Mathematical Modelling of 3D Coastal Morphology

Abstract

The present lecture deals with models for situations in which the spatial dimensions cannot be separated according to the scales of the morphological processes. Rather common examples of such situations are the morphological evolution near structures (e.g, breakwaters), river outflows, tidal inlets, etc. But also in the absence of such distinct disturbances, the system can be more complex than one might expect at first sight, for instance due to the presence of a rip channel and bar system. After an outline of the basic concepts of various state-of-the-art models which are claimed to describe 3D coastal evolutions, the potentials and shortcomings of the various model types will be discussed and the role of the constituent process models will be considered from a morphological modelling point of view. Subsequently, the methodology and some pitfalls of practical application will be discussed, and, finally, I will identify the principal needs for further research and the approaches which may be taken. In their book entitled 'Nearshore Dynamics and Coastal Processes' (1988), Horikawa and his colleagues give an excellent review of the state of the art in 30 coastal morphological modelling, though with the emphasis on Japan. In this lecture, I will not attempt to redo their work, but I will give some additions and comments, based on my own experience and recent European research. The lecture leads to the conclusion, that significant achievements have been made in the numerical modelling of 3D coastal morphology, but that more research over a wide area is needed to make these models robustly applicable to arbitrary situations. Initial sedimentation/erosion models definitely deserve their place in coastal morphological modelling, though not as a quantitative predictor of morphological evolutions, but rather as a tool for process analysis and orientation. The prediction potential of strictly 2D-horizontal morphodynamic models will probably remain restricted to special classes of problems, and to short-term evolutions. The highest expectations concern quasi-3D models, which include the vertical structure of the water and sediment motion. The first results of the "empirical emulation" of such a model by Watanabe and his co-workers are very encouraging. Part of the future research will have to deal with the physical processes which constitute the morphodynamic system. As these can have very complicated interactions in the longer run, especially if the extraneous conditions are stochastic, it is important to have their further investigation defined from a morphodynamic point of view. Another part concerns the 3D morphodynamic process, as such. The present understanding of this process is not good enough to judge the results of 3D coastal evolution models in arbitrary situations. Long-term modelling, at least its physics-based branch, is a new and challenging field, which certainly deserves further exploration. No doubt, this will also he beneficial to medium-term morphodynamics.