Decay of Isotropic Turbulence in the Direct-Interaction Approximation

Abstract

The direct‐interaction equations for the decay of isotropic turbulence are integrated numerically with initial spectra of several shapes and initial values of R_λ ≲ 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.