The Turbulent Structure of the Stable, Nocturnal Boundary Layer

A large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands. To present and organize these data we turn to the parameterized equations for the turbulent variances and covariances. In a dimensionless form these equations lead to a local scaling hypothesis. According to this hypothesis, dimensionless combinations of variables which are measured at the same height can be expressed as a function of a single parameter z/Λ. Here, Λ is called a local Obukhov length and is defined as Λ=−τ3/2T/(kgwθ) where τ and wθ) are the kinematic momentum and heat flux, respectively. Note that, in general, Λ may vary across the boundary layer, because τ and wθ are still unknown functions of height. The observations support local scaling. In particular, they agree with the limit condition for z/Λ→∞, which predicts that locally scaled variables approach a constant value. The latter result is called z-less stratification. An important application of z-less stratification is that both the Richardson number and flux Richardson number should become constant in the stable boundary layer. Next we turn to the vertical profiles of τ and wθ. These profiles can be obtained in principle from a simple boundary-layer model which uses as a closure hypothesis the constant Richardson number and flux Richardson number. The solution for steady-sate conditions loads to wθ/wθ0;=(1−z/h)) and τ/u*2=((1−z/h)3/2, where ;wθ0 and u*2, are the surface temperature and momentum fluxes, respectively, and h is the boundary-layer height. Observations at Cabauw agree reasonably well with these profiles. However, they should not be considered as generally valid similarity expressions.