Dynamical scaling and the finitecapacity anomaly in threewave turbulence
Abstract
We present a systematic study of the dynamical scaling process leading to the establishment of the KolmogorovZakharov (KZ) spectrum in weak threewave turbulence. In the finitecapacity 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.
 Publication:

Physical Review E
 Pub Date:
 March 2010
 DOI:
 10.1103/PhysRevE.81.036303
 arXiv:
 arXiv:0911.0527
 Bibcode:
 2010PhRvE..81c6303C
 Keywords:

 47.35.i;
 82.20.w;
 94.05.Lk;
 Hydrodynamic waves;
 Chemical kinetics and dynamics;
 Turbulence;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 6 pages, 7 figures