Gradient-based similarity in the stable atmospheric boundary layer

Abstract

A structure of the stably-stratified atmospheric boundary layer is examined in terms of a novel gradient-based similarity theory. The presented approach introduces similarity scales based on the vertical gradient of the potential temperature, contrary to the traditional method, which is based on momentum and temperature fluxes. The length scale, defined using the semi-empirical form of the mixing length, is demonstrated to be effective in the entire stable boundary layer. In more complex cases, an alternative formulation of the mixing length, based on vertical velocity or temperature variances, can be employed. The empirical similarity functions of the Richardson number are expressed in analytical form, valid in the entire stable boundary layer. The introduced similarity approach allows for evaluating the minimum values of the dimensionless turbulent heat flux and the temperature standard deviation as functions of the Richardson number. It can also be used as a closure scheme for a single column model.