Related papers: Corner and finger formation in Hele--Shaw flow wit…
It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of non-rotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear…
Asymptotic analysis of the Hele-Shaw flow with a small moving obstacle is performed. The method of solution utilises the uniform asymptotic formulas for Green's and Neumann functions recently obtained by V. Maz'ya and A. Movchan.…
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary…
We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is…
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a…
Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multi-core morphology confined within a microfluidic channel. A variety of new nonequilibrium steady states is…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which…
Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of…
We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…
Hydrodynamic-like electron flows are typically modeled using the Stokes-Ohm equation or a kinetic description that is based on a dual-relaxation time approximation. Such models assume a short intrinsic mean free path $\ell_e$ due to…
In this paper, we will study the following geometric flow, obtained by Goldstein and Petrich while considering the evolution of a vortex patch in the plane under Euler's equations, X_t = -k_s n - (1/2) k^2 T, with s being the arc-length…
We investigate the shallow flow of viscous fluid into and out of a channel whose gap width increases as a power-law ($x^n$), where $x$ is the downstream axis. The fluid flows slowly, while injected at a rate in the form of $t^\alpha$, where…
We solve numerically for the first time the two-fluid, Hall--Vinen--Bekarevich--Khalatnikov (HVBK) equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous…
An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and…
In this article we study Chen's flow of curves from theoreical and numerical perspectives. We investigate two settings: that of closed immersed $\omega$-circles, and immersed lines satisfying a cocompactness condition. In each of the…
We show existence of homothetically shrinking solutions of the fractional mean curvature flow, whose boundary consists in a prescribed numbers of concentric spheres. We prove that all these solutions, except from the ball, are dynamically…
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a…