Autocorrelation function formulations and the turbulence dissipation rate: Application to dispersion models

The classical statistical diffusion theory and the binomial autocorrelation function are used to obtain a new formulation for the turbulence dissipation rate ε. The approach employs the Maclaurin series expansion of a logarithm function contained in the dispersion parameter formulation. The numerical coefficient of this new relation for ε is 100% larger than the numerical coefficient of the classical relation derived from the exponential autocorrelation function. A similar approach shows that the dispersion parameter obtained from the even exponential autocorrelation function does not result in a relation for ε and, therefore, is not suitable for application in dispersion models. In addition, a statistical comparison to experimental ground-level concentration data demonstrates that this newly derived relation for ε as well as other formulations for the turbulence dissipation rate are suitable for application in Lagrangian stochastic dispersion models. Therefore, the analysis shows that there is an uncertainty regarding the turbulence dissipation rate function form and the autocorrelation function form.