Local Similarity in the Stable Boundary Layer and Mixing-Length Approaches: Consistency of Concepts

Abstract

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z _B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ℓ _B  = κ _B z _B , with κ _B ≈ κ, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/Λ naturally appears, and that the α coefficient of the log-linear similarity functions ${\phi_{m,h}=1+\alpha z/\Lambda}$ is equal to c/κ ², where c is a constant close to unity. The predicted value α ≈ 1/κ ² = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed.