Saffman-Taylor Fingers at Intermediate Noise

TL;DR

This paper investigates how intermediate noise influences Saffman-Taylor finger patterns, showing that increased noise leads to a characteristic transverse density profile and affects tip-splitting behavior.

Contribution

It compares boundary-integral and modified DLA models in intermediate noise regimes, revealing their convergence and noise scaling effects on finger morphology.

Findings

Increased noise causes the density profile to approach a cos^2 pattern.

Both models exhibit tip-splitting at intermediate noise levels.

Noise influences the scaling and morphology of the fingers.

Abstract

We study Saffman-Taylor flow in the presence of intermediate noise numerically by using both a boundary-integral approach as well as the Kadanoff-Liang modified Diffusion-Limited Aggregation model that incorporates surface tension and reduced noise. For little to no noise, both models result reproduce the well-known Saffman-Taylor finger. We compare both models in the region of intermediate noise where we get occasional tip-splitting events, focusing on the ensemble-average. We show that as the noise in the system is increased, the mean behavior in both models approaches the $\cos^2(\pi y/W)$ transverse density profile far behind the leading front. We also investigate how the noise scales and affects both models.