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Free-surface disturbances due to the submersion of a cylindrical obstacle

Published online by Cambridge University Press:  06 September 2021

R. Martín Pardo Open the ORCID record for R. Martín Pardo [Opens in a new window]  and
J. Nedić Open the ORCID record for J. Nedić [Opens in a new window]
R. Martín Pardo*
Affiliation:
Department of Mechanical Engineering, McGill University, Montréal, QCH3A 0G4, Canada
J. Nedić*
Affiliation:
Department of Mechanical Engineering, McGill University, Montréal, QCH3A 0G4, Canada
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

JFM classification

Instability: Nonlinear instability Waves/Free-surface Flows: Surface gravity waves Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A1
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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