In natural and restored rivers, protruding river-bed elements can cause complex flow patterns. We hypothesize that, particularly at very low flows, solute spreading in such streams is controlled by different mechanisms than at high flows, questioning existing parameterizations. We investigate two-dimensional flow and transport in a synthetic channel with rough bathymetry under low-flow conditions with a numerical model solving the full shallow-water equations. Recirculation cells form behind protruding bed elements and trap water, macroscopically acting as transient-storage domain. We fit the one-dimensional mobile-immobile transport model to the concentration breakthrough curves of the two-dimensional model and relate the fitted parameters to easy-to-measure properties of the stream. The velocity in the mobile domain undergoes a power-law relation with the discharge and the channel slope, differing from the relationship expected for normal flow in streams with large water depths. Both the fitted dispersion coefficient and the mass-transfer coefficient between the mobile and immobile domains scale linearly with the velocity in the mobile domain. The ratio of immobile to mobile storage volumes β first increases then decreases with increasing discharge. We suggest measuring the surface area of bed elements protruding the water surface and that of the open water. The product of the corresponding area ratio with the velocity exerts a power-law control on β. Altogether, we can relate the coefficients of the mobile-immobile transport model to a few easy-to-measure properties of the stream. The findings of the present work contribute to the understanding of surface transient storage in natural and restored streams.

中文翻译：

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低流量条件下的表面瞬态存储与粗略水深测量

在自然河流和修复河流中，突出的河床元素会导致复杂的流动模式。我们假设，特别是在非常低的流量下，这些流中的溶质扩散由与高流量不同的机制控制，质疑现有的参数化。我们使用求解完整浅水方程的数值模型研究了在低流量条件下具有粗略水深测量的合成通道中的二维流动和传输。再循环单元形成在突出的床元件后面并捕获水，宏观上充当瞬态存储域。我们将一维移动-固定传输模型拟合到二维模型的浓度突破曲线，并将拟合参数与流的易于测量的特性相关联。移动域中的速度与流量和河道坡度呈幂律关系，不同于大水深溪流中正常流动的预期关系。移动域和固定域之间的拟合弥散系数和传质系数都与移动域中的速度成线性比例。固定与移动存储量的比率β随着放电量的增加先增大后减小。我们建议测量突出水面和开放水域的床元素的表面积。相应面积比与速度的乘积对β施加幂律控制。总之，我们可以将移动-固定传输模型的系数与流的一些易于测量的属性相关联。当前工作的发现有助于理解自然和恢复河流中的表面瞬态存储。