Reflection of Obliquely Incident Solitary Waves

Initial-value problem of two-dimensional reflection of solitary waves in shallow water is studied with a finite-difference method. If \(α{>}√3ε (α{=}\)the angle of incidence, ε = a / h , a =wave amplitude, h =undisturbed depth), the solution represents a regular reflection pattern which is composed of incident and reflected waves. On the other hand, if \(α{<}√3ε\), a Mach reflection pattern which consists of three obliquely oriented solitary waves is obtained as an asymptotic solution. This solution agrees very well with the resonantly interacting solitary wave solution predicted by Miles. The run-up at the wall is considerably larger than that in linearized theory when α is close to \(√3ε\), and this result is consistent with that predicted by Miles. It requires the time of order \(100h/√ag(g{=}\)gravitational acceleration) to reach stationary Mach reflection patterns when ε =0.05.