Statistical characteristics of anomalously large surface waves based on computational experiments

Abstract

The computational experiments on modeling surface waves, which are used for studying the statistics of the occurrence of extremely large surface waves depending on the parameters of the initial waves, are considered. The sudden occurrence of abnormally large waves in the ocean is a big hazard for marine vessels and structures. In recent years, incontrovertible evidence of this phenomenon, such as instrumentation records and photographs, has been presented. The main method of studying the phenomenon of rogue waves in this work is computational experiments based on the complete nonlinear hydrodynamic equations of an ideal liquid with a free surface. The method of conformal variables that is used for the original system of equations enables one to make effective and accurate calculations by computers and computing complexes. According to the experimental results, the statistics of the occurrence of anomalously large surface waves is studied. The use of dissipation and pumping in these computational experiments has made it possible to perform continuous calculations that are not stopped if a rogue wave occurs. The intensity of the occurrence of rogue waves depending on the values of the squares of the mean steepness and wave dispersion is estimated. It is shown that doubling the computational region almost doubles the intensity. The proposed procedure of the computational experiments allows estimating the average waiting time of a rogue wave in the assigned region.