Development of Roll-Wave Trains in Open Channels

The maximum depth at wave crest, minimum depth at wave trough, wave period and wave velocity of spontaneously developed roll-wave trains were measured in a laboratory channel. Channel slope (S_O) was varied from 0.05 to 12, normal depth (h_n) was varied by a factor of two, and the Froude number of the undistrubed flow (F) ranged from 3.5 to 5.6. For each of the four properties, a single development curve resulted for all h_n, with S_O and F fixed. The spatial rate of growth of the average maximum depth increased as F was increased by increasing S_O. The growth rate decreased as S_O was increased and F was held fixed. Substantial growth occurs when one wave overtakes and combines with another wave. Growth also occurs without wave overtaking. Spontaneously developed roll waves are shown to be related to periodic permanent roll waves. Methods of applying the laboratory results to other channels with inlet conditions similar to that of the laboratory channel are presented.