Convergence of the vortex filament method

Numerical Simulation of Vortex Breakdown by the Vortex-Filament Method

Numerical Convergence of the Random Vortex Method for Complex Flows

Vortex methods rely principally on a discretization of the continuous two-dimensional time dependent vorticity eld into a large number of vortex \blobs", whose position and strength determine the underlying velocity eld. In this paper, the convergence of the random vortex method (RVM) for a complex ow is studied in function of three discretization parameters. Two of these parameters are related...

Collisions of Vortex Filament Pairs

We consider the problem of collisions of vortex filaments for a model introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88, Z99] to describe the interaction of almost parallel vortex filaments in three-dimensional fluids. Since the results of Crow [C70] examples of collisions are searched as perturbations of antiparallel translating pairs of filaments, with initial perturbations r...

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...

Differential Geometry of the Vortex Filament Equation

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an ...