An analytical and numerical study of a vertically discretized multi-paddle wavemaker for generating free surface and internal waves

A vertically discretized multi-paddle wavemaker is proposed that generates various wave types without the depth-invariant flow condition limitation associated with conventional piston type wavemakers. A first-order mathematical formulation for the paddle stroke is derived and used to selectively generate free surface waves similar to either piston type or flap type wavemakers, depending on the number of utilized paddles. The mathematical formulation is further extended to a multi-phase internal wave case. Paddle discretization performance is evaluated using OpenFOAM, a numerical model that solves the Navier-Stokes equations for two (or more) immiscible and incompressible fluids. Dynamic meshing capability is incorporated in the model. Model results show multiple discrete paddles efficiently generate deep water waves under laminar flow conditions. In intermediate wave conditions, the multi-paddle discretization is less advantageous. Internal waves and resulting free surface waves among air, oil, and water phases are simulated using only two paddles and imposing a fast mode. Model results agree with flow characteristics for both internal and locked free surface waves.