head seas observe 1-3 streaks, while ships operating in following seas observe 2 symmetric streaks. Ships operating in calm seas generate similar wakes to those in following seas, but with reduced wake width and persistence. In addition to the structure of the persistent wake, the far wake is shown to be dominated by ship-induced turbulence and surface-current gradients generating a wide center wake. The redistribution of surface-active substances by surface currents is simulated using a scalar-transport model on the ocean surface. Simulation of surface-roughness modification is accomplished by solving a wave-action balance model which accounts for the relative change in the ambient wave-spectrum by the surface currents and the damping-effects of surface-active substances and turbulence. Simulated returns from synthetic aperture radar are generated with two methods implemented. The first method generates a perfect SAR image where the instrument and platform based errors are neglected, but the impact of a randomized ocean field on the radar cross section is considered. The second method simulates the full SAR process including signal detection and processing. Comparisons are made to full-scale field experiments with good agreement between the structure of the persistent wake and observed SAR imagery. / 1 / It has long been known that ship wakes are observable by synthetic aperture radar. However, incomplete physical understanding has prevented the development of simulation tools that can predict both the structure and persistence of wakes in the ocean environment, which is critical to understanding both the design and operation of maritime remote sensors as well as providing tactically relevant operational guidance and awareness of the maritime domain. It is the focus of this work to develop an end-to-end multi-scale modeling-and simulation methodology that captures the known physics between the source of disturbance and the sensor. This includes turbulent hydrodynamics, free-surface effects, environmental forcing, generation of surface currents and redistribution of surface-active substances, surface-roughness modification, and simulation of the signature from the ocean surface. The end-to-end methodology is based upon several customized computational fluid dynamics solvers and empirical models. The unsteady Reynolds-averaged Navier-Stokes equations, including models to account for environmental effects and near-surface turbulence, are solved at full-scale on domains that extend tens of kilometers behind the ship. A parametric study is undertaken to explore the effects of ship heading, ship propulsion, ocean-wave amplitude and wavelength, and the relative importance of environmental forcing vs. near-surface turbulence on the generation of surface currents that are transverse to the wake centerline. Due to the environmental forcing, the structure of the persistent wake is shown to be a function of the relative angle between the ambient long-wavelength swell and the ship heading. Ships operating in head seas observe 1-3 streaks, while ships operating in following seas observe 2 symmetric streaks. Ships operating in calm seas generate similar wakes to those in following seas, but with reduced wake width and persistence. In addition to the structure of the persistent wake, the far wake is shown to be dominated by ship-induced turbulence and surface-current gradients generating a wide center wake. The redistribution of surface films by surface currents is simulated using a scalar-transport model on the ocean surface. Simulation of surface-roughness modification is accomplished by solving a wave-action-balance model which accounts for the relative change in the ambient surface profile by the surface currents and the damping-effects of surface-active substances and turbulence. Simulated returns from synthetic aperture radar are generated with two methods implemented. The first method generates a perfect SAR image where the instrument and platform based errors are neglected, but the impact of a randomized ocean field on the radar cross section is considered. The second method simulates the full SAR process including signal detection and processing. Comparisons are made to full-scale field experiments with good agreement between the structure of the persistent wake and observed SAR imagery.

