Paralic Confinement: Models and Simulations
- PDF / 1,414,426 Bytes
- 19 Pages / 439.37 x 666.142 pts Page_size
- 71 Downloads / 200 Views
Paralic Confinement: Models and Simulations Emmanuel Frénod · Antoine Rousseau
Received: 14 December 2011 / Accepted: 29 February 2012 / Published online: 14 March 2012 © Springer Science+Business Media B.V. 2012
Abstract This paper deals with the mathematical modelling of confinement of paralic ecosystems. It is based on the recent paper (Frénod and Goubert in Ecol. Model. 200(1– 2):139–148, 2007) that presents a modelling procedure in order to compute the confinement field of a lagoon. Here, we improve the existing model in order to account for tide oscillations in any kind of geometry such as non-rectangular lagoons with a non-flat bottom. The new model, that relies on PDEs rather than ODEs, is then implemented thanks to the finite element method. Numerical results confirm the feasibility of confinement studies thanks to the introduced model. Keywords Mathematical modelling · Numerical modelling · Partial differential equations · Numerical simulations · Finite elements · Confinement · Ecological systems 1 Introduction The concept of confinement was introduced by Guelorget and Perthuisot [7] in 1983. It has latter been widely used, studied, discussed and tested (see Guélorget and Perthuisot [7, 8], Guélorget, Frisoni and Perthuisot [5], Guélorget et al. [6], Ibrahim et al. [10], Debenay, Perthuisot and Colleuil [3], Redois and Debenay [11], Barnes [2], Frénod and Goubert [4] and Tagliapietra et al. [12]) leading to the conclusion that it is a pertinent parameter controlling the features of living benthic population in paralic ecosystems. Benthic species are
E. Frénod Université Européenne de Bretagne, Lab-STICC (UMR CNRS 3192), Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic, 56017, Vannes, France E. Frénod Université de Strasbourg, IRMA, INRIA CALVI, 7 rue René Descartes, 67084 Strasbourg Cedex, France A. Rousseau () Inria, Laboratoire Jean Kuntzmann, 51 rue des mathématiques, 38041 Grenoble Cedex 9, France e-mail: [email protected]
2
E. Frénod, A. Rousseau
species living on the seabed and paralic ecosystems are ecosystems encountered in estuaries, lagoons and closed bays. In all earlier works, no precise definition and no model were given to compute or measure confinement. Yet a biological indicator of confinement, based on species which are specific of each confinement level were existing and well adapted to regions where tide is weak. Until the paper by Frénod and Goubert [4] it was not clear that confinement was also a controlling parameter of tide-influenced paralic ecosystems. In order to help to provide an answer to this question, Frénod and Goubert [4] started with the introduction of a definition of confinement usable for modelling purposes: Definition 1 The confinement value at any point of the lagoon is the time for the sea-water to reach this point. The reason why of such a definition is the following: evaporation process on the lagoon surface induces a water flow from the sea to the lagoon far end. All along this flow, water encounters living organisms that take a s
Data Loading...
