Models for Wave-Bottom Interaction and the Formation of Sand Bars and Sand Ridges

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Bona9974116 The overall technical objective of the project is to developthree-dimensional topographical models that describe seabeddynamics in wave-dominated near-shore zones and shelf regionswhere single and multiple sand bars or sand ridges form a centralmorphological feature. The investigator models and analyses theeffects of waves and currents on coastal dynamics. This ischallenging because of the presence of two free surfaces, thewater surface and the movable bottom, both of which change overtime, and which interact with each other through complex,nonlinear processes. The model features nonlinear, dispersive,dissipative partial differential equations to describe theevolution of waves coming in to the shore from deep water. Theseequations, which are of Boussinesq type, are coupled to a modelfor run-up and reflection at the shoreline. Once the evolution ofthe water surface is approximately known, the velocity field inthe bulk of the fluid may then be determined via potentialtheory. This velocity field is then viewed as driving a viscous,sediment-laden boundary layer in which the sediment transport istaking place. The velocity distribution in this layer isdetermined using ideas similar to those pioneered byLonguet-Higgins. By applying conservation of sediment mass in aninfinitesimal form, a differential equation is thereby inferredthat serves to determine the bottom deformation. Thus the entiremodel is somewhat complicated, consisting of a nonlinearinitial-boundary-value problem for the wave motion coupled in anonlocal way to a conservation law for the bottom movement. Thismodel is developed in detail, analysed and implemented as acomputer code. Model predictions are compared with field data.It is also proposed to link the computer code with input from aGeographical Information System, to allow easier deployment ofthe model in real situations. The underlying motivation for the project is two-fold.First, there is a desire to understand both qualitatively andquantitatively some of the fundamental processes that lead to theformation and maintenance of bottom structure in coastal zonesand on continental shelves. This involves a thorough knowledgeof both the wave environment and the dynamics of the bed as it isinfluenced by waves and by currents. Second, and not lessimportant, the project responds to the need for new and moresophisticated tools to aid in the development of strategies todeal with real coastal engineering problems. The project has thepotential to contribute to the study of a number of importantscientific and environmental issues. The ocean margins in NorthAmerica are vast and in many places, troubled. Indeed, erosionof unconsolidated coastlines is a world-wide phenomenon that isnot well understood. Global warming will aggravate theseproblems by increasing sea levels, thus causing shore retreat andproviding a better base for the scour and erosion associated withwave activity. Fragile Arctic coasts and low-altitude regionsare already displaying unmistakable signs of deterioration causedby these global changes. Severe erosion may well spread to othercoast regions within the next half century, and thus there willbe an increased interest in effective prevention methods. Inaddition to "hard" protection schemes such as the construction ofseawalls and the like, there will be an increased demand for"soft" protection strategies that take advantage of naturalprocesses.