Title: Linear theory for single and double flap wavemakers,
Abstract: In this paper, we are concerned with deterministic wave generation in a
hydrodynamic laboratory. A linear wavemaker theory is developed based on the
fully dispersive water wave equations. The governing field equation is the
Laplace equation for potential flow with several boundary conditions: the
dynamic and kinematic boundary condition at the free surface, the lateral
boundary condition at the wavemaker and the bottom boundary condition. In this
work, we consider both single-flap and double-flap wavemakers. The velocity
potential and surface wave elevation are derived, and the relation between the
propagating wave height and wavemaker stroke is formulated. This formulation is
then used to find how to operate the wavemaker in an efficient way to generate
the desired propagating waves with minimal disturbances near the wavemaker.