Charles R. P. Szinvelski

Short Communication: Semi-analytical solution of the asymptotic Langevin Equation by the Picard Iterative Method

In this work, a semi-analytical solution for the asymptotic Langevin Equation (Random Displacement Equation) applied to the pollutant dispersion in the Planetary Boundary Layer (PBL) is developed and tested. The solution considers as starting point the first-order differential equation for the random displacement, on which is applied the Picard Iterative Method. The new model is parameterized by a turbulent eddy diffusivity derived from the Taylor Statistical Diffusion Theory and a model for the turbulence spectrum, assuming the hypothesis of linear superposition of the mechanical and thermal turbulence mechanisms. We report numerical simulations and comparisons with experimental data and other diffusion models. The main motivation for this work comes from the fact that the round-off error influence and computational time can be reduced in the new method.

Algebraic Formulation for the Dispersion Parameters in an Unstable Planetary Boundary Layer: Application in the Air Pollution Gaussian Model

An alternative formulation for the dispersion parameters in a convective boundary layer is presented. The de- velopment consists of a simple algebraic relation for the dispersion parameters, originated from the fitting of experimental data, in which the turbulent velocity variances and the Lagrangian decorrelation time scales are derived from the turbulent kinetic energy convective spectra. Assuming homogeneous turbulence for elevated regions in an unstable planetary boundary layer (PBL), the present approach, which provides the dispersion parameters, has been compared to the observa- tional data as well as to results obtained by classical complex integral formulations. From this comparison yields that the vertical and lateral dispersion parameters obtained from the simple algebraic formulas reproduce, in an adequate manner, the spread of contaminants released by elevated continuous source in an unstable PBL. Therefore, the agreement with dis- persion parameters available by an integral formulation indicates that the hypothesis of using an algebraic formulation as a surrogate for dispersion parameters in the turbulent convective boundary layer is valid. In addition, the algebraic vertical and lateral dispersion parameters were introduced into an air pollution Gaussian diffusion model and validated with the concentration data of Copenhagen experiments. The results of such Gaussian model, incorporating the algebraic disper- sion parameters, are shown to agree with the measurements of Copenhagen.

Testing Physical and Mathematical Criteria in a New Meandering Autocorrelation Function

An alternative formulation for the low wind speed-meandering autocorrelation function is presented. Employing distinct theoretical criteria, this mathematical formulation, from a physical point of view, is validated. This expression for the meandering autocorrelation function reproduces well-observed wind-meandering data measured in a micrometeorological site located in a pampa ecosystem area (South Brazil). The comparison shows that the alternative relation for the meandering autocorrelation function is suitable to provide meandering characteristic parameters. Employing MacLaurin’s series expansion of a lateral dispersion parameter that represents cases in which turbulence and oscillatory movements associated to the meandering events coexist, a new formulation for the turbulence/meandering dissipation rate has been presented.

OBTAINING THE MEANDERING LOOP PARAMETER IN LOW WIND SPEED CONDITION

The looping parameter m is the main value to characterize the meandering phenomenon. This parameter is relationship with negative lobes in the observed autocorrelation function generated from components of horizontal speed. In this work, we present a study comparing the mean values of the looping parameter between 2 diverse sites in the Brazilian sector.

A THEORETICAL REVIEW OF AUTOCORRELATION FUNCTIONS APPLIED TO HIGH AND LOW WIND SPEED

In this study is analysed an autocorrelation function suggested by Frenkiel (Frenkiel (1953)), to described negative lobes in the meandering phenomenon of the horizontal mean wind vector. This function is a hybrid expression constituted by turbulent and meandering parameters which describe pure and connected states of turbulence and meandering movements. Furthermore, the autocorrelation function is employed to fit meandering observations measured in north Brazil. An additional purpose is employ distinct mathematical and physical criteria to test this mathematical formulation. Employing the Frenkiel’s formula a formulation to the turbulence dissipation rate has been obtained.

UMA NOVA DERIVAÇÃO DA TAXA DE DISSIPAÇÃO TURBULENTA PARA EVENTOS DE TURBULÊNCIA FRACA E BEM DESENVOLVIDA

Neste trabalho e derivado uma nova forma funcional para a taxa de dissipacao turbulenta valida para diferentes tipos de manifestacoes de turbulencia presentes na CLP.

COMPARAÇÃO ENTRE OS PARÂMETROS DE DISPERSÃO ALGÉBRICO E CLÁSSICO VIA MODELO DE PLUMA GAUSSIANA

Comparacao entre os parâmetros de dispersao algebrico eclassico via Modelo de Pluma Gaussiana