arXiv subjects

Dmitry V. Lyubimov

Publications and source records attributed to Dmitry V. Lyubimov.

4 recordsLinked to original sources

arXiv2015

Running interfacial waves in two-layer fluid system subject to longitudinal vibrations

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasi-stationary states of free interface in fluid dynamical systems subject to vibrations, revealed existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the "plus" (or "good") Boussinesq equation. With these equations one can find all time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov, A.A. Cherepanov, Fluid Dynamics, vol. 21, 849-854 (1987)] reveals the instabilities of thin layers to be long-wavelength.

nlin.PS↗

arXiv2014

Elastic and inelastic collisions of interfacial solitons and integrability of two-layer fluid system subject to horizontal vibrations

We study interfacial waves in a system of two horizontal layers of immiscible inviscid fluids involved into horizontal vibrational motion. We analyze the linear and nonlinear stability properties of the solitons in the system and consider two-soliton collision scenarios. We describe the events of explosive formation of sharp peaks on the interface, which may presumably lead to the layer rapture, and find that beyond the vicinity of this peaks the system dynamics can be represented as a kinetics of a soliton gas.

nlin.PS↗

arXiv2006

Averaged dynamics of two-phase media in a vibration field

The averaged dynamics of various two-phase systems in a high-frequency vibration field is studied theoretically. The continuum approach is applied to describe such systems as solid particle suspensions, emulsions, bubbly fluids, when the volume concentration of the disperse phase is small and gravity is insignificant. The dynamics of the disperse system is considered by means of the method of averaging, when the fast pulsation and slow averaged motion can be treated separately. Two averaged models for both nondeformable and deformable particles, when the compressibility of the disperse phase becomes important, are obtained. A criterion when the compressibility of bubbles cannot be neglected is figured out. For both cases the developed models are applied to study the averaged dynamics of the disperse media in an infinite plane layer under the action of transversal vibration.

physics.flu-dyn↗

arXiv2006

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.

physics.flu-dyn↗