Modeling of rogue wave shapes in shallow water

Abstract

Various shapes of rogue waves are discussed within the framework of the mechanism of nonlinear focusing of transient frequency modulated wave groups. A particular attention is paid to the formation of troughs in front of high crests. The conditions of appearance of the "three sisters" are discussed too. It is important to emphasize that this mechanism is not too sensitive to the variation of the shape of transient frequency modulated wave groups. The variable-polarity shape of a rogue wave is more probable than only one crest or one trough, because the generation of the latter ones needs a specific phase relation between individual waves in the group.