Stable boundary layer decoupling: towards a linear stability analysis

Nighttime observations of the very stable boundary layer (VSBL) often show both low temperatures and (very) weak winds near the surface. These weak wind conditons coincide with extremely low intensities of turbulence. As a result, the upper part of the boundary seems to be de-coupled from the surface. This typical behaviour of the VSBL is also reported in several numerical simulation studies for cases where low geostrophic forcing is applied in combination with strong radiative surface cooling.

The present study aims to explain such SBL behaviour by applying theory of linear stability analysis (LSA). Quasi-steady (i.e. surface-coupled and continuous turbulent) solutions of a set of SBL-equations are subjected to this LSA in order to investigate whether these solutions are stable (persist), or that they are unstable. An unstable solution will eventually result in a de-coupled state and refers to the situation indicated above. The method investigates the time-evolution of infinitisimal disturbances of the governing equations, as inspired by the work of Derbyshire(1999), who analysed the stability of (rather unrealistic) linear profiles. However, the present work applies LSA to the more general case with realistic (non-linear) profiles that follow Monin-Obukhov similarity theory.

It is shown that boundary layer decoupling is a real physical phenomenon, caused by a non-linear interaction between SBL stratification and mixing in presence of a no-slip surface boundary condition. The analytical results are compared with detailed numerical results of a column model, and with observational case studies of CASES99 and CABAUW.