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 FH=U(gH)−0.5FH=U(gH)−0.5 approaching the critical value (≈1.0≈1.0), where UU is the speed of the foil, gg is the gravitational acceleration and HH is the depth of quiescent water. The transition from sub-critical to the super-critical state is studied. As FHFH 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.