| Abstract: | In this paper, the authors treat the free‐surface waves generated by a moving disturbance with a constant speed in water of finite and constant depth. Specifically, the case when the disturbance is moving with the critical speed is investigated. The water is assumed inviscid and its motion irrotational. The surface tension is neglected. It is well‐known that the linear theory breaks down when a disturbance is moving with the critical speed. As a remedy to overcome the invalid linear theory, approximate non‐linear theories have been applied with success in the past, i.e. Boussinesq and Korteweg de Vries equations, for example. In the present paper, the authors describe a finite element method applied to the non‐linear water‐wave problems in two dimensions. The present numerical method solves the exact non‐linear formulation in the scope of potential theory without any additional assumptions on the magnitude of the disturbances. The present numerical results are compared with those obtained by other approximate non‐linear theories. Also presented are the discussions on the validity of the existing approximate theories applied to two types of the disturbances, i.e. the bottom bump and the pressure patch on the free‐surface at the critical speed. Copyright © 1999 John Wiley & Sons, Ltd. |
