A Moment-Based Chezy Formula for Bed Shear Stress in Varied Flow

Abstract

Despite its limitations, the Chezy bed shear stress formula is commonly used in depth-averaged flow numerical models as closure for estimating mutual tractive stresses with underneath boundaries. This paper proposes a novel moment-based formula that could be considered a revised version of the Chezy formula and can be used to estimate local variations of the bed shear stress under more complex and varied flow conditions with accelerating–decelerating flow fields. The formula depends on two velocity scales: the depth-averaged velocity, Uo, and a new moment-based velocity scale, u1. The new formula is calibrated using 10 experiments for flow over fixed bedforms, and the calibration coefficient is found to linearly correlate with h/Δ and h/zo ratios. The formula is also applied for the case of air flow across a negative step, jet water flow downstream a gate, and 2D water flow downstream an oblique negative step, and reasonably satisfactory agreement with the measured data is found. The new formula could be used in vertically averaged and moment models to disclose part of the information already lost by the vertical integration procedure.

Keywords

• depth-averaged models
• VAM
• moment of momentum
• Chezy shear stress formula