The third-order structure function is used to study the finite Reynolds number (FRN) effect of turbulence, which refers to the deviation of turbulence statistics observed at finite Reynolds numbers from predictions of the Kolmogorov theories. It is found that the FRN effect decreases as ${\mathrm{CR}}_{\lambda }^{-\mu },$ when $R_{\lambda }$ is high, and $\mu <~6/5.$ Here $R_{\lambda }$ is the Taylor-microscale Reynolds number and C is a constant independent of $R_{\lambda }.$ From the exact spectral equations, the decay exponent μ and the constant C are determined for typical fully developed turbulent flows (freely decaying isotropic turbulence and shear flow turbulence), so that the quantitative prediction of the FRN effect is feasible.

• Received 5 November 1998

DOI:https://doi.org/10.1103/PhysRevE.60.3409