An Improved Model for the Turbulent PBL

Abstract

Second-order turbulence models of the Mellor and Yamada type have been widely used to simulate the planetary boundary layer (PBL). It is, however, known that these models have several deficiencies. For example, assuming the production of the turbulent kinetic energy equals its dissipation, they all predict a critical Richardson number that is about four times smaller than the large eddy simulation (LES) data in stably stratified flows and are unable to distinguish the vertical and lateral components of the turbulent kinetic energy in neutral PBLs, and they predict a boundary layer height lower than expected. In the present model, three new ingredients are employed: 1) an updated expression for the pressure–velocity correlation, 2) an updated expression for the pressure–temperature correlation, and 3) recent renormalization group (RNG) expressions for the different turbulence timescales, which yield 1) a critical Richardson number of order unity in the stably stratified PBL (at level 2 of the model), 2) different vertical and lateral components of the turbulent kinetic energy in the neutral PBL obtained without the use of the wall functions, 3) a greater PBL height, 4) closer comparisons with the Kansas data in the context of the Monin–Obukhov PBL similarity theory, in both stable and unstable PBLs, and 5) more realistic comparisons with the LES and laboratory data.