Proposed here is a study featuring models for the interaction of surface and internal oceanic waves with sediment-laden bottom topography. The project includes derivation and mathematical analysis of models, development of algorithms for the approximation of solutions, implementation of the algorithms as computer codes, comparisons of the output of numerical simulations with field data, the use of the models for prediction and their development as a tool for effective coastal engineering. The basic issue under consideration is challenging in that it involves the temporal evolution of two free surfaces whose dynamics are connected in a complex and nonlinear way. The wave motion involves the deformation of the water's surface, or in the case of internal waves, the pycnoclines. Even over a fixed bottom, these issues are difficult in their exact formulation, and consequently model equations are typically used. In the present conception, the bottom is not fixed, and this added complexity is what makes the issues proposed here for study scientifically very interesting. In view are three-dimensional models that are initiated by incoming wave fields from deep water. These models will allow for long-shore variation and take account of reflection. It is planned to develop such models and to test them extensively against both laboratory experiments and field observation. Comparisons are in view at several sites around the world, including the Field Research Facility of the US Army Corps of Engineers at Duck, NC, a site of the Polish Academy of Sciences on the Baltic Sea, the North Coast of the Magdelan Islands in the Gulf of St. Lawrence, the Gold Coast of Australia, the Island of Djerba off the Tunisian coast and two regions in Morocco (Alger in the Gibraltar Strait and Agadir on the Atlantic coast). <br/><br/>The motivation for carrying out the study outlined above is several-fold. First is the pure science of the subject. The project involves interesting and substantial issues from hydrodynamics, partial differential equations, and sediment transport theory. Secondly, it is an ideal venue in which to acquaint students with interdisciplinary research. There is a strong practical reason for this study as well. The erosion and retreat of coastlines is a worldwide phenomenon. Global warming will increase the activity of storms, raise the sea level, and further degrade the present, sometimes catastrophic state of many beaches. Fragile Arctic coasts, beaches on the Great lakes and on many coastal regions already display the unmistakable signs of deterioration caused by these global changes and aggravated by social developmental pressure. Severe erosion is likely to spread to many coastal areas within half a century and thus increase the demand for effective prevention methods. The present project aims at deepening our understanding of fundamental wave-bottom interaction processes, especially as regards sediment dispersal. Going beyond the science, the project also grapples with the intelligent use of this kind of knowledge in designing coastal protection strategies. With experience already in hand, it is clear that there are a variety of protection options and that it is not always smart to simply build some permanent, often-ugly structure. So-called 'soft' protection methods are a useful addition to the reperatoire of the coastal engineer. These are much less expensive when they can be made to work. The assessment of the practicality of a protection plan, be it 'hard' or 'soft' relies upon the kind of knowledge investigated under the auspices of this project.
FRG: Modeling Waves and Sediment Transport in Coastal Zones