Solução semianalítica para o perfil vertical do vento na camada limite planetária

Abstract

In the present study, using the Generalized Integral Transform Technique (GITT), we derive a semi-analytical solution of the Navier-Stokes equation to obtain the mean wind profile in the atmospheric boundary layer. The technique combines series expansion and an integration employing an inverse-transform pair. The PBL is discretized into N sub-intervals in such manner that inside each sub-region the eddy diffusivity is the average value, this allows the use of realistic eddy diffusivity profiles, which depend on the physical characteristics of the energy-containing eddies. The nonlinear terms are written in terms of kinematical properties of the flow, such as divergence and vorticity, allowing the solutions to be interpreted in terms of large-scale synoptic conditions. The model results are compared to observed wind profiles obtained from the classical Wangara experiment. In addition, the results obtained by the proposed model are compared with the unidimensional model solved by the method of discretization, the model of two layers, with the logarithmic law and the Ekman model. The method used was efficient for the problem studied, since it has presented results consistent with those available in literature.