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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2024

Surface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground

Abstract

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.
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Origin : Publication funded by an institution

Dates and versions

hal-04533458 , version 1 (29-11-2022)
hal-04533458 , version 2 (16-01-2023)
hal-04533458 , version 3 (04-04-2024)

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Luigi C. Berselli, François Legeais, Roger Lewandowski. Surface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground. ESAIM: Mathematical Modelling and Numerical Analysis, 2024, 58 (2), pp.489-513. ⟨10.1051/m2an/2024009⟩. ⟨hal-04533458v3⟩
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