A generalized vortex ring model

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...

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.

A model for universal time scale of vortex ring formation

An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nond...

Evolution of a Curved Vortex Filament into a Vortex Ring

A constrained vortex model with relevance to helicopter vortex ring state

A planar model of a lifting surface descending into its own wake is constructed with the aim of demonstrating some underlying mechanisms of the ‘vortex ring’ state that may be entered by a rotary wing aircraft during a vertical descent. The model uses line vortices that are periodically released from a point in space and then allowed to evolve in a constrained manner. For low descent velocities...