Shocks and finite-time singularities in Hele-Shaw flow
- Los Alamos National Laboratory
- UNIV OF MONTREAL
- UNIV OF CHICAGO
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 960982
- Report Number(s):
- LA-UR-08-06871; LA-UR-08-6871; TRN: US201008%%881
- Journal Information:
- Journal of Physics D, Journal Name: Journal of Physics D
- Country of Publication:
- United States
- Language:
- English
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