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In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
Guo--Tice formally established in 2011 that the Rayleigh--Taylor instability inevitably occurs within stratified compressible viscous fluids in a slab domain $\mathbb{R}^2\times (h_-,h_+)$, irrespecive of the presence of interfacial surface…
We investigate the Rayleigh-Taylor instability at the two interfaces in a phase-separated three-component Bose-Einstein condensate in the mean-field framework. The subsequent dynamics in the immiscible three-component condensate has been…
The Plateau-Rayleigh instability shows that a cylindrical fluid flow can be destabilized by surface tension. Similarly, capillary forces can make an elastic cylinder unstable when the elastocapillary length is comparable to the cylinder's…
When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…
We study the two-phase, horizontally periodic, quasistationary Stokes flow in two dimensions driven by surface tension and gravity effects in the general context of fluids with (possibly) different viscosities and densities. The sharp…
Rayleigh-Taylor (RT) instability occurs in a variety of scenario as a consequence of fluids of different densities pushing against the density gradient. For example, it is expected to occur in the ion acceleration of solid density targets…
We consider the Rayleigh-Taylor instability in the early evolution of the rarefied radio bubbles (cavities) observed in many cooling flow clusters of galaxies. The top of a bubble becomes prone to the Rayleigh-Taylor instability as the…
Using air to displace a viscous fluid contained in Hele-Shaw cell can create a fingering pattern at the interface between the fluids, if the capillary number exceeds a critical value. This Saffman-Taylor instability is revisited for the…
Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work is…
This letter investigates the effect of shear on Rayleigh-Taylor instability (RTI). Even simple uniform shear strongly influences the instability; longer waves are completely stabilized when density stratification is large (higher Atwood…
We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with…
We study the Hele-Shaw immiscible displacements when all surfaces tensions on the interfaces are zero. The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one, in a rectangular Hele-Shaw cell. We…
The Richtmyer-Meshkov instability (RMI) refers to the baroclinic generation of vorticity at a perturbed density interface when impacted by a shock wave. It is often thought of as the impulsive limit of the Rayleigh-Taylor instability (RTI).…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
The hydrodynamic instabilities of propagating interfaces in Hele-Shaw channels or porous media under the influence of an imposed flow and gravitational acceleration are investigated within the framework of Darcy's law. The stability…
The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during…
We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…