Fingering patterns in Hele-Shaw flows are density shock wave solutions of dispersionless KdV hierarchy

Journal Article · Tue Jan 01 00:00:00 EST 2008 · Physical Review Letters

OSTI ID:962284

Teodorescu, Razvan ^[1]; Lee, S - Y ^[2]; Wiegmann, P ^[3]

---

1. Los Alamos National Laboratory
2. MONTREAL, CANADA
3. UNIV OF CHICAGO

We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 962284
• Report Number(s): LA-UR-08-07363; LA-UR-08-7363; PRLTAO; TRN: US200919%%48
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CUSPED GEOMETRIES
DISTRIBUTION
GEOMETRY
HYDRODYNAMICS
SHOCK WAVES
SINGULARITY