The recovery of rivers from releases of organic effluents is heavily influenced by the diffusion of oxygen from the atmosphere, which is usually quantified using a re-aeration coefficient. There are many tens of formulae for estimating the coefficient from commonly used hydraulic variables such as water depth and flow velocity. As well as it being difficult to choose the most appropriate formulae for any particular river reach, another important issue exists for rivers having complex cross-sectional shapes. In such cases there are often significant transverse variations in depth and velocity. Hence, the re-aeration rate must exhibit transverse variations also. The paper presents initial results from a simple theoretical analysis aimed at exposing the significance for estimated re-aeration coefficients of properly capturing the transverse heterogeneity of the physical processes. A cross-section consisting of three zones, namely a rectangular main channel surrounded by two symmetrical rectangular floodplains was used, and attention focused on cases where the floodplains were active. Three strategies for estimating the re-aeration coefficient for the whole channel were considered. Firstly, a simplistic approach in which the coefficient was evaluated only for the hydraulic conditions found in the main channel. Clearly, such an approach would be expected to be dubious because it ignores differences in hydraulic conditions across the channel. Secondly, a naive approach in which the coefficient was evaluated using cross-sectional average hydraulic conditions. This would be expected to be better than the simplistic approach because it attempts to recognise transverse variations in hydraulic conditions. Thirdly, a robust approach in which the coefficient was evaluated as the cross-sectional average of three local values--one.coefficient value for each zone, based on local hydraulic conditions. This would be expected to give the most reliable results because the transverse heterogeneity of the coefficient is properly captured. Using a typical empirical formula for the re-aeration coefficient （5.8U0.5H00.25， where U is velocity and H is water depth) and a modified Manning's resistance formula, general expressions for the re-aeration coefficient for each strategy were obtained in terms of the ratios of flood plain roughness to main channel roughness (γ),flood plain width to main channel width (β) and flood plain depth to main channel depth (η). Calculations were undertaken for 1 ? γ < 4， 0.25 ? β < 4 and 0 ? η < 0.4. The results show that in comparison to the robust approach the simplistic approach overestimates the re-aeration coefficient by up to 100%, with their ratio increasing with increasing γ and β,but gradually decreasing with increasing η. The results for the na?ve approach are more complex. In comparison to the robust approach: when γ is low, it overestimates the re-aeration coefficient (by up to 10%) and β has little effect, but when γ is high， it underestimates the re-aeration coefficient (by up to 15%) and their ratio increases towards unity with increasing β; also, their ratio gradually decreases with increasing η for all γ and β. In conclusion， although it is tempting to evaluate the re-aeration coefficient from cross-sectional average hydraulic conditions, significant errors may be incurred.
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机译：从有机污水释放的河流的恢复受到大气中的氧气扩散的严重影响，这通常是使用重新曝气系数量化的。有许多公式用于估计来自常用液压变量的系数，例如水深和流速。除了难以为任何特定河到达选择最合适的公式之外，还存在具有复杂横截面形状的河流的另一个重要问题。在这种情况下，深度和速度通常存在显着的横向变化。因此，再曝气率也必须表现出横向变化。本文提出了一种旨在使估计捕获物理过程的横向异质性的估计的重新曝气系数的重要性的简单理论分析的初始结果。由三个区域组成的横截面，即使用由两个对称矩形泛洪平坦围绕的矩形主通道，并关注泛洪平有效的情况。考虑了估算整个渠道重新通风系数的三种策略。首先，仅在主通道中发现的液压条件评估系数的简单方法。显然，预计这种方法将是可疑的，因为它忽略了通道上的液压条件的差异。其次，使用横截面平均水力条件评估系数的天真方法。预计这将比简单的方法更好，因为它试图识别液压条件的横向变化。第三，一种稳健的方法，其中系数被评估为三个局部值的横截面平均值 - 基于局部液压条件的每个区域的CO次数。预计这将提供最可靠的结果，因为正确捕获了系数的横突性。利用典型的经验公式用于重新通气系数（5.8U0.5H00.25，其中U为速度和H是水深）和改进的曼宁的抵抗公式，获得了对每个策略的再曝气系数的一般表达式洪水平原粗糙度比主要通道粗糙度（γ）的术语，洪水平移宽度与主沟道宽度（β）和洪水普通深度到主沟道深度（η）。进行1？ γ<4,0.25？ β<4和0？ η<0.4。结果表明，与稳健的方法相比，简单的方法将再曝气系数高达100％，其比率随着γ和β的增加而增加，但随着η的增加而逐渐减小。 Na ve方法的结果更复杂。与稳健的方法相比：当γ低时，它高估了重新曝气系数（高达10％），β几乎没有效果，但是当γ高时，它低估了再曝气系数（最多15 ％）和它们的比率随着β的增加而增加;而且，它们的比率随着η的增加而逐渐减小，所有γ和β增加。总之，尽管评估了从横截面平均水力条件的再曝气系数，但可能会产生显着的误差。
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