Experiments on the motion of solitary grains along the bed of a water-stream

Abstract

Experiments are described in which heavy solid grains are observed as they are propelled one at a time by a water stream over a fixed, plane, bed of grains of the same sort. This is a simplification of a sediment flow in a river, and it allows the motions of a particular grain to be followed. Three modes of movement are observed - rolling, saltating and suspension, characteristics of each mode are described, and multi-exposure photographs of grains are obtained to show the trajectories involved. In the saltation mode, grains follow low, smooth trajectories. Since no random motions are detectable on them, they appear to be governed very largely by ballistic forces; in suspension, grains follow much longer, higher paths which, being wavy, show up the influence of the irregular turbulence in the stream. The change from one mode to the other is readily observed with this technique. The grains spin in all three modes. The mean forward speed of grains ͞U has been measured over a wide range of shear stress, shape and size of grain and of water depth. Two possible types of non-dimensional plots are presented, one of which is most appropriate to studies of the rolling mode, and the other for the suspension mode. Both methods satisfactorily correlate ͞U with various values of the settling speed V g in still water, for particles all of the same shape and size. There is a considerable difference in ͞U for different shapes of grains, angular ones always travelling more slowly than rounded ones. Relative to the mean stream speed ͞u , the grains travel faster at small depths than at large depths, for the same stress and V g . The trajectories of grains confirm that the change from saltation to suspension occurs near a stage when the vertical components of turbulent velocity are approximately equal to the settling velocity of grains. Multi-exposure photographs of trajectories are analysed to determine the angle of friction applicable to the process whereby the motion of grains is retarded by striking the bed. Some experiments have been done with spheres travelling over a bed consisting of cylinders of the same diameter. These travel faster than any natural grains. Their dynamics, when rolling in contact with the cylinders, have been investigated, and a theoretical model evolved to explain the conditions under which their forward motion just stops. This model is shown to give a useful approximation to the forward speed to all types of grain just before they suddenly stop moving; these grains will not travel at all at lower speeds. Finally, an experiment is described where one marked grain is observed while moving in the company of many other grains. Its speed is then reduced below that which it would have as a solitary grain in the same water stream, thus indicating how the friction of the grain load reacts upon the stream to give smaller speeds close to the bed. Appendix 1 gives details of a demonstration that saltation can occur in a laminar flow, with no turbulence present at all. Appendix 2 gives the experimental data, and appendix 3 gives the algebra of the analysis of rolling motion.