This study is concerned with a 29km long barrier island system along the New Brunswick coast of Kouchibouguac Bay. Over the past 150 years these islands have been retreating shorewards and have been affected by storm wave action. The changes in the island configuration, the characteristics of the island topography and the seasonal variations in the beach profile suggests that these islands are similar to better known ones along the United States coastline. The sediment characteristics of these islands reveal that there is an interplay of wind and wave processes on the sands, an interplay that is constantly mixing beach, dune and lagoon sands. The dominant southwest winds in summer cause most of the beach and dune sands to take on the characteristics of wind affected sands while the fall and spring storms impart characteristics of wave deposition to the beach sands at these times. The sediment characteristics revealed seasonal changes in the islands but simulation modelling of the energy distribution of waves in the bay after wave refraction accounts for most of the long term change in the island configuration. This modelling emphasizes field work which revealed that not all parts of the islands are affected by the same storm waves. Nort-northeast waves have a better chance of affecting the southern part of the bay while more easterly approaching waves will only influence the northern part. Over a period of time form 1894 to 1964, wave refraction modelling also shows that much of the change in the configuration of South Beach can be accounted for by wave refraction over a changing offshore bathymetry. Storm wave action thus accounts for most of the change in island configuration but the change around the inlets is most likely dependent upon the ability of these inlets to maintain stability at all times. Richibucto Inlet has achieved a stable equilibrium between the strength of the tidal currents passing through the inlet and the amount of incoming longshore drift, so that its position has remained static over the last 30 years. It is unlikely that Blacklands Gully or Little Gully have achieved this stability. / Thesis / Master of Science (MS)

Un modelo de simulación presenta muchas ventajas en el campo del desarrollo de motores de combustión interna alternativos. Su utilidad es doble. Por un lado, para entender la naturaleza de los fenómenos físicos que suceden en el interior del motor, y por otro, con el fin de optimizar el diseño de los sistemas que integran el mismo. El principal objetivo de esta tesis es desarrollar un modelo de un motor de dos tiempos de 125 cc de altas prestaciones para caracterizar la fluidodinámica interna en los sistemas de admisión, cilindro y escape. Para la construcción del modelo unidimensional del motor es imprescindible conocer información experimental. Por tanto, se han caracterizado de forma experimental los elementos que forman el motor. Por una parte, se ha usado un banco de impulsos para la caracterización dinámica. Por otra parte, se ha empleado un banco de flujo para caracterizar las pérdidas de presión en los elementos. Además, en banco motor, se ha analizado el proceso de combustión, con el objetivo de determinar la ley de liberación de calor. En relación a las tareas de modelado, se ha usado un modelo de diagnóstico para caracterizar del proceso de combustión, experimentando 37 condiciones de operación modificando el régimen de giro, el avance del encendido y usando cinco sistemas de escape. Asimismo, con el fin de poder reproducir el fenómeno de propagación de ondas en el interior del sistema de escape se ha propuesto un modelo de transmisión de calor ya que los modelos convencionales usados en motores de 4T no proporcionan resultados precisos al no contemplar los fenómenos físicos que suceden en el proceso de escape espontáneo de un motor de 2T de estas características. Para ello, se ha caracterizado experimentalmente el fenómeno de propagación de ondas en el interior del sistema de escape midiendo con diversos transductores de presión a lo largo de: un escape de diámetro constante y recto, y varios sistemas de escape derivados del original del motor. El primero se usó para proceder al necesario ajuste de las constantes del modelo mientras que los segundos para realizar la validación del mismo. Para el desarrollo del modelo de transmisión de calor se han contemplado las fluctuaciones de la velocidad instantánea del fluido y la disipación de la turbulencia con una longitud de entrada. Una vez es construido el modelo unidimensional del motor con capacidad de reproducir los complejos fenómenos ondulatorios que existen en el interior de los sistemas de admisión, cilindro y escape, es necesario desarrollar correlaciones para los parámetros que definen la función de Wiebe, usada como ley de liberación de calor en el cilindro. Se ha correlacionado la variación de estos parámetros (en particular, la duración de la combustión y el parámetro de forma) con variables de funcionamiento del motor: régimen de giro y avance del encendido, y variables que se calculan en el modelo: fracción de residuales y densidad de la carga. De esta forma se dispone de un modelo predictivo de las prestaciones del motor si se conoce una correlación para las pérdidas mecánicas, que también ha sido obtenida. El uso del modelo de transmisión de calor propuesto en este trabajo reproduce con precisión la fase y amplitud de la presión de escape con valores inferiores al 1% al comparar el coeficiente de admisión medido y modelado. Las diferencias pueden alcanzar el 7% si se emplean otros modelos encontrados en la literatura. Por otra parte, los resultados obtenidos al usar las correlaciones para la combustión se traducen en: diferencias inferiores al 1.5% entre potencia medida y modelada para todas las condiciones de funcionamiento del motor si el proceso de combustión presenta un coeficiente de variación en la presión del cilindro inferior al 2.5%. Cuando el coeficiente de variación aumenta, debido a la dispersión cíclica, las diferencias entre potencia medida y modelada pueden alcanzar el 4%. Palabras clave: Motores de Combustión Interna Alternativos, Motor de Dos Tiempos, Altas Prestaciones, Instalaciones Experimentales y Medición, Modelado Unidimensional, Modelo de Acción de Ondas, Proceso de Combustión, Transmisión de Calor. / Jiménez Macedo, VD. (2013). Contribución al modelado unidimensional en motores de dos tiempos de altas prestaciones [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/30773