  The assumption of similarity and self-preservation, which permits an
analytical determination of the energy decay in isotropic turbulence, has
played an important role in the development of turbulence theory for more than
half a century. Sedov (1944), who first found an ingenious way to obtain two
equations from one. Nonethless, it appears that this problem has never been
reinvestigated in depth subsequent to this earlier work. In the present paper,
such an analysis is carried out, yielding a much more complete picture of
self-preservation isotropic turbulence. Based on these exact solutions, some
physically significant consequences of recent advances in the theory of
self-preserved homogenous statistical solution of the Navier-Stokes equations
are presented. New results could be obtained for the analysis on turbulence
features, such as the scaling behavior, the spectrum, and also the large scale
dynamics. The general energy spectra and their behavior in different wave
number range are investigated.
