Motion of a vortex filament in an external flow

EXISTENCE OF A STEADY FLOW WITH A BOUNDED VORTEX IN AN UNBOUNDED DOMAIN

We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

Evolution of a Curved Vortex Filament into a Vortex Ring

A Numerical Study of Drop Motion in Poiseuille Flow

The cross-stream migration of a deformable drop in two-dimensional Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (<1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For a viscosity ratio 0.125, the drop moves toward the centre of the channe while for t...

A Numerical Study of Drop Motion in Poiseuille Flow

The cross-stream migration of a deformable drop in two-dimensional Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (<1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For a viscosity ratio 0.125, the drop moves toward the centre of the channe while for t...

The Evolution of a Random Vortex Filament

We study an evolution problem in the space of continuous loops in threedimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Hölder regular loops with index greater than 1/3. When the Hölder regularity of the initial condition X is smaller or equal 1/2 we require X to be a rough p...