Related papers: The Stability of Roll-Waves in Two-Phase Pipe Flow
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin rigid rods. In…
This paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite…
We present initial attempts to include the multi-dimensional nature of radiation transport in hydrodynamical simulations of the small-scale structure that arises from the line-driven instability in hot-star winds. Compared to previous 1D or…
Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity…
Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
The instability of a streak and its nonlinear evolution are investigated by direct numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It is suggested that there exists a traveling-wave solution (TWS). The TWS is localized…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…
The wave propagation problem on a taut cable resting on a bilinear substrate is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to permit…
The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin-Helmholtz and Holmboe instabilities are present. For a fixed…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
We study the stability of multi-layer radial flows in porous media within the Hele-Shaw model. We perform a linear stability analysis for radial flows consisting of an arbitrary number of fluid layers with interfaces separating fluids of…
A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at…
We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or…
Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shear-thinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the…
We investigate the existence and spectral stability of traveling wave solutions for a class of fourth-order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization…