  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.
