A new class of exact solutions in the planar nonstationary problem of motion of a fluid with a free boundary

E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the classical problem of potential unsteady flow of an ideal incompressible fluid with a free boundary. It was previously discovered that in the absence of external forces and capillarity, a wide class of exact solutions of the problem can be described by the Hopf equation for a complex velocity. We here obtain a new class of solutions described by the Hopf equation for a quantity that is the inverse of the complex velocity. These solutions describe the evolution of two-dimensional perturbations of the free boundary in compression or expansion of a circular cavity (in the unperturbed state) in the fluid.

Original languageEnglish
Pages (from-to)344-351
Number of pages8
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume202
Issue number3
DOIs
Publication statusPublished - Mar 2020

Keywords

  • complex
  • exact solution
  • Hopf equation
  • ideal incompressible fluid
  • unsteady planar flow with a free boundary
  • velocity
  • UNSTEADY FLOWS
  • SINGULARITIES
  • ZERO ACCELERATION
  • FREE-SURFACE
  • 2-DIMENSIONAL HYDRODYNAMICS
  • WAVES
  • DYNAMICS

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