  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.
