Euler’s Figures and Extreme Waves

Abstract

It is known that physical processes of generation and transformation of nonlinear waves can differ dramatically; nevertheless, equations and analytical solutions describing these processes are often similar. For example, shock-, soliton-, and cnoidal-like solutions are well known in nonlinear dynamics. However, these well-known waves do not exhaust all waves observed in experiments and in the Nature. For example, parametrically (vertically) excited strongly nonlinear surface waves are not well known. The transformation of these waves into surface craters, jets, drops, and folded wave profiles was observed recently. The appearance of surface bubbles and craters, the collapse of them, and the formation of surface jets may happen on the ocean surface during seaquakes. Another example is forced atomization of liquid surface by highly nonlinear waves. The forms of the surface waves are determined by surface tension and some resonant condition. It is found that the strongly nonlinear Faraday waves correspond to some Euler’s figures.