We aim to test the performances of an incompressible turbulence Reynolds-Averaged Navier–Stokes one-closure equation model in a boundary layer (NSTKE model). We model a new boundary condition for the turbulent kinetic energy $k$ (TKE), and we achieve the mathematical analysis of the resulting NSTKE model. A series of direct numerical simulation are performed, with flat and non trivial topographies, to obtain by interpolation a generic formula for the Prandtl mixing length $\ell =\ell (R{e}_{\star },z)$, $R{e}_{\star }$ being the frictional Reynolds number, and $z$ the distance to the wall. This allows us to carry out numerical simulations at high Reynolds numbers with this turbulence model, in order to discuss its ability to properly reproduce the standard profiles observed in neutral boundary layers, and to assess its advantages, its disadvantages and its limits.

我们旨在测试边界层中不可压缩湍流雷诺平均Navier-Stokes一封闭方程模型的性能（NSTKE模型）。我们为湍动能建模了一个新的边界条件$ķ$（TKE），然后我们对生成的NSTKE模型进行了数学分析。对平面和非平凡的地形进行一系列直接数值模拟，以通过插值获得普朗特混合长度的通用公式$\ell =\ell （\mathrm{[R}{Ë}_{\star }，ž）$， $\mathrm{[R}{Ë}_{\star }$ 是摩擦雷诺数，并且 $ž$到墙的距离。这使我们能够使用该湍流模型在高雷诺数下进行数值模拟，以便讨论其正确再现在中性边界层中观察到的标准轮廓的能力，并评估其优势，劣势和局限性。