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Application of transport equations for constructing exact solutions for the problem of motion of a fluid with a free boundary

Published online by Cambridge University Press:  11 March 2020

E. A. Karabut Open the ORCID record for E. A. Karabut [Opens in a new window] ,
E. N. Zhuravleva  and
N. M. Zubarev
E. A. Karabut*
Affiliation:
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
E. N. Zhuravleva
Affiliation:
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
N. M. Zubarev
Affiliation:
P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119333, Russia Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620016, Russia
*
†Email address for correspondence: [email protected]
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Abstract

A problem of an unsteady plane flow of an ideal incompressible fluid with a free boundary is considered. It is shown that the solution can be found by using a complex transport equation. In this case, the problem is linearized by means of the hodograph transform (the velocity components are chosen as independent variables). Examples of exact solutions are obtained. Various scenarios of formation of singularities on the free boundary within a finite time are considered.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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