The atmospheric boundary layer (ABL) is in continuous turbulent motion. The heating and cooling of the Earth’s surface drives mechanic and thermodynamic processes in the ABL through enhancing and damping of atmospheric turbulence. The surface forcing has a profound effect on the diurnal cycle of temperature,wind and related variables in the ABL. Efforts have been made to model atmospheric turbulence with linear algebraic relations such as the eddy-viscosity hypothesis. Modelling of atmospheric turbulence, however, still remains a great challenge and forms an important problem in the context of numerical weather prediction and climate models. In this thesis a recently developed non-linear turbulence model, the so-called explicit algebraic Reynolds-stress (EARS) model, implemented in the context of a single-column model is used to simulate dry, stratified ABLs.

We propose a new boundary-condition treatment in the EARS model. The boundary conditions correspond to the relations for vanishing buoyancy effects that are valid close to the ground. In the simulation of an idealized diurnal cycle the solutions for the stratified surface layer is in agreement with the surface scaling physics and the Monin–Obukhov functions.

We have carried out simulations of the ABL with varying levels of stratification using the EARS model implemented in the context of a single-column model. We use the same model formulation and coefficients in these simulations with different thermal stratifications of the ABL. Even in the SCM formulation the EARS model solution produces a full Reynolds-stress tensor and heat flux vector. The set-up of the numerical experiments are taken from previously published large-eddy simulation (LES) studies of ABL.

Simulations of stably-stratified ABL show that the EARS model is able to accurately predict the development of a low-level jet and wind turning for different levels of stratification. In addition to first-order statistics, the model also predicts more intricate features of the turbulent ABL such as the relation between vertical and horizontal fluctuations for different stratifications and horizontal heat fluxes caused by wind shear. In the simulations of convective ABL the EARS model correctly predicts the horizontal wind speed and potential temperature profiles. The study also shows that the non-gradient term in the vertical heat flux equation, that naturally appears in the model formulations, gives a large contribution to the heat flux and has a significant influence on the predicted potential temperature profile of the convective ABL. Finally, we study the effects of transitional turbulence in the simulation of diurnal cycle extended to several days. The comparison with the LES shows that the EARS model correctly predicts the mean profiles and surface fluxes at different times of the day, including the low-level jet close to the surface. The model also predicts residual turbulence near the top of the ABL at night. The study demonstrates that the EARS model is able to capture key features of stably-stratified and convective ABLs as well as transitional processes that drive the ABL from one stratification to another.