Introducing and examining of a second order closure boundary layer model

One of the popular and well known models in boundary layer that is implemented in most of the operational and familiar models is the Mellor-Yamada model of atmospheric boundary layer. One reason that this model is so popular is its ability in simulations and exposing of different phenomena in the boundary layer. This model has been constructed based on second order closure hypothesis. Beside all of the positive properties that make this model admirable, it has some deficiency and insufficient accuracy in approximating turbulent terms in relevant equations. The most important weakness of this model is its inability of differentiation between vertical and horizontal components of turbulent kinetic energy (it can not separate from ). This feature of model make it unable to distinguish large eddies which grow up in depth of boundary layer from smaller one that has similar scales in both vertical and horizontal directions. In addition this model assumes that the production of turbulent kinetic energy is equivalent to the consumption of it. This characteristic results in error in small eddies simulation in the boundary layer.
The shortcoming of mentioned model motivate scientist to introduce new models without those deficiencies. Canuto and his team recently introduced a model more compliance with ongoing phenomena in the boundary layer. This model is discussed extensively here and for being implemented in the numerical weather prediction models, it is examined by available Large Eddy Simulation data. The turbulent fluxes such as ، ، are calculated and discussed with details of achievements. The other important variables in the boundary layer that has critical role on setting up of fluxes and currents in turbulent boundary layer like dept of boundary layer and Richardson number are also computed and analyzed.
Results show that the proposed new model is able to distinguish between large and small eddies by differentiating between vertical and horizontal component of variables specially of turbulent kinetic energy. The resulted height of boundary layer has a very good agreement with observation. Various simulations in different scientific centers are presented and are compared with new model results. It is clear in the figures that this model could approximate the turbulent currents better than previous ones.