RENORMALIZATION-GROUP TREATMENT OF 3-DIMENSIONAL TURBULENCE

The renormalization group treatment applied to three-dimensional turbulence is examined carefully. It is shown that the renormalization process is completely different depending on whether deltaLAMBDA much less than k or k much less than deltaLAMBDA when the wavenumber components between LAMBDA and LAMBDA - deltaLAMBDA are eliminated in the Navier-Stokes equations for wavevector k. When deltaLAMBDA much less than k, which seems to be a natural condition, is assumed, the new triple interactions in addition to the ones by Zhou, Vahala and Hossain (Phys. Rev. A37 (1988) 2590) are found to be indispensable. The obtained viscosity is in good agreement with the one reached by Yakhot and Orszag (J. Sci. Comput. 1 (1986) 3), who did choose a parameter epsilon=0 instead of epsilon=4, a honest value. Then, the reasonable numbers are predicted for the Kolmogorov constant and the coefficient of the viscosity.