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Thesis: abstract

In this thesis, we consider various problems related to two topics in two-phase flow and sediment transport.

Part I: the morphodynamics of intertidal mudflats

We review descriptive frameworks for the long-term morphological evolution of intertidal mudflats, focussing on morphodynamic equilibrium.

We develop a process-based morphodynamical model of a flat, and investigate cross-shore sediment transport in idealised geometries, obtaining numerical and analytical results. We use these results to obtain estimates for the equilibrium gradient of the flats; we investigate their sensitivity to the sediment properties and to the choice of models for erosion and deposition, and extend them to cover curved shorelines and non-sinusoidal tides.

We describe a series of numerical experiments on the full morphodynamical system, identifying the equilibrium states of our model. We determine how the morphology depends on sediment supply and tidal range: the results agree well with our analytical estimates. We investigate the effects of tidal asymmetry and a spring-neap cycle.

Part II: gravity-driven flows at low Reynolds number

We develop models for draining gravity currents in a porous medium, and particle-driven or draining viscous-gravity currents. These consist of non-linear diffusion equations with a source or sink term: we describe similarity and other exact solutions, and investigate numerically their intermediate-asymptotic properties. Where we are unable to obtain exact solutions, we develop perturbation schemes and related approximations. Laboratory experiments support our modelling approach.

We construct a model for particle settling through a fluid with a power-law rheology. This model predicts that the particle distribution in a sheared flow becomes stratified: we examine the effect of stratification on the deposits formed by a sheet flow and on the propagation of a current when its bulk density or viscosity depends on the concentration of suspended particles. The results provide a basis for improved models of particle-driven muddy flows.