On the constitutive relation for the Reynolds stresses and the Prandtl-Kolmogorov hypothesis of effective viscosity in axisymmetric strained turbulence

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that t he Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theo ry the effective viscosity is determined for the limiting states of turbule nce. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytic al derivations are in excellent agreement with the data obtained from direc t numerical simulations. [S0098-2202(00)02801-7].