Nascent water waves induced by the impulsive motion of a solid wall

The description of the generation mechanism of impulse surface waves remains an important challenge in environmental fluid mechanics, owing to the need for a better understanding of large-scale phenomena such as landslide-generated tsunamis. In the present study, we investigated the generation phase of laboratory-scale water waves induced by the impulsive motion of a rigid piston, whose maximum velocity $U$ and total stroke $L$ are independently varied, as well as the initial liquid depth $h$ . By doing so, the influence of two dimensionless numbers is studied: the Froude number $\mathrm {Fr}_p$ = $U/(gh)^{1/2}$ , with $g$ the gravitational acceleration, and the relative stroke $\Lambda _p =L/h$ of the piston. During the constant acceleration phase of the vertical wall, a transient water bump forms and remains localised in the vicinity of the piston, for all investigated parameters. Experiments with a small relative acceleration $\gamma /g$ , where $\gamma =U^2/L$ , are well captured by a first-order potential flow theory established by Joo et al. (1990), which provides a fair estimate of the overall free surface elevation and the maximum wave amplitude reached at the contact with the piston. For large Froude numbers, however, wave breaking hinders the use of such an approach. In this case, an unsteady hydraulic jump theory is proposed, which accurately predicts the time evolution of the wave amplitude at the contact with the piston throughout the generation phase. At the end of the formation process, the dimensionless volume of the bump evolves linearly with $\Lambda _p$ and the wave aspect ratio is found to be governed, at first-order, by the relative acceleration $\gamma /g$ . As the piston begins its constant deceleration, the water bump evolves into a propagating wave and several regimes such as dispersive, solitary-like and bore waves, as well as water jets are then reported and mapped in a phase diagram in the ( $\mathrm {Fr}_p$ , $\Lambda _p$ ) plane. While the transition from waves to water jets is observed if the typical acceleration of the piston is close enough to the gravitational acceleration $g$ , the wave regimes are found to be mainly selected by the relative piston stroke $\Lambda _p$ . On the other hand, the Froude number determines whether the generated wave breaks or not.