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

Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 393-402

Résumé

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.

Détail

Keywords: ideal incompressible fluid, unsteady planar flow with a free boundary, complex velocity, Hopf equation.
Mots-clés : exact solution

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