Coarsening dynamics of falling-film solitary waves

Because interfacial wave dynamics on a falling film involves quasisteady localized solitary pulses, its complex spatiotemporal dynamics exhibits certain generic features and scalings. We construct a statistical theory for such dynamics from our earlier theory for binary pulse interaction [Physica D 63, 299 (1993); Phys. Rev. Lett. 75, 1747 (1995); J. Fluid Mech. 294, 123 (1995)]. The theory shows that the average pulse separation increases linearly downstream from the inlet with a universal slope and that the average pulse velocity increases with a generic power of 2/7. Prediction for the final equilibrium separation is also offered by the theory. The coarsening features are driven by an irreversible coalescence of the pulses whose local dynamics can be renormalized via an affine transformation due to the scale invariance of the localized pulses. The generic scalings for the dynamics arise from the affine transformation and are favorably compared to numerical simulation and experimental data.