Abstract:
An experimental and theoretical investigation of the mechanics of alluvial stream bed forms was undertaken. A set of 47 experiments was carried out in which the initial development of an alluvial stream bed from plane bed conditions under the action of flowing water was clearly focussed on, and the subsequent evolution of the bed, possibly to the appropriate equilibrium bed configuration, was also recorded. The set of experimental runs covered a large range of Froude numbers and essentially the full spectrum of equilibrium bed configurations for each of the two (uniformly graded) sediments (of dg=0.20mm and dg=0.82mm respectively, considered. For each experiment, the development of the sediment bed with time was recorded using a bed profile measurement system. From the processed digital bed profiles, the development of each of bed form crest elevations, bed form trough elevations, bed form heights, bed form wavelengths and bed form numbers with time was analysed for the present experiments. The results of these analyses are of value simply in the quantitative records of alluvial bed development that they provide. The experimental results presented herein indicate that the dominant length of the waves that can be expected to form first from flat bed conditions for a given flow system is relatively insensitive to the properties of the associated fluid flow and principally a function of the size of the sediment comprising the sediment bed under consideration. In this regard, the rotational flow stability analyses of Richards (1980, were found to accurately describe the generation of bed forms from plane bed conditions. Richards' 'ripple mode of instability' is predicted to be instigated by the occurrence of a random pile-up of sediment on an otherwise flat bed. In addition, Raudkivi and Witte's 'bed form unification' model of bed development was found to describe the general principles (including bed form speed decreasing with increasing bed form height) and patterns (including instances of bed form coalescence and throughpassing, of bed development (subsequent to bed forms being generated on the bed, observed experimentally. Nevertheless, owing to the infancy of the bed form unification approach to In addition to the experimental investigations carried out, a reformulated, general version of the flow system stability model based upon potential flow theory was developed. The present potential flow stability model was found to predict instability of a flow system in the absence of Kennedy's explicit phase lag β. The instability mechanism was shown to be a bed-water surface interaction mechanism. The increase in the rate of bed development for a flow system that is observed to occur in the vicinity of the condition given by (Fr)2 - (l/kH)tanh kH is therefore predicted by correctly formulated potential flow stability analyses. The results of analyses incorporating Kennedy's phase lag further indicated β to simply be a mathematical parameter of questionable physical basis. describing bed development, these models cannot as yet directly represent the evolution of a given fluid-sediment flow system. The description of the generation and subsequent progressive evolution of alluvial stream bed features (ripples and dunes) that is provided by the combination of Richards' analyses, potential flow analyses and the bed form unification model of bed development was found to be both extensive and accurate.