4TH-ORDER APPROXIMATION OF SHORT-CRESTED GRAVITY-WAVES IN INFINITE DEPTH

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.