Gradient catastrophe and flutter in vortex filament dynamics

Details Gradient catastrophe and flutter in vortex filament dynamics Gradient catastrophe and flutter in vortex filament dynamics

2011-05-30

arxiv.org/abs/1105.6051v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 3 figures, typos corrected, references added

Scientific paper

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.

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