The threedimensional stability of vortex systems in circular tubes or outside a circular cylinder
Abstract
A general theory of the threedimensional longwave linear stability of a system of straight potential vortex filaments inside or outside a circular cylinder is presented. The vortices are assumed to be parallel potential vortex filaments, and the solid cylinder is modeled by a potentialsource surface distribution. Small threedimensional waves are imposed on the vortex filaments, concurrently with fluctuations in the intensity of the source distribution, and with a prescribed unsteady perturbation of the radius of the cylinder. This mathematical model is used to investigate the dynamic and static stability of a vortex filament rotating in a circular tube or outside a circular cylinder. The introduction of timedependent perturbations of the cylinder radius as a controller, and control laws that use measurements of the vortex perturbations, can (theoretically) actively control the stability of the vortex.
 Publication:

8th AIAA Applied Aerodynamics Conference
 Pub Date:
 1990
 Bibcode:
 1990apae.conf..483R
 Keywords:

 Circular Cylinders;
 Circular Tubes;
 Flow Geometry;
 Flow Stability;
 Three Dimensional Flow;
 Vortex Filaments;
 Vortices;
 Computational Fluid Dynamics;
 Flow Distribution;
 Fourier Analysis;
 Fredholm Equations;
 Fluid Mechanics and Heat Transfer