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

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Abstract

We introduce a scalar elliptic equation defined on a boundary layer given by Π 2 × [0, z top ], where Π 2 is a two dimensional torus, with an eddy vertical eddy viscosity of order z α , α ∈ [0, 1], an homogeneous boundary condition at z = 0, and a Robin condition at z = z top. 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 accuratly reproduce profiles close to those predicted by the Monin-Oboukhov theory, by calculating stabilizing functions.
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Dates and versions

hal-03877325 , version 1 (29-11-2022)
hal-03877325 , version 2 (16-01-2023)

Identifiers

  • HAL Id : hal-03877325 , version 1

Cite

Luigi Carlo Berselli, François Legeais, Roger Lewandowski. Surface boundary layers through a scalar equation with an eddy viscosity vanishing at the ground. 2022. ⟨hal-03877325v1⟩
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