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Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier-Stokes model cannot account for both features, and a simple…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at…
In a shear flow particles migrate to their equilibrium positions in the microchannel. Here we demonstrate theoretically that if particles are inertial, this equilibrium can become unstable due to the Saffman lift force. We derive an…
The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the range $Re_\theta=2800-6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This…
In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small…
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…
Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis…
We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size $\varepsilon$. Under the classical Miles-Howard stability…
In this paper, we are interested in the long-time behaviour of stochastic systems of n interacting vortices: the position in R2 of each vortex evolves according to a Brownian motion and a drift summing the influences of the other vortices…
The asymmetries that arise when a mixing layer involves two miscible fluids of differing densities are investigated using incompressible (low-speed) direct numerical simulations. The simulations are performed in the temporal configuration…
The motion and deformation of a droplet suspended in an unbounded fluid with an arbitrary, but Stokesian, imposed flow is investigated when there is a slip at the interface between the two liquids. The boundary condition at the interface is…
The growth of interfacial instabilities during fluid displacements can be driven by gradients in pressure, viscosity and surface tension, and by applying external fields. Since displacements of non-Newtonian fluids such as polymer…
The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned…
We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the…
Interfaces moving in a disordered medium exhibit stochastic velocity fluctuations obeying universal scaling relations related to the presence or absence of conservation laws. For fluid invasion of porous media, we show that the fluctuations…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…