It has been demonstrated by the studies of Stokes (1847) and Lcvi-Civita (1925) that surface waves of finite height which are irrotational and periodic can exist in a liquid under the influence of gravity. Furthermore, it was pointed out by Stokes that such waves produce a transport of mass in the direction of propagation and hence possess a certain horizontal momentum relative to the undisturb…
The analytical study of gravity waves of finite height which are periodic and move without change in shape in an ideal irrotational fluid is a subject which has occupied the attention of physicists and mathematicians ever since Stokes published his classic paper entitled “On the Theory of Oscillatory Waves” in 1847.