Simulation of noise-driven wave dynamics on a falling film

A numerical model developed simulates inlet noise-driven wave dynamics on a falling film at relatively high Reynolds numbers. Two parameters, a normalized Reynolds number and a noise index; are sufficient to specify the wave statistics on most channels. Observed phenomena, like wave inception, downstream wave texture coarsening, initial deceleration and subsequent acceleration of wave speeds, are quantitatively reproduced and explained. Statistical analysis from our simulations suggests that beyond a critical Reynolds number this complex noise-driven spatio-temporal dynamics can be modeled by a deterministic interaction theory based on stable solitary waves that resemble one-hump pulses and a statistical theory with a random-phase description of noise. The ''chaotic'' wave dynamics at higher Reynolds number is hence due to both noise amplification/filtering and intrinsic dynamics.