An integrated law of the wall for hydrodynamically transitional flow over plane beds

The velocity profile for unidirectional currents is usually determined by two forms of the law of the wall, which are valid for smooth and rough boundaries, respectively. The law of the wall for smooth boundaries outside the viscous sublayer and buffer layer applies where the boundary Reynolds number (Re*) is less than 5. The velocity in this case depends only on the dimensionless distance (yd) from the bottom. For rough boundaries where Re* is more than 65, the law of the wall is independent of the boundary Reynolds number, but the bottom roughness (k) has to be taken into account. The mean or median particle grain size (D) is commonly substituted for bottom roughness. At present, there is no generally accepted law of the wall for the transitional flow regime between hydrodynamically smooth and rough conditions. In this paper, an integrated law of the wall is proposed for the transitional regime, yielding velocity profiles that correspond well to observed velocity profiles under these conditions. The result is applied to a set of flume data, using an improved procedure to determine the bedload transport rate. [Copyright &y& Elsevier]