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 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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