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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-12, Vol.44 (18), p.14849-14873
Main Authors: El Jarroudi, Mustapha, Lahrouz, Aadil, Settati, Adel
Format: Article
Language:English
Subjects:
asymptotic behavior
Asymptotic properties
Boundary conditions
bounded domain
Diffusion layers
effective flux boundary condition
Parameters
random oscillating nonlinear reactive transport
Scalars
Thickness
Thin films
turbulent thin layers
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7746