Tidal and density currents' three-dimensional modeling with the finite element method in the St. Lawrence estuary

Period of execution: September 1988 to September 1994

Customer's name: Fisheries and Oceans Canada section Canada Coast Guard, in partnership with the National Research Council of Canada

Summary:

The study's objective consists of modeling the tidal and density current's propagation in the estuary located between Orleans Island and Pointe-des-Monts. Several two-dimensional models were initially tested. At this time various types of elements and resolution methods were adopted with an aim of determining the most promising ways in the realization of a three-dimensional model. From the analysis of the results obtained by various models, it appears that the model using a T63 type element, the Lax-Wendroft method with the diagonal masses matrix and exact integration technique, is not only the most precise but also the most economic. Taking into account the performances of this model, it was possible to use a high resolution meshing (6,000 elements and 25,000 calculations points). This one uses hardly 20 megabytes of memory and turns at a rate of 1000 steps per hour on a PC 450 MHz type computer.

A three-dimensional hydrodynamic model in layers joined by a diffusion-transport model was then developed according to the same technique. By taking into account the density structure's influence on the movement equations, it was possible to show the density currents dominating importance on the St. Lawrence maritime estuary's circulation.

The model proved to be an effective instrument to study and analyze the density structure's influence on tidal current propagation. It makes it possible to reproduce the principal elements of estuarine circulation: strong tidal currents in the middling estuary, barotropic and baroclinic instabilities in the maritime estuary. The models' results allow us to believe that these instabilities, caused by the complex estuary's bathymetry and density gradient's presence, would be at the origin of the two swirls observed in the St. Lawrence maritime estuary. The influence of the Coriolis force on the creation of these swirls is also discussed.

This model is intended mainly for the simulation of coastal processes such as tidal currents, density currents, conservative material diffusion and transport. It can also be used to study the weather forces' influence on oceanic circulation. Other uses are possible taking into account the fact that the Navier-Stokes equations are common to several disciplines such as fluid mechanics, meteorology and oceanography. Some improvements of the model are envisaged: ice cover formation and drift off calculation, air-water-ice interactions and sediment transport mechanism studies.

Principal activities carried out:

• Review and criticism of modeling work completed on the St. Lawrence;
• Construction of two meshings with irregular triangular elements which reproduce the shape of the St. Lawrence estuary between the Orleans Island and a cross section between Matane and Pointe des Monts;
• Improvement of the performances of several 2D hydrodynamic modules developed by Dr. J.L. Robert using various spatial and temporal 2D discretization types;
• Development of a new module based on the use of exact integration principles of all the Navier-Stokes equations' two-dimensional formulation terms;
• Development of a temporal module making it possible to use, in an optimal way the new hydrodynamic module by using a Lax-Wendroft type diagram with diagonal masses matrix;
• Validation of the new numerical codes programming with a series of numerical tests;
• Development of a new reverse modeling technique to fix the in-layer hydrodynamic model's initial conditions;
• Realization of simulations corresponding to real hydrodynamic conditions with various 2D hydrodynamic modules;
• Various hydrodynamic models' results validation with tidal and current measurements carried out in the St. Lawrence over the last 20 years;
• Various 2D hydrodynamic modules' behaviour comparison and analysis;
• Development of two new hydrodynamic modules based on the use of exact integration principles of all the Navier-Stokes equations' three-dimensional formulation terms as well as the diffusion transport equation;
• Realization of simulations corresponding to real hydrodynamic conditions with the 3D barotropic and baroclinic hydrodynamic modules (density effects);
• Validating the 3D barotropic and baroclinic hydrodynamic models' results with tidal and current measurements carried out in the St. Lawrence over the last 20 years.

Reports, Presentations, Publications:

Gagnon, M., 1994. Modélisation tridimensionnelle des courants de marée et de densité de l'estuaire du Saint-Laurent par la méthode des éléments finis. Thèse de Doctorat, Université Laval, juin 1994, 419pp.

Gagnon, M., J.L. Robert et Y. Ouellet, 2001. Development and use of multiple-levelled finite element model for simulating hydrodynamic processes in coastal waters: tested in St.Lawrence estuary. En préparation.

Gagnon, M., J.L. Robert et Y. Ouellet, 2001. Développement d'un modèle 2D quasi-quadratique aux éléments finis pour la modélisation de la marée et des courants de marée: validation dans l'estuaire du Saint-Soumis à Revue Européenne d'éléments finis.

En révision.

Gagnon, M., J.L. Robert and Y. Ouellet, 1994. 3D finite element model of Tides and Tidal Streams in the St.Lawrence Estuary. Zone Cotière Canada 94. Halifax, Nouvelle Écosse, septembre 1994.

Gagnon, M., J.L. Robert and Y. Ouellet, 1992. High resolution 2D-3D model of Tides and Tidal Streams in the St.Lawrence Estuary. Mesoscale Meteorology and Oceanography conference. 26th annual congress of Canadian Meteorology and Oceanography Society, Université Laval, juin, 1992.

Gagnon, M., J.L. Robert and Y. Ouellet, 1991. 2D-3D Finite Element Tidal Model of St.Lawrence Estuary. International Liège Colloquium on Ocean Hydrodynamics. Liège, mai 1991.

Gagnon, M., J.L. Robert, 1992. Comparaison et performance de deux modèles multi-couches utilisant la méthode des éléments finis pour la modélisation des processus côtiers où: Evaluation and performance of two multiple-levelled finite element model for simulating hydrodynamic processes in coastal waters. Contract with National Research Council of Canada. Civil Engineering Department, Laval University, Sainte-Foy, oct. 1992, GCS92-04, 134pp.

Gagnon, M. 1989. La modélisation des courants de marée barotropes et baroclines dans l'estuaire du Saint-Laurent et analyse de deux logiciels destinés o la modélisation des processus côtiers. Civil Engineering Department, Laval University, nov. 1989, GCS-89-01, 66pp.

Gagnon, M., E. Légaré, 1989. Comparaison entre deux modèles hydrodynamiques destinés à la modélisation des processus côtiers. Civil Engineering Department, Laval University, nov. 1989, GCS-89-02, 42pp.

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