An extended similarity theory for the stably stratified atmospheric surface layer

Abstract

AbstractAn 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 = N L/u*. Here, N is the Brunt‐Väisälä 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.