On the universality of the dissipation rate functional form and of the autocorrelation function exponential form

An alternative formulation for the turbulence dissipation rate ε is presented. The development consists on a binomial expansion of an algebraic relation for the lateral dispersion parameter σy, originated from the fitting of experimental data. The new formulation keeps the same physical premises contained on the classical, largely used one, but the numerical coefficient increases by a factor of 50%. The new expression leads to dissipation rate values, which are shown to be in good agreement with those previously determined in the convective boundary layer. Furthermore, a statistical comparison to observed concentration data shows that the alternative relation for the dissipation rate is suitable for application in Lagrangian stochastic dispersion models. Motivated by these results, a new form for the autocorrelation function has also been obtained. Once the procedures that originated both the new and classical formulations are similar, only starting from a different expression for σy, this study shows that there is no universal certainty regarding the dissipation rate functional form and the autocorrelation function exponential form.