Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional-Derivative Equation

Zhang，Yong1; Liu，Xiaoting2; Lei，Dawei3; Yin，Maosheng4; Sun，Hong Guang3; Guo，Zhilin5; Zhan，Hongbin6

2024-03-01

10.1029/2023WR036089

Water Resources Research   影响因子和分区

0043-1397

1944-7973

Hydrologically mediated hot moments (HM-HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection-dispersion equation” (IT-fADE) to simulate HM-HMs of TAD. The model is approximated using an L1-based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT-fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub-diffusion arising from sudden shifts in hydraulic gradient within a regional-scale alluvial aquifer, (b) transient sub- or super-diffusion due to convergent or push-pull tracer experiments within a local-scale fractured aquifer, and (c) transient sub-diffusion likely attributed to multiple-conduit flow within an intermediate-scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT-fADE aptly capture the ephemeral nature and evolving memory of HM-HMs of TAD by incorporating multiple stress periods into the model. The sequential HM-HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT-fADE to capture hot phenomena of TAD in aquatic systems.

anomalous diffusion aquifers fractional derivative model hydrologically mediated hot moments

SCI ; EI

英语

其他

ENVIRONMENT/ECOLOGY

2-s2.0-85186437060

Scopus

1.Department of Geological Sciences,University of Alabama,Tuscaloosa,United States
2.Institute of Science and Technology Research,China Three Gorges Corporation,Beijing,China
3.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University,Nanjing,China
4.EIT Institute for Advanced Study,Ningbo,China
5.School of Environmental Science and Engineering,Southern University of Science and Technology,Shenzhen,China
6.Department of Geology and Geophysics,Texas A&M University,College Station,United States

Zhang，Yong,Liu，Xiaoting,Lei，Dawei,et al. Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional-Derivative Equation[J]. Water Resources Research,2024,60(3).

Zhang，Yong.,Liu，Xiaoting.,Lei，Dawei.,Yin，Maosheng.,Sun，Hong Guang.,...&Zhan，Hongbin.(2024).Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional-Derivative Equation.Water Resources Research,60(3).

Zhang，Yong,et al."Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive Fractional-Derivative Equation".Water Resources Research 60.3(2024).