通过标量方程计算地面涡流粘度消失的地表边界层

R. Lewandowski, François Legeais, L. Berselli
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引用次数: 0

摘要

我们引入了一个定义在边界层上的标量椭圆方程,该边界层由 $\Pi_2 \times [0, z_{top}]$ 给出,其中 $\Pi_2$ 是一个二维环,具有阶数为 $z^\alpha$ 的垂直涡流粘度,$\alpha \ in [0, 1]$,在 $z=0$ 处为均质边界条件,在 $z=z_{top}$ 处为罗宾条件。我们证明了该边界问题弱解的存在,并区分了 $0 \le \alpha <1$ 和 $\alpha = 1$ 两种情况。 然后,我们进行了几次数值模拟,通过计算稳定函数,表明我们的模型能够准确地再现接近莫宁-奥布霍夫理论预测的剖面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Surface boundary layers   through  a scalar equation with  an eddy viscosity vanishing at the ground
We introduce a scalar elliptic equation defined on a boundary layer given by $\Pi_2 \times [0, z_{top}]$, where $\Pi_2$ is a two dimensional torus, with an eddy vertical eddy viscosity of order  $z^\alpha$, $\alpha \in [0, 1]$, 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  $0 \le \alpha <1$ and $\alpha = 1$.  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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