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N. M. Zubarev

Publications and source records attributed to N. M. Zubarev.

10 recordsLinked to original sources
arXiv2026

Development of strongly nonlinear structures at the charged boundary of a non-conducting liquid in an electric field

Direct numerical simulation of the strongly nonlinear stages of instability development for a non-conducting liquid with a charged free surface in a normal electric field is performed. It is demonstrated that two main stages of the instability can be distinguished: an initial stage, during which dimples appear on the surface, and a developed stage, during which these dimples transform into expanding bubbles. The bubble size increases with increasing applied field, despite the fact that the scale corresponding to the dominant mode of the instability decreases.

physics.flu-dyn↗
arXiv2019

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

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.

physics.flu-dyn↗
arXiv2014

Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small interface angle approximation (gravity and capillary forces are neglected) admit exact solutions in the implicit form. The analysis of these solutions shows that, in the general case, weak root singularities are formed on the interface in a finite time for which the curvature becomes infinite, while the slope angles remain small. For Atwood numbers close to unity in absolute values, the surface curvature has a definite sign correlated with the boundary deformation directed towards the light fluid. For fluids with comparable densities, the curvature changes its sign in a singular point. In the particular case of fluids with equal densities, the obtained results are consistent with those obtained by Moore based on the Birkhoff-Rott equation analysis.

physics.flu-dyn↗
arXiv2005

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.

physics.flu-dyn↗
arXiv2004

Exact solutions for equilibrium configurations of charged conducting liquid jets

A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a round jet. A critical value of the linear electric charge density is determined, for which the jet surface becomes self-intersecting, and the jet splits into two. It exceeds the density value required for the excitation of the linear azimuthal instability of the round jet. Hence, there exists a range of linear charge density values, where our solutions may be stable with respect to small azimuthal perturbations.

physics.flu-dyn↗
arXiv2004

Equilibrium Configurations of the Charged Surface of a Conducting Liquid at a Finite Interelectrode Distance

The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of finding the profile of a progressive capillary wave on the free surface of a liquid layer of a finite depth, which was solved by Kinnersley. This analogy allowed exact solutions to be obtained for the geometry of liquid electrodes, which expand the existing notions about the possible stationary states of the system.

physics.flu-dyn↗
arXiv2004

Dynamics of the Free Surface of a Conducting Liquid in a Near-Critical Electric Field

Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.

physics.flu-dyn↗
arXiv2000

Formation of Root Singularities on the Free Surface of a Conducting Fluid in an Electric Field

The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.

physics.flu-dyn↗
arXiv2000

Charged-Surface Instability Development in Liquid Helium; Exact Solutions

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.

physics.flu-dyn↗