Similarity Formulation for the Transport Terms of the Turbulent Kinetic Energy Budget Equation

In this work a similarity formulation for the transport terms of the turbulent kinetic energy (TKE) budget equation, for a convective boundary layer (CBL) is provided. This task is complicated to carry out the experimental doe to the difficulty associated to the measurements of pressure turbulent fluctuations. Therefore, employing a large eddy symulation (LES), all terms of the TKE budget equation were determined for a CBL. The simulation consists of a full diurnal PBL cycle utilizing, at the surface, a forcing obtained from experimental data, so that the numerical experiment represents a more realistic case than a idealized CBL. From these data, polynomials that describe the TKE transport terms vertical profiles were adjusted for a CBL in terms of the convective velocity scale and friction velocity. The found polynomial fits are a good description of the LES data. The figures below show the interpolated polynomials for the vertical profiles of the transport terms, normalized by (w_*^3) and to the terms of transport function of z/L for the surface layer, normalized by (u_*^3/kz), where k is the von Kàrmàn constant.