We exploit Monin–Obukhov similarity theory and Townsend’s attached-eddy hypothesis and arrive at a logarithmic-linear law for the streamwise velocity variance in the surface layer of stably stratified boundary layers. To test the logarithmic-linear law, we conduct large-eddy simulations (LES) of stably stratified turbulent boundary layers at various stratification conditions. The LES results give strong support to the scaling, and the logarithmic-linear law is found to be valid in the wake layer (i.e., outside the surface layer) of strongly stratified boundary layers. A detailed analysis shows that this is because stable thermal stratification suppresses the large-scale detached eddies in the wake layer.

我们利用莫宁-奥布霍夫相似理论和汤森的附加涡流假设，得出了稳定分层边界层表层流向速度变化的对数线性定律。为了测试对数线性定律，我们在各种分层条件下对稳定分层的湍流边界层进行大涡模拟 (LES)。LES结果有力地支持了标定，发现对数线性定律在强分层边界层的尾流层（即地表层外）中是有效的。详细分析表明，这是因为稳定的热分层抑制了尾流层中的大规模分离涡流。