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Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II.

Authors
  • Lushnikov, Pavel M1, 2
  • Zubarev, Nikolay M3, 4
  • 1 Department of Mathematics and Statistics, University of New Mexico, New Mexico 87131, USA. , (Mexico)
  • 2 Landau Institute for Theoretical Physics, 2 Kosygin Street, Moscow 119334, Russia.
  • 3 Institute for Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg 620016, Russia.
  • 4 Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia.
Type
Published Article
Journal
Physical Review Letters
Publisher
American Physical Society
Publication Date
May 18, 2018
Volume
120
Issue
20
Pages
204504–204504
Identifiers
DOI: 10.1103/PhysRevLett.120.204504
PMID: 29864357
Source
Medline
License
Unknown

Abstract

Relative motion of the normal and superfluid components of helium II results in the quantum Kelvin-Helmholtz instability (KHI) at their common free surface. We found the integrability and exact growing solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two classical fluids, the dynamics of a helium II free surface allows reduction to the Laplace growth equation, which has an infinite number of exact solutions, including the generic formation of sharp cusps at the free surface in a finite time.

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