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We present a systematic study of the dynamical scaling process leading to theestablishment of the Kolmogorov--Zakharov (KZ) spectrum in weak 3-waveturbulence. In the finite capacity case, in which the transient spectrumreaches infinite frequency in finite time, the dynamical scaling exponent isanomalous in the sense that it cannot be determined from dimensionalconsiderations. As a consequence, the transient spectrum preceding theestablishment of the steady state is steeper than the KZ spectrum. Constantenergy flux is actually established from right to left in frequency space afterthe singularity of the transient solution. From arguments based on entropyproduction, a steeper transient spectrum is heuristically plausible.

Dynamical Scaling and the Finite Capacity Anomaly in 3-Wave Turbulence