Gradient-based scales and similarity laws in the stable boundary layer

Three gradient-based scaling systems for the stably stratified boundary layer are introduced and examined by using data collected during the SHEBA field programme in the Arctic. The resulting similarity functions for fluxes and variances are expressed in an analytical form, which is expected to be essentially unaffected by self-correlation in a very stable regime. The flux Richardson number Rf is found to be proportional to the Richardson number Ri, with the proportionality coefficient varying slightly with stability, from 1.11 to 1.47. The Prandtl number decreases from 0.9 in nearly neutral conditions to 0.7 for larger values of Ri. The negative correlation coefficient between the vertical velocity and temperature, -r(w theta), has a local maximum at Ri of about 0.08, and monotonically decreases with larger values of the Richardson number. The turbulent kinetic energy budget indicates that for Ri > 0.7, turbulence must be non-stationary, i.e. decaying or sporadic. Turbulence within the stably stratified boundary layer can be classified by four regimes: 'nearly neutral' (0 < Ri < 0.02), 'weakly stable' (0.02 < Ri < 0.12), 'very stable' (0.12 < Ri < 0.7), and 'extremely stable' (Ri > 0.7). Copyright (C) 2010 Royal Meteorological Society