On the Trajectories of Particles in Solitary Waves

Abstract

Across the country, school students learn that ocean waves cause water particles to form looping paths, traveling in circles which become smaller as you look deeper underwater. In this paper, we investigate the approximations which are used to make this claim. Furthermore, we investigate closer approximation techniques which show that these looping paths actually propogate forward with the wave's motion. Finally, we investigate the specific case of the soliton, which causes particles underneath to travel in a forward-moving arc, with no looping motion at all. With this background, we examine the recent work of A. Constantin and collaborators, specifically his conclusion that our results for the soliton hold for any solitary wave.