Related papers: Equilibrium configuration of a rectangular obstacl…
Something as simple as Couette and Poiseuille onedimensional flow of a newtonian fluid between infinite parallel walls provides an illuminating example of the contrasting physics of laminar and turbulent flow: the difference between their…
Inertial microfluidics is a promising tool for many lab-on-a-chip applications. Particles in channel flows with Reynolds numbers above one undergo cross-streamline migration to a discrete set of equilibrium positions in square and…
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…
Motion of a cylinder dynamically interacting with n point vortices in a perfect fluid is considered. A nonliniear Poisson structure and two integrals of motion are found. The equations of motion a priori are not Hamiltonian. For n=1, the…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
Transient Navies--Stokes equations for laminar flow of incompressible fluid in a channel with permeable wall are reduced to a single equation for the transversal profile of longitudinal flow velocity. Small--amplitude harmonic perturbation…
In the present paper, microcanonical measures for the dynamics of three dimensional (3D) axially symmetric turbulent flows with swirl in a Taylor-Couette geometry are defined, using an analogy with a long-range lattice model. We compute the…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively…
Incompressible fluids in microfluidic networks with non-rigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC circuits. This is due to the elastic deformation of channel walls that can store and…
We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable…
The flow of a colloidal solution between two parallel disks rotating with the same angular velocity about two non-coincident axes was studied. The problem has been approached from two perspectives, the first wherein the stress is expressed…
Vortex stretching in a compressible fluid is considered. Two-dimensional and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows.…
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we…
The incompressible flow around a circular cylinder, positioned at the center of an unconfined planar counterflow, is studied by means of numerical solutions of the conservation equations and linear stability analysis. The flow is completely…
Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a…
The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…
The primary bifurcation of the flow past three-dimensional axisymmetric bodies is investigated. We show that the azimuthal vorticity generated at the body surface is at the root of the instability, and that the mechanism proposed by…
The interaction of a suspension of rotating colloids with a periodically patterned structure is here investigated by means of continuum theoretical predictions and hydrodynamic simulations. Close to the obstacle surface, rotors circulate…
We review works on the asymptotic stability of the Couette flow. The majority of the paper is aimed towards a wide range of applied mathematicians with an additional section aimed towards experts in the mathematical analysis of PDEs.