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Analytical modeling of hyporheic flow for in-stream bedforms: Perturbation method and implementation

Frei, Sven, Azizian, Morvarid, Grant, Stanley B., Zlotnik, Vitaly A., Toundykov, Daniel
Environmental modelling & software 2019 v.111 pp. 375-385
biogeochemical cycles, hyporheic zone, mathematical theory, stream channels, topography
Hyporheic flow and nutrient turnover in hyporheic systems are strongly influenced by in-stream bedforms. An accurate representation of topographical variations of the stream-streambed interface is therefore essential in analytical models in order to represent the couplings between hydrological and biogeochemical processes correctly. The classical Toth approach replaces the streambed surface topography by a flat surface which is identical to a truncation of the original physical flow domain into a rectangle. This simplification can lead to biased estimates of hyporheic flow and nutrient cycling within hyporheic systems. We present an alternative analytical modeling approach for solving hyporheic problems without domain truncation that explicitly accounts for topographical variations of the streambed. The presented approach is based on the application of perturbation theory. Applications of the method to hyporheic systems, ranging from the centimeter-scale of rippled bedforms to riffle structures of 10 m and larger scale, indicate a high accuracy of the approach.