Sand Bed Friction Factors for Oscillatory Flows

Published data from the Carstens, Neilsen, and Altinbilek (4) oscillatory water tunnel tests are plotted as friction factor versus Reynolds number. These data, for three sand sizes and for both rippled and flat movable beds, are analyzed in a manner analogous to early treatment of flow in rough pipes that produced the Moody diagram. Laminar, transitional, and turbulent regimes are defined. The turbulent regime data are further analyzed to find the relative roughness, a combination of ripple height, grain size, and bottom particle displacement, which will predict the friction factor. The ripple heights for the 0.585mm sand increased with increasing Reynolds number while the ripple heights for the 0.297mm and 0.190mm sands decreased with increasing Reynolds number. Considering rippled beds only, the friction factor is proportional to the grain size divided by the square root of the Reynolds number. Grain roughness contributes 64% to 100% of the total bottom roughness, based on the relative roughness term.