Relation Between Bed Forms and Friction in Streams

Laboratory and field studies of alluvial streams have shown that the form of the bed varies with hydraulic quantitites such as discharge and depth, and with sediment size. When the bed consists of medium or finer sand and when the velocity is only slightly greater than the critical value for which bed sediment starts to move, that is, when the sediment discharge is small, ripples form on the bed. If the mean velocity is increased beyond the value which will just produce ripples, the sediment discharge will increase and the bed form will tend to change such that the friction factor increases to a maximum and then decreases. A velocity and sediment discharge is finally reached where the ripples tend to be obliterated. This is the bed condition known as transition. Some workers report that before transition occurs the bed forms increase in length and height keeping a sharp crest like that of ripples. Herein, those sharp crested forms that have a length from crest to crest of 1 ft or less are called ripples and those longer than 1 ft are called dunes. The present investigation is concerned with developing a relationship between the friction factors of beds covered with dunes or ripples and the size and other geometric properties of these bed forms. It starts with a bed which is already developed and relates the geometry of the bed form to the resistance that the bed offers to the flow. Experiments were made in two flumes with different fine sands in each flume. Unpublished data from experiments in a third flume were also used. The bed forms in these experiments were all shorter than 1 ft and, according to the definition adopted, were considered as ripples. In addition, publishing data from several sets of experiments with sediments ranging in mean size from 0.12 mm to 2.28 mm were compared with those obtained in the writers' experiments.