The Wiener–Hermite expansion with a renormalized, time‐dependent moving base is used to calculate the evolution of the energy spectra of several homogeneous, isotropic flows. The results compare well with laboratory experiments and with numerical simulation experiments. Wiener– Hermite calculations have been done previously for high Reynolds numbers by Hogge and Meecham [J. Fluid Mech. 85, 325 (1978)]with some success. In this work moderate Reynolds numbers are treated.