Bed shear stress estimation of shallow and wide flows over sandy beds in transitionally rough regime at threshold conditions using velocity characteristics

Estimating bed shear stress (BSS) is essential to determine the critical shear stress under incipient motion conditions of sediments which typically occur within transitionally rough regime for sandy beds. Considering most of the studies have focused on fully rough regime, this study aims to cover knowledge gaps of the velocity-based methods of BSS estimation in transitionally rough regime of shallow and wide flows over sand particles of 0.43–1.94 mm, at three different water depths of 99–140 mm. In this specific conditions, the existing research gaps in applicability of applying quadratic stress law, possibility of using boundary layer characteristics method (BLCM), determination the values of the virtual bed level (Δ z ) and roughness length ( z 0 ) for the log-fit method and innovatively development of a water surface velocity approach were explored. The velocity profiles were best described by logarithmic trendlines, outperforming the power law and validated using the parabolic law. Water surface and average flow velocity approaches yielded average absolute percentage change relative to the Reynolds method (AAPC-RSS) of 13% and 17%, which improved to 4% when grouped by shear Reynolds number. Applying the Darcy-Weisbach equation gave 11% AAPC-RSS, reduced to 9% with sidewall correction for average flow velocity approach. Log-fit methods applied to the wall-shear layer or to the combined with intermediate layer yielded ∼30% AAPC-RSS with Δ z = 0 and von Kármán constant of κ = 0.4. The one-point log-fit method, with z 0 = 0.034 D 50 , achieved 8% AAPC-RSS, and 11% for z 0 = 0.11 ν / u ∗ + 0.03 k s . For the BLCM, empirical constant of C = 4.3 (range 4.2–4.6) was identified, providing an AAPC-RSS of 21%. Overall, water surface and average flow velocity approaches were practical and accurate. The log-fit method though underestimated, remained robust, while the log-fit one-point approach was effective for limited data but was measurement-error-sensitive, and BLCM recommended for full available profiles.