Resonance wave pumping: wave mass transport pumping

It has been previously reported that pinching at intrinsic resonance frequencies a valveless pump (or Liebau pump) results in a strong pulsating flow. A free-surface version of the Liebau pump is presented. The experiment consists of a closed tank with a submerged plate separating the water into a free-surface and a recirculation section connected through two openings at each end of the tank. A paddle is placed at an off-centre position at the free-surface and controlled in a heaving motion with different frequencies and amplitudes. Near certain frequencies identified as resonance frequencies through a linear potential theory analysis, the system behaves like a pump. Particle Image Velocimetry (PIV) is performed in the near free surface region and compared with simulations using Volume of Fluid (VOF) method. The mean eulerian mass flux field ($\rho \boldsymbol{u}$) is extracted. It is observed that the flow is located in the vicinity of the surface layer suggesting Stokes Drift (or Wave Mass Transport) is the source of the pumping. A model is developped to extend the linear potential theory to the second order to take into account these observations.