Modified log-wake-law for smooth rectangular open channel flow

Smooth rectangular open channel flow is a benchmark for studying river hydraulics and sediment transport. Such a flow is more complicated than the classic boundary layer flow at least in two ways: (i) the maximum velocity occurs below the water surface, which is called the velocity-dip-phenomenon and (ii) the velocity distribution is affected not only by the channel bottom but also by the side-walls and the free surface. This fundamental flow is approximated herein by three hypotheses: (i) the velocity-dip-position shifts exponentially from the water surface to half flow depth as the width-depth ratio decreases from infinity to zero; (ii) the conventional wake-law for the centreline velocity distribution results from boundary shear stresses including the bottom, side-walls, and water surface in terms of secondary currents; and (iii) the cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law. These hypotheses are well supported by flume data.