We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Weak solution for the Hele-Shaw problem: Viscous shocks and singularities.
- Authors
Lee, S.-Y.; Teodorescu, R.; Wiegmann, P.
- Abstract
In Hele-Shaw flows, a boundary of a viscous fluid develops unstable fingering patterns. At vanishing surface tension, fingers evolve to cusp-like singularities preventing a smooth flow. We show that the Hele-Shaw problem admits a weak solution where a singularity triggers viscous shocks. Shocks form a growing, branching tree of a line distribution of vorticity where pressure has a finite discontinuity. A condition that the flow remains curl-free at a macroscale uniquely determines the shock graph structure. We present a self-similar solution describing shocks emerging from a generic (2, 3)-cusp singularity-an elementary branching event of a branching shock graph.
- Subjects
FLUIDS; SURFACE chemistry; SURFACE tension; VORTEX motion; FLUID mechanics
- Publication
JETP Letters, 2010, Vol 92, Issue 2, p91
- ISSN
0021-3640
- Publication type
Article
- DOI
10.1134/S0021364010140043