Extension of the skin shear stress Li's relationship to the flat bed

A proper estimation of the skin shear stress is necessary for a proper evaluation of sediment flux at the sediment-fluid interface. Several empirical formulas of the skin shear stress have been proposed in the literature for rippled bed as function of the factor form / ( and are respectively the height and wavelength of the bedform). These formulas express that in the presence of bedform, is a partition of the total shear stress . In contrast, when the bottom is flat, is exactly equal to . Based on in situ measurements, Li (J Geophys Res 99:791-799, 1994) has proposed a new formula of depending on (*)/ ( (*) is the friction velocity, ), but not as a function of /. This formulation appears physically more realistic, but does not cover the flat bottom range. The purpose of this short note is therefore the extension of the Li's expression to this type of bottom.