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This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

With a continuing and rising demand for hydrocarbons, the energy companies are installing infrastructure ever further offshore, where such infrastructure is often exposed to extreme waves. This thesis explores some aspects of wave-structure interaction, particularly the maximum water surface elevation increase in severe storms due to these local interactions. The effects on wave-structure interactions of column cross-sectional shape are investigated using linear and second-order wave diffraction theory. For multi-column structures, the excitation of locally resonant wave modes (near-trapping) is studied for several column cross-sectional shapes, and a simple method for estimating the surface elevation mode shape is given. The structure of the quadratic transfer functions for second-order sum wave elevation is investigated and an approximation assuming these QTFs are flat perpendicular to the leading diagonal is shown to be adequate for the first few lowest frequency modes. NewWave-type focused wave groups can be used as a more realistic model of extreme ocean waves. A Net Amplification Factor based on the NewWave model is given as an efficient tool for finding the incident frequencies most likely to cause a violent wave-structure interaction and where these violent responses are likely to occur. Statistics are collected from Monte Carlo type simulations of random waves to verify the use of the Net Amplification Factor. Going beyond linear calculations, surface elevation statistics are collected to second-order and a `designer' wave is found to model the most extreme surface elevation responses. A `designer' wave can be identified at required levels of return period to help to understand the relative size of harmonic components in extreme waves. The methods developed with a fixed body are then applied to an identical hull which is freely floating, and the responses between the fixed and moving cases are compared. The vertical heave motion of a semi-submersible in-phase with the incident wave crests is shown to lead to a much lower probability of water-deck impact for the same hull shape restrained vertically. The signal processing methods developed are also applied to a single column to allow comparison with experimental results. Individual harmonic components of the hydrodynamic force are identified up to at least the fifth harmonic. Stokes scaling is shown to hold even for the most violent interactions. It is also shown that the higher harmonic components of the hydrodynamic force can be reconstructed from just the fundamental force time history, and a transfer function in the form of a single phase and an amplitude for each harmonic. The force is also reconstructed well to second-order from the surface elevation time history using diffraction transfer functions. Finally, possible causes of damage to a platform high above mean water level in the North Sea are investigated.

This thesis describes experiments that were carried out using focused wave groups in the UK Coastal Research Facility (UKCRF). Considerable effort was put into calibrating the UKCRF to determine the relationship between the input signals sent to the paddles and the waves generated in the facility. Focused wave groups of various sizes and phases, based on NewWave theory were generated, and measurements were made of the resulting surface elevation data, water particle kinematics, wave runup and overtopping volumes. NewWave theory models the profile of extreme waves in a Gaussian (random) sea. The thesis describes the first time this model has been applied in the context of coastal wave transformation. A method for the separation of the underlying harmonic structure of a focused wave group is described and results presented. This technique has been used in relatively deep water but is shown to work successfully in the coastal zone until wave overturning. A method has been devised to provide a theoretical Stokes-like expansion of the free and bound waves to model the surface elevation and water particle kinematics of the focused wave groups. Satisfactory agreement is achieved between the theoretical predictions of UKCRF measurements. Suggestions are made for an improved model. The underlying harmonic structure of the focused wave groups is presented as stacked time histories that give insight into the wave transformation process from deep to shallow water. Particular attention is paid to the low frequency wave generated as the wave group interacts with the beach. This is compared to the low frequency wave that is generated by a solitary wave in the UKCRF. Runup and overtopping measurements are in reasonable agreement with predictions based on certain empirical formulae, but not others. These comparisons are useful in identifying those formulae able to predict runup and overtopping of extreme waves in the coastal zone.

A significant proportion of the world's population and physical assets are located in low lying coastal zones. Accurate prediction of wave induced run-up and overtopping of sea defences are important in defining the extent and severity of wave action, and in assessing risk to people and property from severe storms and tsunamis.This thesis describes a one-dimensional numerical model based on the Boussinesq equations of Madsen and Sorensen (1992) and the non-linear shallow water equations. The model is suitable for simulating propagation of weakly non-linear and weakly dispersive waves from intermediate to zero depth, such that any inundation and/or overtopping caused by the incoming waves is also calculated as part of the simulation. Wave breaking is approximated by locally switching to the non-linear shallow water equations, which can model broken waves as bores. A piston paddle wavemaker is incorporated into the model for complete reproduction of laboratory experiments. A domain mapping technique is used in the vicinity of the paddle to transform a time-varying domain into a fixed domain, so that the governing equations can be more readily solved.First, various aspects of the numerical model are verified against known analytical and newly derived semi-analytical solutions. The complete model is then validated with laboratory measurements of run-up and overtopping involving solitary waves. NewWave focused wave groups, which give the expected shape of extreme wave events in a linear random sea, are used for further validation. Simulations of experiments of wave group run-up on a plane beach yield very good agreement with the measured run-up distances and free surface time series. Wave-by-wave overtopping induced by focused wave groups is also successfully simulated with the model, with satisfactory agreement between the experimental and the predicted overtopping volumes. Repeated simulations, now driven by second order paddle displacement signals, give insight into second order error waves spuriously generated by using paddle signals derived from linear theory. Separation of harmonics reveals that the long error wave is significantly affecting the wave group shape and leading to enhanced runu-up distances and overtopping volumes. An extensive parameter study is carried out using the numerical model investigating the influence on wave group run-up of linear wave amplitude at focus, linear focus location, and wave group phase at focus. For a given amplitude, both the phase and the focus location significantly affect the wave group run-up. It is also found that the peak optimised run-up increases with the wave amplitude, but wave breaking becomes an inhibiting factor for larger waves. This methodology is proposed for extreme storm wave induced run-up analysis.

