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Of all the various types of fluid wave motion that occur in nature, surface water waves are not only the most easily observed but of great scientific importance because of their impact on coastal and offshore structures and ship dynamics, their implication for sediment transport and coastal morphology and their overall effect on the energy and momentum exchange between the atmosphere and oceans.
On the other hand there are fascinating mathematical problems associated with water waves of great interest to both pure and applied mathematicians, and the water wave equations have spawned whole areas of mathematics, for example the theory of the Korteweg-deVries equation. While there has been substantial progress in the theory of water waves - particularly 2D water waves - there is a potential for significant advances in the analytical and numerical aspects of 3D nonlinear waves, including qualitative aspects that heretofore not been predicted or anticipated. In addition, the recent development of mathematical theories for non-linear, interacting and breaking waves have pointed the way to new ideas for theores of waves interacting with wind, turbulence and other waves. In all cases experimental data is beginning to be available to discriminate between and contribute to conflicting mathematical theories, and there are new possibilities for computing critical aspects of these phenomena and these need to be discussed in detail.