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

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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.

Original languageEnglish
Article numberA13
Number of pages19
JournalJournal of Fluid Mechanics
Volume890
DOIs
Publication statusPublished - 10 May 2020

Keywords

  • waves/free-surface flows
  • waves
  • FREE-SURFACE
  • WAVES
  • PLANE
  • free-surface flows
  • BRANCH POINT SINGULARITIES
  • HYDRODYNAMICS

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