Quasi 2-layer morphodynamic model and Lagrangian study of bedload

Abstract

Conventional morphodynamic models are typically based on a coupled system of hydrodynamic equations, a bed-update equation, and a sediment-transport equation. However, the sediment-transport equation is almost invariably empirical, with numerous options available in the literature. Bed morphological evolution predicted by a conventional model can be very sensitive to the choice of sediment-transport formula. This thesis presents a physics-based model, where the shallow water-sediment-mixture flow is idealised as being divided into two layers of variable (in time and space) densities: the lower layer concerned with bedload transport, and the upper layer representing sediment in suspension. The model is referred to as a Quasi-2-Layer (Q2L) model in order to distinguish it from typical 2-Layer models representing stratified flow by two layers of different but constant and uniform densities. The present model, which does not require the selection of a particular empirical formula for sediment transport rates, is satisfactorily validated against widely used empirical expressions for bedload and total transport rates. Analytical solutions to the model are derived for steady uniform flow over an erodible bed. Case studies show that the Q2L model, in contrast to conventional morphodynamic approaches, yields more realistic results by inherently including the influence of the bed slope on the sediment transport. This conclusion is validated against experimental data from a steep sloping duct. An analytical study using the Q2L model investigates the influence of bed-slope on bedload transport; the resulting expressions are in turn used to modify empirical sediment transport formulae (derived for horizontal beds) in order to render them applicable to arbitrary stream-wise slopes. The Q2L model provides an alternative approach to studying sediment-transport phenomena, whose adequate analysis cannot be undertaken following coniv ventional approaches without further increasing their degree of empiricism. The Q2L model can also lead to the enhancement of conventional morphodynamic models. For coarse sediments and/or relatively low flow velocities, bedload transport is usually responsible for most sediment transport. Bedload transport consists of a combination of particles rolling, sliding and saltating (hopping) along the bed. Hence, saltation models provide considerable insight into near-bed sediment transport. This thesis also presents an analysis of the statistics and mechanics of a saltating particle model. For this purpose, a mathematically simple, computationally efficient, stochastic Lagrangian model has been derived. This model is validated satisfactorily against previously published experimental data on saltation. The model is then employed to derive two criteria aimed at ensuring that statistically convergent results are achieved when similar saltation models are employed. According to the first criterion, 103 hops should be simulated, whilst 104 hops ought to be considered according to the second criterion. This finding is relevant given that previous studies report results after only a few hundred, or less, particle hops have been simulated. The model also investigates sensitivity to the lift force formula, the friction coefficient, and the collision line level. A method is proposed by which to estimate the bedload sediment concentration and transport rate from particle saltation characteristics. This method yields very satisfactory results when compared against widely used empirical expressions for bedload transport, especially when contrasted against previously published saltation-based expressions.