Theory of the Saffman-Taylor ‘‘finger’’ pattern. I
- 1 April 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 33 (4) , 2621-2633
- https://doi.org/10.1103/physreva.33.2621
Abstract
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.This publication has 13 references indexed in Scilit:
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