Logarithmic-Linear Law of the Streamwise Velocity Variance in Stably Stratified Boundary Layers

Xiang I. A. Yang, Peng E. S. Chen, Ruifeng Hu, Mahdi Abkar*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


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.

Original languageEnglish
JournalBoundary-Layer Meteorology
Pages (from-to)199-213
Number of pages15
Publication statusPublished - May 2022


  • Attached-eddy hypothesis
  • Large-eddy simulation
  • Monin–Obukhov similarity theory
  • Scaling
  • Velocity variance


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