Gradient catastrophe and flutter in vortex filament dynamics
Exactly Solvable and Integrable Systems
2015-05-28 v2 Mathematical Physics
math.MP
Fluid Dynamics
Abstract
Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes motion of filament with slow varying curvature and torsion. Geometrically this catastrophe manifests as a rapid oscillation of a filament curve in a point that resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painlev\'e-I equation.
Cite
@article{arxiv.1105.6051,
title = {Gradient catastrophe and flutter in vortex filament dynamics},
author = {B. G. Konopelchenko and G. Ortenzi},
journal= {arXiv preprint arXiv:1105.6051},
year = {2015}
}
Comments
11 pages, 3 figures, typos corrected, references added