An extended similarity theory for the stably stratified atmospheric surface layer

An advanced similarity-theory formulation for the wind and temperature profiles in the stably stratified atmospheric surface layer (ASL) is developed with due regard to the effect of the free-flow static stability on the ASL. In the revised log-linear profiles, empirical coefficients traditionally considered as universal constants, namely the slope factors in the z-less stratification layer (beyond the logarithmic sub-layer), become functions of the dimensionless number S = NL/u(*). Here, N is the Brunt-Vaisala frequency in the free flow, L is the Monin-Obukhov length, and u(*) is the friction velocity. The number S indicates how strongly the ASL is affected by the free-flow stability. This new formulation leaves room for the occurrence of well developed turbulence at much higher Richardson numbers, Ri, than had been suspected. Moreover, it results in a pronounced dependence of the turbulent Prandtl number on Ri in a wide range of Ri, including the z-less stratification layer, in correspondence with long-standing empirical evidence. The traditional Monin-Obukhov similarity theory disregards the above essential features of the stably stratified ASL. New data from measurements over a slightly inclined plateau in West Greenland provide experimental support for the proposed theory.