Related papers: Kelvin-Helmholtz instability in binary fluids with…
We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well known, macroscopic and ideal shear-driven instability. In sufficiently low density plasmas, also the microscopic Hall magneto-shear instability can…
The cross-magnetic-field (i.e., perpendicular) profile of ion temperature and the perpendicular profile of the magnetic-field-aligned (parallel) plasma flow are sometimes inhomogeneous for space and laboratory plasma. Instability caused by…
We examine the linear stability of fluid interfaces subjected to a shear flow. Our main object is to generalize previous work to arbitrary Atwood number, and to allow for surface tension and weak compressibility. The motivation derives from…
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a…
Flow-induced instabilities are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts. We continue the study started in the first paper of this series by…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…
We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding \cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest…
The objective of this work is to investigate the unexplored laminar-to-turbulent transition of a heated flat-plate boundary layer with a fluid at supercritical pressure. Two temperature ranges are considered: a subcritical case, where the…
The essence of shear instability is fully revealed both mathematically and physically. A general sufficient and necessary stable criterion is obtained analytically within linear context. It is the analogue of Kelvin-Arnol'd theorem, i.e.,…
In this paper, the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability(RTI, KHI and RTKHI, respectively) system is investigated using a multiple-relaxation-time discrete Boltzmann model. Both the morphological boundary length and…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the…
Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows generated…
This article revisits the instability of sharp shear interfaces, also called vortex sheets, in incompressible fluid flows. We study the Birkhoff-Rott equation, which describes the motion of vortex sheets according to the incompressible…
When a barotropic shear layer becomes unstable, it produces the well known Kelvin-Helmholtz instability (KH). The non-linear manifestation of KH is usually in the form of spiral billows. However, a piecewise linear shear layer produces a…
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…
Double-diffusive convection refers to mixing where the effects of thermal and composition gradients compete to determine the stability of a fluid. In addition to the familiar fast convective instability, such fluids exhibit the slow, direct…
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…
Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable.…