Explosive Development of the Quantum KelvinHelmholtz Instability on the HeII Free Surface
Abstract
We analyze nonlinear dynamics of the KelvinHelmholtz quantum instability of the HeII 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 $\phi^4$ KleinGordon 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 KelvinHelmholtz quantum instability and electrohydrodynamic instability of the free surface of liquid helium charged by electrons is considered.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.04318
 Bibcode:
 2019arXiv191204318Z
 Keywords:

 Physics  Fluid Dynamics;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 8 pages, 2 figures