Decay of Isotropic Turbulence in the Direct-Interaction Approximation

The direct-interaction equations for the decay of isotropic turbulence are integrated numerically with initial spectra of several shapes and initial values of Rλ ≲ 40. Results are presented for the evolution of total energy, dissipation, energy transfer, skewness factor, and other integral quantities, together with the associated wavenumber spectra. Similarity and self-preservation features of the evolving spectra are exhibited. The results are compared with grid-turbulence measurements by Stewart and Townsend. Results are also given for the time-correlation of the total velocity at a fixed point in space and for the time-correlation and response functions of individual wavenumber modes.