With a continuing and rising demand for hydrocarbons, the energy companies are installing infrastructure ever further offshore, where such infrastructure is often exposed to extreme waves. This thesis explores some aspects of wave-structure interaction, particularly the maximum water surface elevation increase in severe storms due to these local interactions. The effects on wave-structure interactions of column cross-sectional shape are investigated using linear and second-order wave diffraction theory. For multi-column structures, the excitation of locally resonant wave modes (near-trapping) is studied for several column cross-sectional shapes, and a simple method for estimating the surface elevation mode shape is given. The structure of the quadratic transfer functions for second-order sum wave elevation is investigated and an approximation assuming these QTFs are flat perpendicular to the leading diagonal is shown to be adequate for the first few lowest frequency modes. NewWave-type focused wave groups can be used as a more realistic model of extreme ocean waves. A Net Amplification Factor based on the NewWave model is given as an efficient tool for finding the incident frequencies most likely to cause a violent wave-structure interaction and where these violent responses are likely to occur. Statistics are collected from Monte Carlo type simulations of random waves to verify the use of the Net Amplification Factor. Going beyond linear calculations, surface elevation statistics are collected to second-order and a `designer' wave is found to model the most extreme surface elevation responses. A `designer' wave can be identified at required levels of return period to help to understand the relative size of harmonic components in extreme waves. The methods developed with a fixed body are then applied to an identical hull which is freely floating, and the responses between the fixed and moving cases are compared. The vertical heave motion of a semi-submersible in-phase with the incident wave crests is shown to lead to a much lower probability of water-deck impact for the same hull shape restrained vertically. The signal processing methods developed are also applied to a single column to allow comparison with experimental results. Individual harmonic components of the hydrodynamic force are identified up to at least the fifth harmonic. Stokes scaling is shown to hold even for the most violent interactions. It is also shown that the higher harmonic components of the hydrodynamic force can be reconstructed from just the fundamental force time history, and a transfer function in the form of a single phase and an amplitude for each harmonic. The force is also reconstructed well to second-order from the surface elevation time history using diffraction transfer functions. Finally, possible causes of damage to a platform high above mean water level in the North Sea are investigated.

This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

A significant proportion of the world's population and physical assets are located in low lying coastal zones. Accurate prediction of wave induced run-up and overtopping of sea defences are important in defining the extent and severity of wave action, and in assessing risk to people and property from severe storms and tsunamis.This thesis describes a one-dimensional numerical model based on the Boussinesq equations of Madsen and Sorensen (1992) and the non-linear shallow water equations. The model is suitable for simulating propagation of weakly non-linear and weakly dispersive waves from intermediate to zero depth, such that any inundation and/or overtopping caused by the incoming waves is also calculated as part of the simulation. Wave breaking is approximated by locally switching to the non-linear shallow water equations, which can model broken waves as bores. A piston paddle wavemaker is incorporated into the model for complete reproduction of laboratory experiments. A domain mapping technique is used in the vicinity of the paddle to transform a time-varying domain into a fixed domain, so that the governing equations can be more readily solved.First, various aspects of the numerical model are verified against known analytical and newly derived semi-analytical solutions. The complete model is then validated with laboratory measurements of run-up and overtopping involving solitary waves. NewWave focused wave groups, which give the expected shape of extreme wave events in a linear random sea, are used for further validation. Simulations of experiments of wave group run-up on a plane beach yield very good agreement with the measured run-up distances and free surface time series. Wave-by-wave overtopping induced by focused wave groups is also successfully simulated with the model, with satisfactory agreement between the experimental and the predicted overtopping volumes. Repeated simulations, now driven by second order paddle displacement signals, give insight into second order error waves spuriously generated by using paddle signals derived from linear theory. Separation of harmonics reveals that the long error wave is significantly affecting the wave group shape and leading to enhanced runu-up distances and overtopping volumes. An extensive parameter study is carried out using the numerical model investigating the influence on wave group run-up of linear wave amplitude at focus, linear focus location, and wave group phase at focus. For a given amplitude, both the phase and the focus location significantly affect the wave group run-up. It is also found that the peak optimised run-up increases with the wave amplitude, but wave breaking becomes an inhibiting factor for larger waves. This methodology is proposed for extreme storm wave induced run-up analysis.

This thesis describes experiments that were carried out using focused wave groups in the UK Coastal Research Facility (UKCRF). Considerable effort was put into calibrating the UKCRF to determine the relationship between the input signals sent to the paddles and the waves generated in the facility. Focused wave groups of various sizes and phases, based on NewWave theory were generated, and measurements were made of the resulting surface elevation data, water particle kinematics, wave runup and overtopping volumes. NewWave theory models the profile of extreme waves in a Gaussian (random) sea. The thesis describes the first time this model has been applied in the context of coastal wave transformation. A method for the separation of the underlying harmonic structure of a focused wave group is described and results presented. This technique has been used in relatively deep water but is shown to work successfully in the coastal zone until wave overturning. A method has been devised to provide a theoretical Stokes-like expansion of the free and bound waves to model the surface elevation and water particle kinematics of the focused wave groups. Satisfactory agreement is achieved between the theoretical predictions of UKCRF measurements. Suggestions are made for an improved model. The underlying harmonic structure of the focused wave groups is presented as stacked time histories that give insight into the wave transformation process from deep to shallow water. Particular attention is paid to the low frequency wave generated as the wave group interacts with the beach. This is compared to the low frequency wave that is generated by a solitary wave in the UKCRF. Runup and overtopping measurements are in reasonable agreement with predictions based on certain empirical formulae, but not others. These comparisons are useful in identifying those formulae able to predict runup and overtopping of extreme waves in the coastal zone.