Numerical modelling of water-wave evolution based on the Zakharov equation (Q2774091)

The goal is to develop a new approach to numerical modelling of water wave evolution based on the Zakharov integrodifferential equation. The authors propose a Hamiltonian formulation of surface wave dynamics, review several widely used computational techniques, and discuss the computational strategy for Zakharov equation. In particular, an efficient Runge-Kutta-type algorithm is presented. In order to outline inherent limitations of any numerical modelling of water waves and to address the problem of predictability of the evolution of gravity and gravity-capillary waves, the authors consider the long-term evolution of wave systems with different numbers of interacting modes, and discuss a simple model of three-dimensional sporadic crescent-shaped patterns on water surface and the evolution of a single gravity wave with a large number of random satelites. In order to illustrate the properties of the present method, the authors give three different numerical examples.