An alternative formulation for the dispersion parameters in a convective boundary layer is presented. The development 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 observational 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 dispersion 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 dispersion parameters, are shown to agree with the measurements of Copenhagen.
h i g h l i g h t s• We propose a new mathematical expression to describe the meandering phenomenon.• We employ wind data measured in a nocturnal PBL to obtain experimental ACF. • The new ACF satisfactorily represents the negative lobes of the meandering phenomenon.
a b s t r a c tIn this study a new mathematical expression to describe the observed meandering autocorrelation functions in low-wind speed is proposed. The analysis utilizes a large number of best fit curves to show that the proposed theoretical function well reproduces the general form and the negative lobes characterizing the experimental meandering autocorrelation function. Further, the good agreement of the measured autocorrelation curves with the proposed algebraic autocorrelation function allows to calculate the magnitudes of the meandering period and of the loop parameter. The results agree with the values presented and discussed in the literature. Therefore, the new formulation describing experimental meandering autocorrelation functions can be used to simulate the dispersion of contaminant during low wind episodes and to determine relevant meandering parameters.
Abstract.A new formulation for the turbulence dissipation rate ε occurring in meandering conditions has been presented. The derivation consists of a MacLaurin series expansion of a lateral dispersion parameter that represents cases in which turbulence and oscillatory movements associated to the meandering events coexist. The new formulation presents the identical physical premises contained in the classical and largely used one, but the new formulation derived from meandering situations is expressed in terms of the loop parameter m that controls the absolute value of the negative lobe in the meandering autocorrelation function. Therefore, the m magnitude regulates the turbulence dissipation rate. This dissipation rate decreases for cases in which turbulence and low frequency horizontal wind oscillations coexist and increases for a fully developed turbulence. Furthermore, a statistical comparison to observed concentration data shows that the alternative relation for the turbulent dissipation rate occurring in situations of meandering enhanced dispersion is suitable for applications in Lagrangian Stochastic dispersion models.
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