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Tidal sea mathematical modelling: Current applications and future developments
Authors:Y Coeffe  S Courtier  B Latteux
Abstract:The purpose of this paper is to describe the contribution of the LNH/EDF, France, which work on the two following topics in sea modelling: (a) calibration and use of mathematical tools in order to perform numerical forecasts and simulation of sea patterns; and (b) important research effort, in order to develop ever more accurate numerical algorithms and to understand ever better the physical processes.Simulating marine flows means in any case filtering of the sea-phenomenon on both time and space scales. The use of such filters related to the preponderant scales in each study leads to parameterize the unsolved scales through specific behaviour laws such as turbulence and dispersion.Specific properties of sea modelling at LNH are based on the splitting-up technique applied to each term of the shallow water equations. The advective transport is solved through a Lagrangian method. The diffusive and propagative part is solved through two different algorithms depending on which method is used, a finite-difference method or a finite-element method.The current applications of tidal computations are numerous and various, the examples given in this paper concern on one hand the simulations of uncovering tidal flats in the estuary of the River Canche and on the other hand of storm surge and tide interaction in the North Sea and English Channel. Some future developments among others are relative to the improvement of the properties of the solver of the advective term, and the treatment of uncovering and overcovering tidal areas. About the mixing properties of fluid, some research work concerns the better understanding and modelling of the big vortex shedding behind a hindrance cross a flow; therefore an experiment is done at this time which will provide a data collection useful to the calibration of a 2D-turbulence model.Other simulations and research works are performed in fields connected to tidal current computations such as thermal impact or bed-load transport studies which lead to the problems of long term simulation and modelling of residual currents which are of a lower order of accuracy.In order to conclude, the necessity is stressed of a double effort, scientific on one hand and algorithmic on the other hand.
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