Gradient-based similarity in the stable atmospheric boundary layer

A single-column model of the evolving stable boundary layer (SBL) is tested for self-similar properties of the flow and effects of ambient forcing. The turbulence closure of the model is diagnostic, based on the K-theory approach, with a semi-empirical form of the mixing length, and empirical stability functions of the Richardson number. The model results, expressed in terms of local similarity scales, are universal functions, and are satisfied in the entire SBL. Based on similarity expression, a realizability condition is derived for the minimum allowable turbulent heat flux in the SBL. Dimensionless scalar gradients and standard deviations, scaled by the flux-based local scales, are shown constant only in the near-neutral range. This implies that the "z-less" hypothesis in stable conditions is not general, and valid only in a limited range of thermal stability. The standard deviations of scalars, scaled by flux-based local scales, are found to have a minimum of about 2 at the Richardson number Ri = 0.09.