Singularities of the hele-shaw flow and shock waves in dispersive media

Eldad Bettelheim*, Oded Agam, Anton Zabrodin, Paul Wiegmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Kortevegâ€"de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.

Original languageAmerican English
Article number244504
JournalPhysical Review Letters
Issue number24
StatePublished - 9 Dec 2005
Externally publishedYes


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