  The last stage of evolution toward the stationary Kolmogorov spectrum of
hydrodynamic turbulence is studied using the Leith model. This evolution is
shown to manifest itself as a reflection wave in the wavenumber space
propagating from the largest toward the smallest wavenumbers, and is described
by a self-similar solution of a new (third) kind. This stage follows the
previously studied stage of an initial explosive propagation of the spectral
front from the smallest to the largest wavenumbers reaching arbitrarily large
wavenumbers in a finite time, and which was described by a self-similar
solution of the second kind. Nonstationary solutions corresponding to"warm
cascades" characterised by a thermalised spectrum at large wavenumbers are also
obtained.
