Igor L. Kliakhandler

Viscous damping and instabilities in stratified liquid film flowing down a slightly inclined plane

A reduced nonlinear model for density stratified viscous film flowing down a slightly inclined wall is derived and explored. Under buoyancy stable stratification the system exhibits various long‐wavelength instabilities of noninertial, purely kinetic origin. Unlike many existing models for the film interface evolution in the present study regularization of the pertinent long‐scale dynamics is provided directly by the film viscosity rather than surface tension.

Long interfacial waves in multilayer thin films and coupled Kuramoto-Sivashinsky equations

The coupled Kuramoto–Sivashinsky (CKS) equations for multilayer downflowing films are derived and explored. The CKS equations exhibit a wealth of dynamical behaviour, displaying travelling periodic waves, regular and chaotic-like patterns, coexistence of different attractors, and perfect and imperfect synchronization of the interfaces. New physical effects are found, such as suppression of the Rayleigh–Taylor instability for heavy-top stratified films, and new surface-tension-driven instability.

KINETIC ALPHA EFFECT IN VISCOSITY STRATIFIED CREEPING FLOWS

It is shown that viscosity stratified plane Poiseuille flow may exhibit a long‐wavelength instability of a purely kinetic nature formally resembling the so‐called alpha effect known in magnetohydrodynamics or in anisotropic three‐dimensional flows of homogeneous fluids. In the absence of the alpha effect, the system may display a peculiar type of long‐wavelength instability, where the latter is controlled by the surface tension. The weakly nonlinear equation for the evolving interfaces is derived and solved numerically.

The effect of heat conduction in the vapor on the dynamics of downflowing condensate

A vapor fills the gap between two vertical plates, one hot and one cold. The temperatures are adjusted so that condensate forms on the cold wall. It is the dynamics of the system that is examined. The paper extends the one-sided model of evaporation–condensation to account the heat conduction in the vapor phase, which turns out to be important in many condensation problems. For the considered flow, both vapor recoil and Marangoni effect are stabilizing; as a result, the condensate becomes unstable at nonzero Reynolds numbers in contrast to the usual film flow down a vertical wall. A nonlinear evolution equation is derived and analyzed for the interaction of viscous shear and evaporation–condensation. It turns out that the one-sided model of heat and mass transfer gives a very good description of the initial stage of thin-film growth; in later stages, however, the heat conduction through the vapor becomes important when the film is sufficiently thick.

Short-wavelength instability in presence of a zero mode: anomalous growth law

Abstract A nonlinear model that combines onset of nonoscillatory short-wavelength instability and a long-wave zero mode is investigated numerically. Due to the coupling to the zero mode, the systems dynamics drastically differs from those in traditional short-wavelength models. In agreement with independent recently published results, we conclude that, immediately beyond the instability threshold, the system demonstrates a chaotic behavior, which makes it cognate to the long-wave systems. An essentially novel result is that a mean amplitude of the dynamical patterns grows linearly with the overcriticality. The corresponding scaling power 1 is just between the values 1 2 and 3 2 , characteristic, respectively, for the traditional short- and long-wave models.

Inertial effects and long waves in multilayer plane Poiseuille flows

The objective of this work is to clarify the role of inertial effects on the long-wavelength instabilities and dynamics of multilayer plane Poiseuille flows. A weakly nonlinear set of equations governing the evolution of interfacial waves is derived and examined. Numerical simulations show that for the flows irregular interface profiles are generic. For some systems a curious behaviour of interfaces is revealed: depending on initial conditions, interfaces evolve into irregular or soliton-like structures.

Gravitational oscillations of a capped liquid-air column

We study the gravitational oscillations of liquid confined in a vertical tube, immersed in a liquid bath, with air trapped above the liquid column. The trapped air acts as a nonlinear spring, in addition to the gravitational restoring force. The presence of the trapped air introduces two new parameters in the problem. One parameter denoted α governs the effect of compression and expansion and the other parameter denoted β governs the effect of initial pressure of the trapped air. In the absence of viscosity, the ordinary differential equations governing the upward and downward motion of the liquid in the tube are different and, considered separately, are conservative. Together, however, they describe the damped oscillations due to irreversible energy losses at the end of the tube in the bath. Numerical simulations show the effects of α and β on the oscillations. A Shanks approximate provides a surprisingly good estimation of the nonlinear damping. Taking into account viscous losses, a first order asymptot...