Evolution of a curved vortex filament into a vortex ring

Evolution of a Curved Vortex Filament into a Vortex Ring

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...

Statistics of a vortex filament model

A random field composed by Poisson distributed Brownian vortex filaments is constructed. The filament have a random thickness, length and intensity, governed by a measure γ. Under appropriate assumptions on γ we compute the scaling law of the structure function and get the multifractal scaling as a particular case.

The Gibbs ensemble of a vortex filament

Certain investigations of turbulent 3-D fluids seem to indicate that the vorticity field of the fluid is strongly concentrated along thin structures, called vortex filaments. A. Chorin has developed a statistical-mechanics theory of vortex filaments to describe the statistics of turbulent flows, see [4]. In his investigations vortex filaments are modelled by trajectories of self-avoiding walks ...

Vortex ring

By rigorous mathematical method, we construct traveling wave solutions with a stationary or traveling vortex ring to the Gross-Pitaevskii equation iût = ε 2 4 û + ( Ṽ − |û| ) û, û ∈ H(R), where the unknown function û is defined as û : R × R → C, ε is a small positive parameter and Ṽ is a smooth potential.