Rogue wave formation under the action of quasi-stationary pressure

Highligts
• A vortical model of rogue wave on deep water is proposed.
• The wind action is simulated by the pit of pressure on the free surface.
• The fluid motion is described by an exact solution of 2D hydrodynamic equations.
• Values optimal for rogue wave formation are found numerically.

The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary “pit”. The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.