A higher order theory for deep water waves

The classical problem of describing the characteristics of deep water waves of finite amplitude is considered. The method of analysis initially follows that of Nekrasov, but differs in that a non-linear algebraic equation is derived. This equation is solved to the third, fifth and fifteenth order by means of a digital computer and the data is presented in tabular form. Expressions for the wave speed and wave shape, predicted by the analysis, are compared with the results obtained by Stokes. The highest wave in water is also discussed

Geomorphology and earth system science

Earth system science is an approach to obtain a scientific understanding of the entire Earth system on a global scale by describing how its component parts and their interactions have evolved, how they function, and how they may be expected to continue to evolve on all time-scales. The aim of this review is to introduce some key examples showing the role of earth surface processes, the traditional subject of geomorphology, within the interacting Earth system. The paper considers three examples of environmental systems in which geomorphology plays a key role: (i) links between topography, tectonics, and atmospheric circulation; (ii) links between geomorphic processes and biogeochemical cycles; and (iii) links between biological processes and the earth’s surface. Key research needs are discussed, including the requirement for better opportunities for interdisciplinary collaboration, clearer mathematical frameworks for earth system models, and more sophisticated interaction between natural and social scientists