The hierarchy of turbulence equations is closed by several methods, but good results for higher Reynolds numbers are obtained only for a closure by specification of initial conditions. Four terms of an exponential series, which is an iterative solution of the Navier–Stokes equation, are used in the closure. A complete solution, in the sense that the evolution of all of the initially specified spectra can be calculated, is obtained. This cannot be done by using a Taylor series, regardless of how many terms are retained. The results indicate that purely viscous decay becomes negligible compared with inertial decay as Reynolds number becomes large.