This dissertation, "Mass Transport Due to Surface Waves in a Water-mud System" by Lingyan, Huang, 黃凌燕, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled MASS TRANSPORT DUE TO SURFACE WAVES IN A WATER-MUD SYSTEM submitted by Huang Lingyan for the degree of Doctor of Philosophy at The University of Hong Kong in October 2005 The objective of the present work is to investigate the mass transport due to surface waves in a water-mud system. To study the dynamics without the excessive mathematical complication, it is assumed that there exist two superimposed shallow homogeneous layers of fluids subject to a periodic external wave forcing on the free surface, where the upper-layer is clear water as a Newtonian viscous fluid and the lower-layer mud is a shear-thinning power-law non-Newtonian fluid. To conveniently handle the mass transport which is Lagrangian by nature, the Lagrangian coordinates are adopted in this work. In this thesis, the two-layer system problem is solved by different stages. First, the problem is simplified to a single uniform layer of power-law fluid mud lying on a horizontal rigid bed and subject to a periodic external pressure load on the free surface. In this part, we shall develop a fully discrete Fourier-Chebyshev collocation method to find solutions of the first- and second-order nonlinear equations of motion of the mud. In the second part, we shall present a theoretical study on the mass transport due to external forcing of a spatially and temporally periodic surface pressure in a two- ilayer Newtonian viscous system, where the upper-layer is a very low viscosity fluid (e.g. clear water) and the lower-layer mud is a highly viscous fluid (e.g. concentrated fluid mud). Based on the Lagrangian coordinates, a perturbation analysis is carried out to the second order to find the mean Lagrangian drifts in the two layers. The first-order variables including displacements, velocity and pressure are found as part of the solutions. The analytical expression is obtained for the mass transport velocity in each layer, respectively. Through some numerical cases, the effects of external forcing magnitude and different mud properties on the mass transport velocity are investigated. In the third stage, the mass transport due to the above-mentioned standing wave forcing in a water-mud system, in which the lower-layer mud is a shear-thinning power-law non-Newtonian fluid, is investigated by a Fourier-Chebyshev collocation spectral method in space and 4th-order finite-difference scheme in time discretization. First, based on the assumptions of shallowness and small deformations, a perturbation analysis is carried out to the second order to yield the nonlinear governing equations of motion in terms of the Lagrangian variables. In the two-layer system, the governing equations are cast into a coupled time-dependent partial differential equation group. The Fourier-Chebyshev collocation method developed in the first part is then used to discretize the spatial derivatives in conjunction with a 4th-order finite-difference scheme in time-discretization. At last, some discussion on the mass transport under waves in a two-layer system and the application of the spectral method to time-dependent convection- diffusion equations will be presented. ii DOI: 10.5353/th_b3538045 Subjects: Water waves Sediment transport - Mathematical models Mud Viscous flow Lagrangian functions