Vortex ring bubbles

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.

Visualization Methods for Vortex Rings and Vortex Breakdown Bubbles

Vortex breakdown bubbles are a subject which is of interest in many disciplines such as aeronautics, mixing, and combustion. Existing visualization methods are based on stream surfaces, direct volume rendering, tensor field visualization, and vector field topology. This paper presents a topological approach which is more closely oriented at the underlying theory of continuous dynamical systems....

A Coaxial Vortex Ring Model for Vortex Breakdown

Denis Blackmore Department of Mathematical Sciences and Center for Applied Mathematics and Statistics New Jersey Institute of Technology Newark, NJ 07102-1982 [email protected] ∗ ∗ ∗ Morten Brøns Department of Mathematics Technical University of Denmark DK-2800 Kgs. Lyngby, Denmark [email protected] ∗ ∗ ∗ Arnaud Goullet Department of Mathematical Sciences New Jersey Institute of Technology New...

Evolution of a Curved Vortex Filament into a Vortex Ring

Vortex nucleation by collapsing bubbles in Bose-Einstein condensates.

Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was fou...