Analytic Theory of the Selection Mechanism in the Saffman-Taylor Problem
Physical Review Letters1986Vol. 56(19), pp. 2032–2035
Citations Over TimeTop 1% of 1986 papers
Abstract
We present an analytic approach to the problem of predicting the widths of fingers in a Hele-Shaw cell. Our analysis is based on the WKB technique developed recently for dealing with the effects of surface tension in the problem of dendritic solidification. We find that the relation between the dimensionless width $\ensuremath{\lambda}$ and the dimensionless group of parameters containing the surface tension, $\ensuremath{\nu}$, has the form $\ensuremath{\lambda}\ensuremath{-}\frac{1}{2}\ensuremath{\sim}{\ensuremath{\nu}}^{\frac{2}{3}}$ in the limit of small $\ensuremath{\nu}$.
Related Papers
- → Accuracy of the Transmission Coefficient across Parabolic Barriers as Obtained from a Generalized WKB Approach(1987)4 cited
- → On the precision of mode delays derivation with the use of the WKB method(2015)3 cited
- → A Study of the Perey Effect by the WKB Method(1980)13 cited
- → Application of the higher order modified WKB method to the Lennard-Jones potential(1974)4 cited
- → Correction for the Uniform WKB Wave Functions and the WKB Phase Shifts(1974)3 cited