Time Compression Approximation Relationship for Infiltration in the Presence of a Shallow Water Table: Evaluating the Role of Péclet Number

Yao, Lili; Wang, Dingbao; Hooshyar, Milad; Singh, Arvind; Sivapalan, Murugesu

doi:10.1029/2018wr023293

Cited by 3 publications

(3 citation statements)

References 44 publications

(58 reference statements)

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“…and reveals the relative importance of tracer streamwise advection (in the active layer) and vertical diffusion (Fischer et al, 1979;Yao et al, 2018).…”

Section: Analytical Solutions Of Concentration Momentsmentioning

confidence: 99%

“…The governing equation (equation ) can be nondimensionalized as

({, \begin{array}{l} \frac{\partial f_{a} ({,,, ξ, ζ, τ)}{\partial τ} + Pe \frac{\partial f_{a}}{\partial ξ} = D \frac{\partial^{2} f_{a}}{\partial ξ^{2}} + \frac{\partial^{2} f_{a}}{\partial ζ^{2}} ({, R \leq ζ \leq 1) \\ \frac{\partial f_{s} ({,,, ξ, ζ, τ)}{\partial τ} = \frac{\partial^{2} f_{s}}{\partial ζ^{2}} ({, 0 \leq ζ \leq R) \end{array}),

where

τ = \frac{{italictD}_{z}}{{((), L_{s} + L_{a})}^{2}}

is the dimensionless time indicating a timescale for the tracers to spread uniformly in depth. Pe is the dimensionless parameter known as Péclet number

Pe = \frac{c ((), L_{s} + L_{a})}{D_{z}},

and reveals the relative importance of tracer streamwise advection (in the active layer) and vertical diffusion (Fischer et al, ; Yao et al, ).…”

Section: Analytical Solutions Of Concentration Momentsmentioning

confidence: 99%

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Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

Singh

et al. 2019

Water Resources Research

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The process of burial and exhumation of bedload particles within a certain depth of the riverbed leads to vertical exchange of particles, which significantly affects the characteristics of streamwise bedload transport. In this paper, we revisit the classic active layer formulation and extend it by incorporating the burial and exhumation through conceptualizing the fluctuations of bed surface as the relative vertical movement of buried tracer particles in the substrate layer (i.e., we change the static reference system to the fluctuating riverbed surface). We theoretically demonstrate, for the first time, the emergence of the transient anomalous diffusion (both superdiffusion and subdiffusion) and power‐law advective slowdown at the intermediate timescales, which are induced by the nonequilibrium transport as characterized by the inhomogeneous vertical mixing of tracers due to particle burial and exhumation. Neglecting the ballistic regime at extremely short times, at small and large timescales, the transport regimes show normal diffusion. This result further implies that for the most typical fluvial riverbed with finite vertical exchange depth (i.e. nonaggrading or nondegrading bed), the subdiffusion of bedload tracers for large timescale transport may still be transient, which will eventually converge to the normal diffusion as time increases. Comparing the obtained analytical solutions with available numerical results as well as field observations, we show that the proposed formulation can capture well anomalous diffusion and the power‐law slowdown of the advective velocity of bedload tracers at intermediate timescales, and more importantly the transition from anomalous to normal diffusion at large timescales.

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“…and reveals the relative importance of tracer streamwise advection (in the active layer) and vertical diffusion (Fischer et al, 1979;Yao et al, 2018).…”

Section: Analytical Solutions Of Concentration Momentsmentioning

confidence: 99%

“…The governing equation (equation ) can be nondimensionalized as

({, \begin{array}{l} \frac{\partial f_{a} ({,,, ξ, ζ, τ)}{\partial τ} + Pe \frac{\partial f_{a}}{\partial ξ} = D \frac{\partial^{2} f_{a}}{\partial ξ^{2}} + \frac{\partial^{2} f_{a}}{\partial ζ^{2}} ({, R \leq ζ \leq 1) \\ \frac{\partial f_{s} ({,,, ξ, ζ, τ)}{\partial τ} = \frac{\partial^{2} f_{s}}{\partial ζ^{2}} ({, 0 \leq ζ \leq R) \end{array}),

where

τ = \frac{{italictD}_{z}}{{((), L_{s} + L_{a})}^{2}}

is the dimensionless time indicating a timescale for the tracers to spread uniformly in depth. Pe is the dimensionless parameter known as Péclet number

Pe = \frac{c ((), L_{s} + L_{a})}{D_{z}},

and reveals the relative importance of tracer streamwise advection (in the active layer) and vertical diffusion (Fischer et al, ; Yao et al, ).…”

Section: Analytical Solutions Of Concentration Momentsmentioning

confidence: 99%

Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

Singh

et al. 2019

Water Resources Research

Self Cite

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show abstract

“…In this study, the TOUGH2 simulation software will be used to address challenges such as lack of basic data, scarcity of parameters, and the many uncertainties in the pollution process. Compared to the HYDRUS series of software [30], TOUGH2 allows for appropriate parametrization of underground structures and their properties. It can simulate multiple parameter sets, and through automatic model calibration, local and global sensitivity analysis, data analysis, and uncertainty analysis, it effectively resolves issues related to the lack of simulation parameters and the highly nonlinear problem-solving process [31].…”

Section: Introductionmentioning

confidence: 99%

Identification of Environmental Damage Process of a Chromium-Contaminated Site in China

Cao,

Wang,

et al. 2024

Water

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Identifying the source and impact pathways of soil heavy-metal pollution is critical for its assessment and remediation. Numerical simulation has been widely used to simulate soil heavy-metal pollution processes and predict risks. However, traditional numerical simulation software requires a large number of parameters, which are difficult to obtain in site-scale studies. This study proposes a rapid method for identifying soil heavy-metal pollution processes using the TOUGH2/EOS7 software. It has automatic calibration and uncertainty analysis capabilities, which can effectively reduce the demand for parameters. This study established a method, including model selection, simulation, validation, and error analysis, to verify the effectiveness of the proposed method. This study identified the most realistic scenario for chromium pollution and simulated its release over 20 years, and the results met accuracy requirements with a best-case fit of 0.9998. The results showed that the method can quickly identify the source and impact pathways of soil heavy-metal pollution, providing strong evidence for environmental damage assessment.

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Modeling slope rainfall-infiltration-runoff process with shallow water table during complex rainfall patterns

Chui

Chen

2021

Journal of Hydrology

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Time Compression Approximation Relationship for Infiltration in the Presence of a Shallow Water Table: Evaluating the Role of Péclet Number

Cited by 3 publications

References 44 publications

Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

Identification of Environmental Damage Process of a Chromium-Contaminated Site in China

Modeling slope rainfall-infiltration-runoff process with shallow water table during complex rainfall patterns

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