2 research outputs found
Gradient catastrophe and flutter in vortex filament dynamics
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.Comment: 11 pages, 3 figures, typos corrected, references adde