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Family of self-similar solutions with a free boundary in a fluid wedge

Published online by Cambridge University Press:  03 November 2025

Evgenii Karabut Open the ORCID record for Evgenii Karabut [Opens in a new window]  and
Helena Zhuravleva Open the ORCID record for Helena Zhuravleva [Opens in a new window]
Evgenii Karabut*
Affiliation:
Lavrentyev Institute of Hydrodynamics , Siberian Branch, RAS, Novosibirsk, Russia
Helena Zhuravleva
Affiliation:
Lavrentyev Institute of Hydrodynamics , Siberian Branch, RAS, Novosibirsk, Russia
*
Corresponding author: Evgenii Karabut, eakarabut@gmail.com
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Abstract

Plane unsteady potential flows of an ideal incompressible fluid with a free boundary are considered in the absence of external forces and surface tension. At the initial time, the flow occupy a wedge with an angle at the apex. For different initial flow velocities and values of the angle at the vertex, a family of exact solutions is found. A method for finding solutions based on reducing the boundary-value problems to systems of ordinary differential equations.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows Mathematical Foundations: General fluid mechanics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1022 , 10 November 2025 , A22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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