Longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind

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RESEARCH ARTICLE

Longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind Haoze Fang1 · Zhonghua Yang1 · Huilin Wang1 · Yujie Fan1 Received: 15 June 2020 / Accepted: 30 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract The longitudinal dispersion coefficient is an important index for contaminant transports in rivers. Investigating it by using an analytical approach is conducive to obtain its expression with physical meanings and wide application ranges. However, the analytical solutions are extremely complex for subsequent derivations when many influencing factors, such as benthic vegetation and surface wind, are considered. This study combines turbulent flow theory and Biot’s theory for poroelasticity into a two-layer flow model and acquires the analytical solutions of velocity. A database is generated from the analytical solutions to search a more concise expression of velocity through genetic programming. A formula for longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind is deduced on the basis of this expression. Calculated coefficients from the formula are compared with the experimental coefficients from the model and real vegetation to show its validity. The formula indicates that the longitudinal dispersion coefficients are mainly affected by turbulent effect, vegetation height, and surface wind. The growth of vegetation height can weaken the influence of surface wind on longitudinal dispersion coefficient. Keywords Longitudinal dispersion coefficients · Vegetation · Wind effect · Genetic programming · Analytical solutions · Contaminant transport

Introduction Rivers, as important components of wetland, affect irrigated agriculture and food security (Immerzeel et al. 2010). Freshwater resources in rivers are vital for maintaining biodiversity (V¨or¨osmarty et al. 2010; Strayer and Dudgeon 2010). With the developments in industry and agriculture, heavy metal and antibiotic pollutions in rivers are becoming increasingly serious (Yi et al. 2011; Watkinson et al. 2009). Thus, many types of chemical compounds are found in accessible freshwater (Loos et al. 2009). The consequent Responsible Editor: Marcus Schulz Both submerged vegetation and surface wind are included in the consideration. The analytical solutions are combined with genetic programming. The impact of vegetation is subdivided into height and permeability for discussion.  Zhonghua Yang

[email protected] 1

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, Hubei, China

eutrophication of freshwater results in huge economic losses (Dodds et al. 2009). From the existing circumstances, problems about contamination in rivers need to be solved. Investigating the mechanism of contaminant transport is helpful for building solutions to these problems. Dispersion, which is caused by nonuniform timeaveraged velocity distribution in shear flow, is a research focus for contaminant transpo