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/z_o 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.

中文翻译：

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基于矩量的化学方程式求解层流中的床剪应力

尽管有其局限性，但Chezy床剪切应力公式通常在深度平均流量数值模型中用作闭合，用于估计边界下方的相互牵引应力。本文提出了一种新颖的基于矩的公式，可以将其视为Chezy公式的修订版，并可以用来估计在更复杂和变化的流动条件下，随着加速和减速流场的变化，床层剪应力的局部变化。该公式取决于两个速度标度：深度平均速度Uo和新的基于矩的速度标度u ₁。使用10个实验对固定床形上的流动对新公式进行了校准，发现校准系数与h / Δ和h / z _o比率。该公式也适用于空气流经负阶跃，闸门下游为喷射水流，斜负阶跃为下游的二维水流的情况，并且与测量数据有合理令人满意的一致性。新公式可用于垂直平均和矩模型中，以披露垂直积分过程已经丢失的部分信息。