TY - JOUR

T1 - Exact Solutions to the Problem of Dynamics of a Liquid with a Free Surface between Two Approaching Vertical Walls

AU - Zhuravleva, E. N.

AU - Zubarev, N. M.

AU - Zubareva, O. V.

AU - Karabut, E. A.

N1 - Funding Information: This work was supported in part by the Russian Foundation for Basic Research, project nos. 19-01-00096 and 19-08-00098. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/12

Y1 - 2021/12

N2 - Exact solutions of the classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded from above by the free surface and from the sides by two solid vertical walls approaching each other with a constant velocity. Solutions are obtained for a situation where the capillary and gravity forces are absent, and the fluid motion is entirely determined by the motion of the walls. Singularities inevitably arise in the solutions of the equations of motion in a finite time: this time is limited from above by the moment of collision of the walls. Examples of exact solutions corresponding to the formation of bubbles, cusps, and droplets are considered.

AB - Exact solutions of the classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded from above by the free surface and from the sides by two solid vertical walls approaching each other with a constant velocity. Solutions are obtained for a situation where the capillary and gravity forces are absent, and the fluid motion is entirely determined by the motion of the walls. Singularities inevitably arise in the solutions of the equations of motion in a finite time: this time is limited from above by the moment of collision of the walls. Examples of exact solutions corresponding to the formation of bubbles, cusps, and droplets are considered.

KW - exact solutions

KW - formation of singularities in a finite time

KW - free boundaries

KW - unsteady flows

UR - http://www.scopus.com/inward/record.url?scp=85127126200&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0fa3c580-ca50-34d7-a850-8a548602095b/

U2 - 10.1134/S1028335821120090

DO - 10.1134/S1028335821120090

M3 - Article

AN - SCOPUS:85127126200

VL - 66

SP - 348

EP - 352

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 12

ER -