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.
Предметные области OECD FOS+WOS
- 2.05 ТЕХНОЛОГИЯ МАТЕРИАЛОВ
- 1.03 ФИЗИЧЕСКИЕ НАУКИ И АСТРОНОМИЯ