Waves induced by a two-dimensional foil advancing in shallow water

The waves generated by a two-dimensional (2D) foil moving in shallow water at subcritical, super-critical and hyper-critical speeds have been investigated. The velocity potential theory is adopted to prescribe the flow with vortex shedding. The fluid-structure interaction, as well as the fully nonlinear free surface movement, is tackled by the mixed-Euler-Lagrangian method through a time stepping scheme. It has been observed that upstream solitary waves emerge when the depth Froude number F-H = U(gH)-(0.5) approaching the critical value (approximate to 1.0), where U is the speed of the foil, g is the gravitational acceleration and H is the depth of quiescent water. The transition from sub-critical to the super-critical state is studied. As F-H keeps increasing to a hyper-critical state, a single upstream soliton is caught up with by the foil. When the foil travels with a negative attack angle at hyper-critical speed, a 'reversed soliton' has been found. (C) 2015 Elsevier Ltd. All rights reserved.