A three-dimensional numerical model for eutrophication and pollutant transport

Mathematical analysis of a three-dimensional eutrophication model

“…Two-dimensional depth-averaged models for nutrient-phytoplankton have been given by Arino et al [3] and Cioffi and Gallerano [9] for the case of shallow water, by means of different systems of partial differential equations. For the fully three-dimensional case, several numerical models have been proposed, for instance, by Drago et al [15], Yamashiki et al [33] or Park et al [27], but any of them presents theoretical results of existence or uniqueness of solution, only numerical simulations for particular lagoons and bays. The most remarkable result of existence of (periodic) solution for a nutrient-phytoplankton-zooplankton-oxygen model can be found in the recent paper of Allegretto et al [2].…”

Optimal control of a bioreactor

“…In this work we have considered a relatively simple -although realistic enough -model, where only four biological variables appear (the formulation of the biochemical interaction terms and their meaning can be found, for instance, in Canale [8] or Drago et al [13]). Thus, we consider u ¼ ðu 1 ; u 2 ; u 3 ; u 4 Þ; where: u 1 : Generic nutrient concentration, for instance, nitrogen (as will be considered in our case) or phosphorus, u 2 : Phytoplankton concentration, u 3 : Zooplankton concentration, u 4 : Organic detritus concentration.…”

“…Two-dimensional depth-averaged models for nutrient-phytoplankton have been given by Arino et al [7], and Cioffi and Gallerano [11], for the case of shallow water. For the fully three-dimensional case, several numerical models have been proposed, for instance, by Drago et al [13], Yamashiki et al [19] or Park et al [16], but no one gives theoretical results of existence or uniqueness of solution, but only numerical simulations for particular areas. The most remarkable results of existence of solution for a nutrient-phytoplankton-zooplankton-oxygen model can be found in the paper of Allegretto et al [3] (for a particular periodic case), and in the recent work of the authors [6] (presenting also 0096-3003/$ -see front matter Ó 2010 Elsevier Inc. All rights reserved.…”

Pollution release tied to invariant manifolds: A case study for the coast of Florida

“…The argument above only holds if there is a reasonable difference between the motion of the tracers and the pure Lagrangian model. In reality, contaminant are not advected exactly as fluid particles and their motion is best described by an advection-diffusion equation [39,40], for example. The parcels in Fig.…”