Noise-driven interfaces and their macroscopic representation

Marco Dentz (1) , Insa Neuweiler (2) , Yves Méheust (3) , Daniel M. Tartakovsky (4)

1 IDAEA - Institute of Environmental Assessment and Water Research
2 Institute of Fluid Mechanics in Civil Engineering
3 GR - Géosciences Rennes
4 MAE - UC San Diego - Department of Mechanical and Aerospace Engineering [Univ California San Diego]

We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1+1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

Domaines: Mécanique [physics]; Sciences de la Terre

Marco Dentz, Insa Neuweiler, Yves Méheust, Daniel M. Tartakovsky. Noise-driven interfaces and their macroscopic representation. Physical Review E , 2016, 94 (5), pp.052802. ⟨10.1103/PhysRevE.94.052802⟩. ⟨insu-01406307⟩