  We present a systematic study of the dynamical scaling process leading to the
establishment of the Kolmogorov--Zakharov (KZ) spectrum in weak 3-wave
turbulence. In the finite capacity case, in which the transient spectrum
reaches infinite frequency in finite time, the dynamical scaling exponent is
anomalous in the sense that it cannot be determined from dimensional
considerations. As a consequence, the transient spectrum preceding the
establishment of the steady state is steeper than the KZ spectrum. Constant
energy flux is actually established from right to left in frequency space after
the singularity of the transient solution. From arguments based on entropy
production, a steeper transient spectrum is heuristically plausible.
