SCALING EXPONENTS OF THE 2ND-ORDER STRUCTURE-FUNCTION OF TURBULENCE

The Kolmogorov equation, which is an exact relationship between the se cond-order structure function D-LL(r) and the third-order structure fu nction D-LLL(r), is applied to study the relative scaling of D-LL(r) a gainst -D-LLL(r) according to the extended self-similarity (ESS) metho d. it is found that the relative ESS scaling exponent S-2 is greater t han the real (or theoretical) inertial range scaling exponent zeta(2) of D-LL(r) in the case of normal scaling (zeta(2) = 2/3) as well as an omalous scaling (zeta(2) = 0.7): S-2 greater than or equal to 0.7 when zeta(2) = 2/3 and S-2 > 0.72 when zeta(2) = 0.7. Therefore, the exper imental and numerical results St = 0.7 favours the Kolmogorov 2/3 law (zeta(2) = 2/3) rather than anomalous scaling (zeta(2) = 0.7). Previou sly the results S-2 = 0.7 were interpreted as clear evidence of anomal ous scaling (zeta(2) = 0.7) based upon the assumption that zeta(2) = S -2.