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Early dynamics of the collapse of a wedge-shaped depression on a water free surface

Published online by Cambridge University Press:  26 September 2025

Yağmur Ece Uçar ,
Hamdi Kayaslan ,
Oguz Yilmaz  and
Alexander A. Korobkin
Yağmur Ece Uçar*
Affiliation:
Department of Mathematics, Izmir Institute of Technology, Izmir 35430, Turkey
Hamdi Kayaslan
Affiliation:
Department of Mathematics, Izmir Institute of Technology, Izmir 35430, Turkey
Oguz Yilmaz
Affiliation:
Department of Mathematics, Izmir Institute of Technology, Izmir 35430, Turkey
Alexander A. Korobkin
Affiliation:
School of Engineering, Mathematics and Physics, University of East Anglia, Norwich NR47TJ, UK
*
Corresponding author: Yağmur Ece Uçar, yagmuraydin@iyte.edu.tr
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Abstract

The early stage of a gravity-driven flow resulting from the sudden removal of a floating body is investigated. Initially, the fluid is at rest, with a rigid, symmetric wedge floating on its surface. The study focuses on the initial evolution of the wedge-shaped depression formed on the water’s free surface. The fluid has finite depth, and the resulting flow is assumed to be governed by potential theory. The initial flow is described by a linear boundary-value problem, which is solved using conformal mapping and the theory of complex analytic functions. The behaviour of the flow velocity near the corner points of the fluid domain is analysed in detail. It is shown that the linear theory predicts a power-law singularity in the flow velocity at the vertex of the wedge-shaped depression, with the exponent depending on the wedge angle. As the cavity extends toward the bottom, the flow singularity at the vertex becomes stronger. The local flow near the vertex is shown to be self-similar at leading order in the short-time limit. At the other two corner points – where the initial free surface intersects the surface of the wedge – the linear theory predicts continuous velocities with singular velocity gradients. Theoretical predictions are compared with numerical results obtained using OpenFOAM. Good agreement is observed at short times, except in small vicinities of the corner points, where inner solutions are required. In practical applications, understanding the short-time behaviour of the depressions is important for predicting jet formation in regions of high surface curvature.

JFM classification

Mathematical Foundations: General fluid mechanics Mathematical Foundations: Computational methods Wakes/Jets: Jets

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A51
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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