Asymptotic behavior of a random oscillating nonlinear reactive transport in thin turbulent layers

We consider a nonlinear reactive transport of a scalar field in a domain composed of a bounded region lined by turbulent thin layers. We suppose that these layers display a cellular microstructure with thin varying thickness. We suppose that, within the layers, the diffusion, reaction, and velocity coefficients admit random large-scale structures. Under mixing properties of the diffusion, reaction, and velocity processes, we study the asymptotic behavior of the problem with respect to a vanishing parameter describing the thickness of the layers. We derive the effective flux boundary condition on the surface of the fixed region which coincides with the lower surface of the layers. This flux boundary condition consists in a generalized nonlinear Robin condition involving some nonlocal random effects which emerge asymptotically due to the random fluctuations of the reactive transport parameters in the layers.