Longitudinal Structure Functions in Decaying and Forced Turbulence

In order to reliably compute the longitudinal structure functions in decaying and forced turbulence, local isotropy is examined with the aid of the isotropic expression of the incompressible conditions for the second and third order structure functions. Furthermore, the Karman-Howarth-Kolmogorov relation is investigated to examine the effects of external forcing and temporally decreasing of the second order structure function. On the basis of these investigations, the scaling range and exponents $\zeta_n$ of the longitudinal structure functions are determined for decaying and forced turbulence with the aid of the extended-self-similarity (ESS) method. We find that $\zeta_n$'s are smaller, for $n \geq 4$, in decaying turbulence than in forced turbulence. The reasons for this discrepancy are discussed. Analysis of the local slopes of the structure functions is used to justify the ESS method.