Modeling Hydrologically Mediated Hot Moments of Transient Anomalous Diffusion in Aquifers Using an Impulsive FractionalDerivative Equation
Academic Article
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
abstract
AbstractHydrologically mediated hot moments (HMHMs) 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 advectiondispersion equation (ITfADE) to simulate HMHMs of TAD. The model is approximated using an L1based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the ITfADE 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 subdiffusion arising from sudden shifts in hydraulic gradient within a regionalscale alluvial aquifer, (b) transient sub or superdiffusion due to convergent or pushpull tracer experiments within a localscale fractured aquifer, and (c) transient subdiffusion likely attributed to multipleconduit flow within an intermediatescale karst aquifer. The impulsive terms and fractional differential operator integrated into the ITfADE aptly capture the ephemeral nature and evolving memory of HMHMs of TAD by incorporating multiple stress periods into the model. The sequential HMHM 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 ITfADE to capture hot phenomena of TAD in aquatic systems.
