Saffman-Taylor fingers at intermediate noise.

Area of Science:

• Fluid dynamics
• Complex systems

Background:

• Saffman-Taylor flow describes viscous fingering in fluid displacement.
• Understanding the impact of noise on these instabilities is crucial for predicting pattern formation.

Purpose of the Study:

• To numerically investigate Saffman-Taylor flow under intermediate noise conditions.
• To compare the Kadanoff-Liang modified diffusion-limited aggregation model with a boundary-integral approach.
• To analyze the effect of noise scaling on flow behavior and transverse density profiles.

Main Methods:

• Numerical simulations using a boundary-integral approach.
• Utilizing the Kadanoff-Liang modified diffusion-limited aggregation model with surface tension and reduced noise.
• Focusing on ensemble-average behavior and tip-splitting events.

Main Results:

• Both models accurately reproduce the Saffman-Taylor finger in low-noise conditions.
• Intermediate noise leads to occasional tip-splitting events.
• Increasing noise drives the mean transverse density profile towards cos^{2}(πy/W) in both models.

Conclusions:

• The study quantifies the influence of noise on Saffman-Taylor flow dynamics.
• Both numerical models demonstrate convergence to a universal transverse density profile with increasing noise.
• Noise scaling significantly affects the behavior and morphology of the Saffman-Taylor finger.