Transient Solute Dispersion in Wetland Flows With Submerged Vegetation: An Analytical Study in Terms of Time‐Dependent Properties

Abstract

Predicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications in water resources. While a semianalytical study has been made for the steady dispersion with a continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907), an in‐depth analytical investigation has yet to be performed for the more complicated case of transient dispersion due to an instantaneous release. In regard to the pioneering benchmark observation (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229) of transient solute dispersion in a submerged vegetated flow for an instantaneous source release at the top of the canopy, an extensive analytical effort is paid in this work to derive the time‐dependent basic properties and to investigate the temporal evolution of concentration distribution. Obtained large‐time asymptotic dispersivities agree well with available experimental results (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229), with higher significance ( R2=0.87, n=24) for correlation between analytical results and experimental data. Analytical solutions covering effects of dispersivity, skewness, and kurtosis of detailed concentration distribution are compared satisfactorily with numerical results obtained by the random displacement method. The findings illuminate the applicability of this analytical approach in environmental risk assessment and water quality management.

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

“…With the local moments P n (z, θ, t) integrated over θ ∈ [0, 2π), namely P n O (z, t), one can expand the two-dimensional time-dependent concentration P O (x, z, t) in the series of Hermite polynomials. For example, given the moments, Gram-Charlier Type A series (Kendall & Stuart 1958;Blinnikov & Moessner 1998) and its Edgeworth form (Chatwin 1970) are widely used in 'reconstructing' the cross-sectional-averaged concentration in the streamwise direction (Chatwin 1970;Wang & Chen 2017a) and full positional concentration field (Li et al 2018;Guo, Jiang & Chen 2020). Therefore, it is beneficial to examine the applicability of the expansion in the transport of micro-swimmers, which can approximate the two-dimensional concentration field of the micro-swimmers patch.…”

Solute Dispersion From a Continuous Release Source in a Vegetated Flow: An Analytical Study

“…(2019). The above velocity model and turbulent diffusivity profile were demonstrated to well predict the transient dispersion for solute transport in the SVF in our previous work (Guo et al., 2020).…”

“…As shown in Figure 4 in Guo et al. (2020), the velocity gradient and the vertical turbulent diffusivity are small in the canopy layer, especially in the wake zone, which leads to the high concentration in the canopy layer at the small time. At a large time, the solute cloud has been mixed thoroughly in the vertical direction.…”

“…At a large time, the solute cloud has been mixed thoroughly in the vertical direction. Hence, the vertical concentration approaches to be relatively uniform, as seen in Figures 12d and 13d in Guo et al (2020).…”

“…Based on the double‐averaging method (Nepf & Ghisalberti, 2008; Nikora et al., 2007; Righetti, 2008), solute transport of passive tracers through an SVF can be characterized by the advection‐diffusion equation for the space‐time averaged concentration (Guo et al., 2020; Nepf, 2012; Nepf & Ghisalberti, 2008; Rubol et al., 2016; Tanino & Nepf, 2008) $$$\frac{\partial {C}_{\mathrm{I}}^{\ast }}{\partial {t}^{\ast }}+{U}^{\ast }\left({y}^{\ast }\right)\frac{\partial {C}_{\mathrm{I}}^{\ast }}{\partial {x}^{\ast }}=\frac{\partial }{\partial {y}^{\ast }}\left[{D}_{y}^{\ast }\left({y}^{\ast }\right)\frac{\partial {C}_{\mathrm{I}}^{\ast }}{\partial {y}^{\ast }}\right],$$$ where $${C}_{\mathrm{I}}^{\ast }$$ is time‐space averaged concentration (kg m −3 ), t * is time (s), U *( y *) is time‐space averaged velocity along the longitudinal direction (m s −1 ), y * is the vertical coordinate (m), x * is the longitudinal coordinate (m), and $${D}_{y}^{\ast }\left({y}^{\ast }\right)$$ is the turbulent diffusion coefficient in the vertical direction (m 2 s). The turbulent diffusion in the longitudinal direction is neglected, compared with the longitudinal shear dispersion (Elder, 1959; Fischer, 1973, 1979).…”