Hyporheic exchange in riverbeds is driven by current‐bed topography interactions. Because riverbeds exhibit topographic roughness across scales, from individual grains to bedforms and bars, they can exhibit fractal patterns. This study analyzed the influence of fractal properties of riverbed topography on hyporheic exchange. A set of synthetic fractal riverbeds with different scaling statistics was used as inputs to sequentially coupled numerical simulations of turbulent channel flow and hyporheic flow. In the analysis, the maximum power spectrum (dune size) and the fractal dimension (topographic complexity) were considered as independent variables and we then investigated how interfacial fluxes and hyporheic travel times are functionally related to these variables. As the maximum power spectrum increases (i.e., dune height to flow depth ratio), the average interfacial flux increases logarithmically whereas it increases exponentially with an increase in fractal dimension. Hyporheic exchange is more sensitive to additional roughness (larger fractal dimensions) than to bedform size (larger maximum power). Our results imply that fractal properties of riverbeds are crucial to predicting hyporheic exchange. The predictive relationships we propose could be integrated with reduced complexity, large‐scale models. They can also be used to design artificial topographies that target hyporheic ecosystem services.

中文翻译：

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疏水交换对河床分形特性的敏感性

河床中的亲水交换受当前床地形相互作用的驱动。由于河床从单个晶粒到床形和条形，在各个尺度上都表现出地形粗糙度，因此它们可以表现出分形图案。本研究分析了河床地形的分形特性对低渗交换的影响。一组具有不同比例统计量的合成分形河床被用作对湍流河道水流和低渗流的数值模拟进行顺序耦合的输入。在分析中，最大功率谱（沙丘大小）和分形维数（地形复杂度）被视为独立变量，然后我们研究了界面通量和流变时间与这些变量在功能上的关系。随着最大功率谱的增加（即沙丘高度与流深之比），平均界面通量对数增加，而随着分形维数的增加而指数增加。亲水性交换对附加粗糙度（较大的分形维数）比对床形大小（较大的最大功率）更敏感。我们的结果表明，河床的分形特性对于预测水流交换至关重要。我们建议的预测关系可以与降低复杂性的大型模型集成。它们还可以用于设计针对水生生态系统服务的人工地形。我们的结果表明，河床的分形特性对于预测水流交换至关重要。我们建议的预测关系可以与降低复杂性的大型模型集成。它们还可以用于设计针对水生生态系统服务的人工地形。我们的结果表明，河床的分形特性对于预测水流交换至关重要。我们建议的预测关系可以与降低复杂性的大型模型集成。它们还可以用于设计针对水生生态系统服务的人工地形。