Multiple Time Scales Of Fluvial Processes And Mathematical River Modelling

Complex interactions exist among flow, sediment transport and bed deformation of alluvial rivers, which normally exhibit multiple time scales and essentially. However, without sufficient justifications, these interactions are ignored to different extents in existing mathematical river models, which have been one of the most important uncertainty sources and therefore largely puzzled the choice of end-users of mathematical river models. In this dissertation, the theory of multiple time scales for alluvial rivers will be developed, which facilitates quantitative investigation of the relative time scales of the interactions among the flow, sediment transport and bed deformation. Complemented by numerical case studies of typical bed load sediment transport processes, the conditional applicabilities of the concept of bed load sediment transport capacity, capacity and non-capacity models, as well as coupled and decoupled mathematical models will be investigated.Based on the basic mass and momentum conservation laws of fluid dynamics, the complete depth-integrated governing equations are firstly derived, which fully accounts for the interactions among the flow, sediment transport and bed deformation of alluvial rivers. The governing equations are discretized by the finite volume method, the numerical fluxes are estimated by the TVD (total variation diminishing) version of the second order SLIC (slope limited centered) scheme, which can automatically capture shock waves and discontinuities featured by hyperbolic equations.With the help of the theory of characteristics, the partial differential governing equations are rewritten as compatibility equations along the characteristics, which are ordinary differential equations. Time scales are defined along characteristics, which are applicable to bed load and suspended sediment transport, uniform and nonuniform sediment transport. Particular attention will be paid to two categories of relative time scales, i.e., the relative time scale for sediment adaptation to capacity, and the relative time scale for bed deformation. The former quantifies the relative rates of the sediment adaptation to the variation of the sediment transport capacity, which facilitates the investigation of the applicability of the concept of sediment transport capacity. The later quantifies the relative rates of bed deformation in relation to the variation of the flow depth, which can be used to reveal the feedback effects of bed deformation on the flow evolution.The conditional applicabilities of the concept of bed load transport capacity, capacity and non-capacity models are firstly investigated. The relative time scale for sediment adaptation is analyzed under both static and dynamic conditions, which indicates that irrespective of uniform or nonuniform sediment, the adaptation of bed load transport to capacity could mostly be fulfilled instantly. However, perturbation imposed to alluvial rivers militates against the adaptation, rendering the capacity assumption conditional, rather than universal. The greater the perturbation, the longer the spatial distance it takes for sediment adaptation. Direct numerical comparisons are carried out between capacity and non-capacity models in relation to typical bed load transport processes, showing substantial errors by the capacity model as compared to the non-capacity model. Non-capacity modelling is critical for bed load transport.Bed load transport in typical ephemeral (Nahal Yatir, Israel) and perennial rivers (Oak Creek, America) is investigated. The contrasting magnitudes of bed load transport rates when estimated against a pure flow parameter are reconciled by taking into account of the effects of sediment properties. Especially, it is shown that the very high bed load transport rates by flash flood flow in Nahal Yatir can adapt to capacity instantly. On the one hand, this provides theoretical basis for application of bed load transport capacity formula to bed load transport in ephemeral rivers. On the other hand, it provides direct field evidence for the present analyses of relative time scale for bed load sediment adaptation.The relative time scale for bed deformation is also analyzed under both static and dynamic conditions. Complemented by numerical comparisons between coupled and decoupled models, it is shown that the feedback impacts of bed deformation induced by bed load transport on the flow evolution are limited, with negligible differences between the coupled and decoupled models. These indicate that traditional decoupled mobile bed models are applicable for bed load transport modelling in alluvial rivers.Lastly, uncertainties related to numerical representation of the bed grain size stratigraphy are investigated. Although the active layer formulation has been used to modelling the bed grain size stratigraphic evolution for over four decades, satisfactory agreement has not yet reached. It is proposed here that the estimation of the size fraction at the lower interface of the active layer, which is based on a pure empirical relation, might be one of the major uncertainty sources. A physically based relation is proposed and tested against typical bed load transport processes, revealing its better performance as compared to the traditional pure empirical relation.