Integral Model of the Propagation of Stationary Potential Waves in Fluids

摘要

Much attention in fluid mechanics is traditionally devoted to the study of potential waves. For these waves, the constructive nature of the classical analytical models of fluid flows was originally demonstrated in [1] and definitions of the main properties of waves (in' particular, the concepts of the group and phase velocities) were introduced [2, 3]. The important role played by nonlinear effects (which, together with dispersion, determine the disturbed surface shape) was established [4], and effective methods for the investigation of complex equations were developed [5]. The current interest in studying potential waves is related to the search for a mathematical description of the complicated pattern of the disturbed sea surface [TJ^jncluding the waves of an anomalously large amplitude (rogue or freak waves), which cause considerable damage to seaside structures and ships.