Renormalization-group theory of turbulence: Ad-dimensional ε expansion

The renormalization-group (RG) method applied to homogeneous and isotropic turbulence is built up as an expansion around the particular dimension where the energy cascade reverses. As usual, the expansion parameter is related to the turbulent expression of the Reynolds number (λ¯∼${\mathrm{\epsilon }}^{1/2}$). The eddy-damped quasinormal Markovian approximation, which has been found to be consistent with RG at order ${\mathrm{\epsilon }}^1$ by Dannevick, Yakhot, and Orszag [Phys. Fluids 30, 2021 (1987)], is used to obtain a constraint on the Kolmogorov constant in such a way that no adjustable parameters are needed. Furthermore, several constants appearing in theories widely used in turbulence modeling are estimated and compared with their experimental values.