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Explosive Development of the Kelvin–Helmholtz Quantum Instability on the He-II Free Surface

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Abstract

We analyze nonlinear dynamics of the Kelvin–Helmholtz quantum instability of the He-II free surface, which evolves during counterpropagation of the normal and superfluid components of liquid helium. It is shown that in the vicinity of the linear stability threshold, the evolution of the boundary is described by the |ϕ|4 Klein–Gordon equation for the complex amplitude of the excited wave with cubic nonlinearity. It is important that for any ratio of the densities of the helium component, the nonlinearity plays a destabilizing role, accelerating the linear instability evolution of the boundary. The conditions for explosive growth of perturbations of the free surface are formulated using the integral inequality approach. Analogy between the Kelvin–Helmholtz quantum instability and electrohydrodynamic instability of the free surface of liquid helium charged by electrons is considered.

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Funding

The work of N.M.Z was supported in part by the Russian Academy of Sciences (program no. 2 of the Presidium of the Russian Academy of Sciences), Ural Branch of the Russian Academy of Sciences (project no. 18-2-2-15), and Russian Foundation for Basic Research (project no, 19-08-00098). The research of P.M.L. on analysis of explosive instability was performed within State assignment “Dynamics of Complex Media.” The research of P.M.L. was supported in part by the National Science Foundation (grant no. DMS-1814619).

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Authors and Affiliations

  1. Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, 620016, Yekaterinburg, Russia

    N. M. Zubarev

  2. Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    N. M. Zubarev

  3. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia

    P. M. Lushnikov

  4. Department of Mathematics and Statistics, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    P. M. Lushnikov

Authors
  1. N. M. Zubarev
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  2. P. M. Lushnikov
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Correspondence to N. M. Zubarev or P. M. Lushnikov.

Additional information

Contribution for the JETP special issue in honor of I. M. Khalatnikov’s 100th anniversary

Translated by N. Wadhwa

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Zubarev, N.M., Lushnikov, P.M. Explosive Development of the Kelvin–Helmholtz Quantum Instability on the He-II Free Surface. J. Exp. Theor. Phys. 129, 651–658 (2019). https://doi.org/10.1134/S1063776119100157

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  • DOI: https://doi.org/10.1134/S1063776119100157

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