<p> The principal object of this study is to find weak and strong type estimates concerning functions in weighted Lp spaces and their maximal functions. We also apply these results to the study of convolution integrals. </p> / Thesis / Master of Science (MSc)

The unsteady nature of coastal hydrodynamics is associated with complex boundary layer dynamics and hence engineering predictions of shear stresses and sediment transport are difficult. This thesis explores some of the complex hydrodynamic problems and boundary layer behaviour in the coastal zone and seeks to provide new and improved modelling approaches. The latest experimental results are used to inform the model development process. New laboratory experiments carried out as part of this thesis illustrate the value of convolution integral calculations for both pressure and skin friction forces on particles on the bed. The experiments also highlight the importance of the phase differences between free stream velocity and boundary layer shear stresses. The use of a “bed” shear stress as a model input is found to be problematic whenever there is a large vertical gradient in the boundary layer shear stress. New experimental and modelling work has helped to improve our understanding of sheet flow boundary layer dynamics. This thesis builds on some of these new discoveries to propose a new simplified model framework for sheet flow sediment transport prediction using convolution integrals. This time domain technique has the advantage of simplicity while incorporating the most important physical processes from more detailed models. The new model framework could be incorporated into any depth averaged coastal hydrodynamic modelling software package. Boundary layer analysis techniques presented in the thesis provide an improved understanding of the effective roughness of mobile beds and can be used to calculate instantaneous shear stress profiles throughout the mobile bed boundary layer. New solutions for swash zone hydrodynamics are presented which illustrate the limitations of the previous benchmark analytical model for swash hydrodynamics. It is shown that real swash necessarily involves a much larger influx of mass and momentum than the analytical solution which was previously used by many in the swash sediment transport research community. Models for swash boundary layer development are also presented.