Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows

The logarithmic layer of double-averaged (in time and space) streamwise velocity profiles obtained from field measurements made in the Swiss rivers, Venoge and Chamberonne is parameterized and discussed. Velocity measurements were made using a 3D Acoustic Doppler Velocity Profiler. Both riverbeds are hydraulically rough, composed of coarse gravel, with relative submergences ($h/{D}_{50}$) of 5.25 and 5.96, respectively. From the observations, the flow may be divided into three different layers: a roughness layer near the bed, an equivalent logarithmic layer and a surface or outer layer. It was found that a logarithmic law can describe the double-averaged profiles in the layer $0.30<z/h<0.75$. The parameterization of the logarithmic law is discussed. Special emphasis is given to the geometric parameters roughness and zero-displacement heights and to the equivalent von Karman constant.