Exact Local Solutions for the Formation of Singularities on the Free Surface of an Ideal Fluid

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Exact Local Solutions for the Formation of Singularities on the Free Surface of an Ideal Fluid. / Zubarev, N. M.; Karabut, E. A.

In: JETP Letters, Vol. 107, No. 7, 01.04.2018, p. 412-417.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{8c870253e4d048be84238cb6c65a3859,

title = "Exact Local Solutions for the Formation of Singularities on the Free Surface of an Ideal Fluid",

abstract = "A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the pressure is a quadratic function of the velocity components is possible in the absence of external forces and capillarity. It has been shown that equations of plane potential flow for this situation are linearized in conformal variables and are then easily solved analytically. The found solution includes an arbitrary function specifying the initial shape of the surface of the fluid. The developed approach makes it possible for the first time to locally describe the formation of various singularities on the surface of the fluid—bubbles, drops, and cusps.",

author = "Zubarev, {N. M.} and Karabut, {E. A.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Inc.",

year = "2018",

month = apr,

day = "1",

doi = "10.1134/S0021364018070135",

language = "English",

volume = "107",

pages = "412--417",

journal = "JETP Letters",

issn = "0021-3640",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "7",

}

RIS

TY - JOUR

T1 - Exact Local Solutions for the Formation of Singularities on the Free Surface of an Ideal Fluid

AU - Zubarev, N. M.

AU - Karabut, E. A.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the pressure is a quadratic function of the velocity components is possible in the absence of external forces and capillarity. It has been shown that equations of plane potential flow for this situation are linearized in conformal variables and are then easily solved analytically. The found solution includes an arbitrary function specifying the initial shape of the surface of the fluid. The developed approach makes it possible for the first time to locally describe the formation of various singularities on the surface of the fluid—bubbles, drops, and cusps.

AB - A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the pressure is a quadratic function of the velocity components is possible in the absence of external forces and capillarity. It has been shown that equations of plane potential flow for this situation are linearized in conformal variables and are then easily solved analytically. The found solution includes an arbitrary function specifying the initial shape of the surface of the fluid. The developed approach makes it possible for the first time to locally describe the formation of various singularities on the surface of the fluid—bubbles, drops, and cusps.

UR - http://www.scopus.com/inward/record.url?scp=85048208212&partnerID=8YFLogxK

U2 - 10.1134/S0021364018070135

DO - 10.1134/S0021364018070135

M3 - Article

AN - SCOPUS:85048208212

VL - 107

SP - 412

EP - 417

JO - JETP Letters

JF - JETP Letters

SN - 0021-3640

IS - 7

ER -

ID: 13794496