Gradient catastrophe and flutter in vortex filament dynamics
arXiv:1105.6051 · doi:10.1088/1751-8113/44/43/432001
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 Painlevé-I equation.
11 pages, 3 figures, typos corrected, references added
References in corpus (5)
- On the stability of a singular vortex dynamics
- Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
- Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity
- The double scaling limit method in the Toda hierarchy
- Singular sectors of the 1-layer Benney and dToda systems and their interrelations