Gradient catastrophe and flutter instability in the motion of a vortex filament within the localized induction approximation are analyzed. It is shown that the origin of this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes the motion of a 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. © 2011 IOP Publishing Ltd.
Gradient catastrophe and flutter of vortex filament dynamics
ORTENZI, GIOVANNI
2011-01-01
Abstract
Gradient catastrophe and flutter instability in the motion of a vortex filament within the localized induction approximation are analyzed. It is shown that the origin of this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes the motion of a 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. © 2011 IOP Publishing Ltd.
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