TY - JOUR

T1 - Application of transport equations for constructing exact solutions for the problem of motion of a fluid with a free boundary

AU - Karabut, E. A.

AU - Zhuravleva, E. N.

AU - Zubarev, N. M.

PY - 2020/5/10

Y1 - 2020/5/10

N2 - 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.

AB - 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.

KW - waves/free-surface flows

KW - waves

KW - FREE-SURFACE

KW - WAVES

KW - PLANE

KW - free-surface flows

KW - BRANCH POINT SINGULARITIES

KW - HYDRODYNAMICS

UR - http://www.scopus.com/inward/record.url?scp=85081537664&partnerID=8YFLogxK

U2 - 10.1017/jfm.2020.119

DO - 10.1017/jfm.2020.119

M3 - Article

AN - SCOPUS:85081537664

VL - 890

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A13

ER -