40: (10) 5875-5895 NOV 15 1989

**Abstract:**

An analytic theory using WKBJ methods for selection with
local perturbations in the Saffman-Taylor [Proc. R. Soc. London Ser. A
245, 312 (1958)] problem is presented. I obtain qualitative agreement
with previously published phenomenology, including symmetric narrowed fingers
for local reductions in the surface-tension parameter, narrowed asymmetric
fingers for local increases, and scaling of the tip curvature and asymmetry
with the square root of the surface-tension parameter. The source
of the universality in the perturbed problem is discussed, giving some
explanation of why the experimental perturbations can be modeled by locally
varying surface tension. Very good quantitative agreement between
theory and a numerical simulation of the same perturbation is shown, with
no adjustable parameters to fit. Finally, I outline experiments
to test new behavior predicted by the theory; a quantitative prediction
observable experimentally is given.