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

• Published in: Atmospheric environment (1994) Vol. 39; no. 10; pp. 1917 - 1924
• Main Authors: Degrazia, Gervásio A., Acevedo, Otávio C., Carvalho, Jonas C., Goulart, Antônio G., Moraes, Osvaldo L.L., Campos Velho, Haroldo F., Moreira, Davidson M.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-03-2005; Elsevier Science
• Subjects: Autocorrelation function; Convection, turbulence, diffusion. Boundary layer structure and dynamics; Dispersion parameters; Earth, ocean, space; Exact sciences and technology; External geophysics; Meteorology; Turbulence dissipation rate; Autocorrelation function; Dispersion parameters; Turbulence dissipation rate; Shape function; Lateral dispersion; Lagrangian model; stochastic models; Atmospheric turbulence; Atmospheric boundary layer; Convective layer; Atmospheric dispersion; troposphere
• ISSN: 1352-2310; 1873-2844
• DOI: 10.1016/j.atmosenv.2004.12.011

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 σ
y
, 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 σ
y
, this study shows that there is no universal certainty regarding the dissipation rate functional form and the autocorrelation function exponential form.