Similarity Laws for Localized Scour

The object of this study is to develop similarity criteria for sediment-transport rate and for scour depth in localized-scour situations. The principal assumption is that in an area of localized scour, the velocity and velocity distribution are the results of the disturbance element around which scour was occurring. For flow situations that are free from (a) gravity waves, (b) sediment inflow from upstream, and (c) extraneous influences on the flow pattern such as dunes passing through the scour hole, the following criteria are presented. For sediment-transport rate f = Q_S/(N_S² – N_SC²)^5/2 V B D_g; and for scour depth f = S/L(N_S² – N_SC²)^5/2 (D_g/L) (V t/L). To apply the similarity relations to a given situation of localized scour, a minimum of two model tests is required. The first is an empirical determination of the sediment number with zero transport, Nsc. The second is for the empirical determination of the left side of the above equations. The procedure is demonstrated for the case of a horizontal cylinder settling into the scour hole in oscillatory flow.