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

Published online by Cambridge University Press:  03 April 2025

Wladimir Sarlin Open the ORCID record for Wladimir Sarlin [Opens in a new window] ,
Zhaodong Niu ,
Alban Sauret Open the ORCID record for Alban Sauret [Opens in a new window] ,
Philippe Gondret Open the ORCID record for Philippe Gondret [Opens in a new window]  and
Cyprien Morize Open the ORCID record for Cyprien Morize [Opens in a new window]
Wladimir Sarlin*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, F-91405 Orsay, France Laboratoire d’Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Zhaodong Niu
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, F-91405 Orsay, France Laboratoire d’Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Alban Sauret
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park 20742, MD, USA Department of Chemical and Biomolecular Engineering, University of Maryland, College Park 20742, MD, USA
Philippe Gondret
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, F-91405 Orsay, France
Cyprien Morize
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, F-91405 Orsay, France
*
Corresponding author: Wladimir Sarlin, [email protected]
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Abstract

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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A25
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Sarlin et al. supplementary material movie 1

210715 Dispersive wave generated by the impulsive motion of a rigid piston in a water channel. The translating wall experiences a constant acceleration phase, followed by a constant deceleration of equal duration. The total stroke of the piston is 7 cm, its maximal velocity 0.42 m/s and the initial water depth is 20 cm.
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Sarlin et al. supplementary material movie 2

210706 Solitary wave generated by the impulsive motion of a rigid piston in a water channel. The translating wall experiences a constant acceleration phase, followed by a constant deceleration of equal duration. The total stroke of the piston is 15 cm, its maximal velocity is 0.47 m/s and the initial water depth is 10 cm.
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Sarlin et al. supplementary material movie 3

210610 Spilling breaking bore generated by the impulsive motion of a rigid piston in a water channel. The translating wall experiences a constant acceleration phase, followed by a constant deceleration of equal duration. The total stroke of the piston is 30 cm, its maximal velocity is 0.6 m/s and the initial water depth is 3 cm.
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Sarlin et al. supplementary material movie 4

210702 30.0 Plunging breaking bore generated by the impulsive motion of a rigid piston in a water channel. The translating wall experiences a constant acceleration phase, followed by a constant deceleration of equal duration. The total stroke of the piston is 30 cm, its maximal velocity is 1.09 m/s and the initial water depth is 3 cm.
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File 11.1 MB
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Sarlin et al. supplementary material movie 5

210702 14.5 Water jet generated by the impulsive motion of a rigid piston in a water channel. The translating wall experiences a constant acceleration phase, followed by a constant deceleration of equal duration. The total stroke of the piston is 14.5 cm, its maximal velocity is 1.19 m/s and the initial water depth is 3 cm.
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File 9.4 MB