L'absorption Dynamique des Ondes de Gravité en Régime Instationnaire

This study deals with the dynamic absorption of water waves. We focus here our attention on the case of a simple devce, a 2D piston, in order to exploit the well-known expressions of the potential as far as possible in the design of new absorption laws. We consider a semi-infinite two dimensional wave tank closed by a mobile vertical plane. An unsteady wave train generated at infinity impiges on this plate. The problem of the dynamic absorption consists in finding, in real time, the velocity to be given to the plate so that the radiated and the reflected wave trains should cancel each other. We propose here to derive this velocity from the forces measured on the plate. We first derive a frequency dependant transfer function between the optimal velocity of the paddle and the total force for the case of steady time harmonic incident waves. As a consequence of the linear approach, we choose, the time domain velocity leading to the complete absorption of the incident wave train is obtained by convolutiong the inverse Fourier transform of this transfer function with the measured hydrodynamic force. Unfortunately, the impulse response function of the ideal absorber derived that way is not causal; thus, it cannot be used just as is as the control loop of the physical absorbing device. So, we suggest two causal non ideal approximations of the ideal non-causal controller.