MERCY NWANSIMDI SOMEZE

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.