Upper limit for wind shear in stably stratified conditions expressed in terms of a bulk Richardson number

Profile measurements of wind and potential temperature from a land site (obtained by a RASS for several years) and an offshore site (obtained at the meteorological mast on the research platform FINO 1 for one year) are used to analyse the temporal evolution of wind speed and wind shear under statically stable conditions, especially in situations with low-level jets. In both cases a bulk Richardson number is calculated from the data. Data analysis indicates that there seems to exist a lower bound for the bulk Richardson number during stable stratification which is greater than zero. At this lower bound the flow reaches its maximum possible vertical wind shear. Even larger shear would then mean production of new turbulence which in turn would reduce the shear. Therefore, at this lower bound, the flow is in equilibrium between production and depletion of turbulence characterized by an equilibrium Richardson number. This equilibrium Richardson number is found here at about 0.1 for the land site and 0.04 for the marine site. For situations where maximum shear occurs, this shear can be compared to the shear described by the logarithmic vertical wind profile law for stable stratification. This allows the derivation of relations for the equilibrium Richardson number and the constant in the correction term of the logarithmic wind law in terms of the stratification parameter z∕L*$z/L_{ast}$ and the surface roughness zT$z_{T}$ for temperature.