Attracting Manifold for a Viscous Topology Transition
arXiv:patt-sol/9510004 · doi:10.1103/PhysRevLett.75.3665
Abstract
An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid layer in an unstable Hele-Shaw flow. Under the separation of time scales near a bifurcation point, a long-wavelength mode entrains higher-frequency modes, as described by a version of Hill's equation. In the slaved dynamics, the initial-value problem is solved explicitly, yielding the time and analytical structure of a singularity which is associated with the motion of zeroes in the complex plane. This suggests a general mechanism of singularity formation in this system.
4 pages, RevTeX, 3 ps figs included with text in uuencoded file, accepted in Phys. Rev. Lett