Theory of the Saffman-Taylor ‘‘finger''pattern. I

D. Kessler, H Levine

Research output: Contribution to journalArticlepeer-review


In a series of two papers, we present a comprehensive approach to the pattern formed via viscous ‘‘fingering'' in a Hele Shaw cell, the Saffman-Taylor finger pattern. We explain how the ‘‘finger'' width is selected and why this selection cannot be computed via asymptotic analysis in the (large) capillary number. Also, we derive the spectrum of small oscillations around the steady-state shape and show that the selected shape is stable. In this paper, we set up the mathematical and numerical formalism, and demonstrate stability for the λ=(1/2) solution. We also consider the effects of noise on the stability analysis.
Original languageAmerican English
Pages (from-to)2621-2633
JournalPhysical Review A (Atomic, Molecular and Optical Physics)
Issue number4
StatePublished - 1986


Dive into the research topics of 'Theory of the Saffman-Taylor ‘‘finger''pattern. I'. Together they form a unique fingerprint.

Cite this