On modelling of periodic surface waves of an ideal heavy incompressible fluid

An algorithm for modelling periodic surface waves of an ideal heavy incompressible fluid is presented, which, unlike most of the known ones, does not use hypotheses about the form of the potential function specifying the laminar flow. The analysis shows that the studied laminar flow is not a potential flow. The algorithm is based on the study of cyclic motion of a fluid particle within the laws of classical mechanics. The equations of motion using functions of velocity and pressure gradient, periodic in time, are obtained. It is shown that the implementation of these equations is equivalent to the execution of the Euler equation and the continuity equation. The model admits the existence of large amplitude waves embedded in the flow of periodic waves, the so-called rogue waves.