A method of matching is applied to the energy spectrum equations in the modified cumulant expansion theory for Burgers and two‐ and three‐dimensional Navier–Stokes turbulence, in order to investigate the asymptotic behavior of the energy spectrum in the limit of large Reynolds number and time. It is shown analytically that the spectrum has a similar structure with respect to both Reynolds number and time, and that there is no single similarity law which is valid throughout the wavenumbers, but instead there are several subranges of the wavenumbers which have different similarity laws.