Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExplosive Development of the Quantum Kelvin-Helmholtz Instability on the He-II Free Surface
87
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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 $|phi|^4$ 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.
rate research
Read More
A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.
The nonlinear dynamics of charged-surface instability development was investigated for liquid helium far above the critical point. It is found that, if the surface charge completely screens the field above the surface, the equations of three-dimensional (3D) potential motion of a fluid are reduced to the well-known equations describing the 3D Laplacian growth process. The integrability of these equations in 2D geometry allows the analytic description of the free-surface evolution up to the formation of cuspidal singularities at the surface.
The macroscopic dynamics of a droplet impacting a solid is crucially determined by the intricate air dynamics occurring at the vanishingly small length scale between droplet and substrate prior to direct contact. Here we investigate the inverse problem, namely the role of air for the impact of a horizontal flat disk onto a liquid surface, and find an equally significant effect. Using an in-house experimental technique, we measure the free surface deflections just before impact, with a precision of a few micrometers. Whereas stagnation pressure pushes down the surface in the center, we observe a lift-up under the edge of the disk, which sets in at a later stage, and which we show to be consistent with a Kelvin-Helmholtz instability of the water-air interface.
Applying the method of integral estimates to the analysis of three-wave processes we derive the sufficient criteria for the hard loss of stability of the charged plane surface of liquids with different physical properties. The influence of higher-order wave interactions on the instability dynamics is also discussed.
We report experimental results for the Kelvin-Helmholtz instability between two immiscible fluids in parallel flow in a Hele-Shaw cell. We focus our interest on the influence of the gap size between the walls on the instability characteristics. Experimental results show that the instability threshold, the critical wavelength, the phase velocity and the spatial growth rate depend on this gap size. These results are compared to both the previous two-dimensional analysis of Gondret and Rabaud (1997) and the three-dimensional analysis recently derived by Plourabou=E9 and Hinch (2001), showing that the agreement is still not complete especially when gap size increases.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
