The nonlocal model of porewater irrigation: Limits to its equivalence with a cylinder diffusion model
Burrows maintained by animals in aquatic sediments ventilate the sediment and can substantially alter the rates and pathways of biologically-mediated decomposition reactions. A well known and effective way of modeling the impact of such bioirrigation in sediment diagenetic models is to assume that solutes diffuse into an annulus of sediment surrounding the burrow; the reaction diffusion equations are represented in cylindrical polar co-ordinates. More commonly, bioirrigation of sediments is represented by one-dimensional "nonlocal" irrigation models. Their use is typically justified by the assertion that a nonlocal model is equivalent to a radially-integrated two-dimensional diffusion model in cylindrical-polar co-ordinates. In this paper we highlight limits to this equivalence, drawing on examples from both single-species and multiple-species reaction diffusion models. A modified derivation of the nonlocal model using a higher order Taylor series approximation was tested but found to provide little improvement over the original model. We suggest some approaches for choosing nonlocal coefficients and identify particular limitations to be alert to when applying the nonlocal model.
Grigg, Nicola J., Bernard P. Boudreau, Ian T. Webster, and Phillip W. Ford. 2005. "The nonlocal model of porewater irrigation: Limits to its equivalence with a cylinder diffusion model." Journal of Marine Research 63, (2). https://elischolar.library.yale.edu/journal_of_marine_research/86