On the generation of water waves in a flume

The present paper proposes a simple model for the calculation of a time series to control the horizontal motion of the piston of a wavemaker. It is assumed that the initial conditions correspond to water at rest. It is assumed that parameters of kinematics of the fluid (displacement, velocity and acceleration fields) at the initial time are equal to zero. In the first interval the amplitudes grow to an asymptote that corresponds to a regular monochromatic wave. In the second interval the waves decay. Calculated time series were fed in to the control system of our wavemaker and the measured horizontal displacements of the piston compared. The control series was supplemented by terms corresponding to the Stokes type solution by addition of terms with multiples of the basic frequency.