Issue |
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
|
|
---|---|---|
Page(s) | 489 - 513 | |
DOI | https://doi.org/10.1051/m2an/2024009 | |
Published online | 04 April 2024 |
Surface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground
1
Università di Pisa, Dipartimento di Matematica, Via Buonarroti 1/c, I-56127 Pisa, Italy
2
IRMAR, UMR CNRS 6625, University of Rennes and Odyssey team, INRIA Rennes, France
* Corresponding author: roger.lewandowski@univ-rennes1.fr
Received:
16
January
2023
Accepted:
30
January
2024
We introduce a scalar elliptic equation defined on a boundary layer given by Π2 × [0, ztop], where Π2 is a two dimensional torus, with an eddy vertical viscosity of order zα, α ∈ [0, 1], an homogeneous boundary condition at z = 0, and a Robin condition at z = ztop. We show the existence of weak solutions to this boundary problem, distinguishing the cases 0 ≤ α < 1 and α = 1. Then we carry out several numerical simulations, showing the ability of our model to accurately reproduce profiles close to those predicted by the Monin–Obukhov theory, by calculating stabilizing functions.
Mathematics Subject Classification: 35Q30 / 35D30 / 76D03 / 76D05
Key words: Boundary layers / eddy viscosities / degenerate elliptic equations
© The authors. Published by EDP Sciences, SMAI 2024
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