M. Ioualalen, 4TH-ORDER APPROXIMATION OF SHORT-CRESTED GRAVITY-WAVES IN INFINITE DEPTH, Comptes rendus de l'Academie des sciences. Serie 2, Mecanique, physique, chimie, sciences de l'univers, sciences de la terre, 316(9), 1993, pp. 1193-1200
From observations and measurements one can easily see that water wave
fields are mainly three-dimensional. The main purpose of this Note is
to provide accurate approximate analytical solutions of three-dimensio
nal gravity waves. The computed profiles extend the third order soluti
ons given by, Hsu et al. (1979) up to the fourth order, using a pertur
bation method with a small parameter epsilon. The proposed solutions m
ay be easily exploited and they represent a good approximation of the
physical surface wave.