Finite groups of gravity waves

Groups of gravity waves of finite length created in deep, originally quiescent water by an oscillating or moving surface pressure are constructed by superposition of the Cauchy-Poisson solution. This construction gives substance and reassurance to the concept of “wave packets” progressing with group velocity associated with the individual waves in the packets, a concept so important to water-wave research. The effects of viscosity are taken into account, thereby not only justifying the extensively used but completely artificial damping factor initiated by Lamb (1916, see Lamb 1945, p. 413), but also showing the hitherto largely unexplored spatial damping of waves.