On the energy transfer to small scales in a discrete model of one-dimensional turbulence

We consider a discrete one-dimensional model that was investigated numerically by Daumont and Peyrard [Chaos 13, 624 (2003)] as a model for turbulence in fluids, i.e., for the energy transfer from large to small scales. They found numerically that there exist two different regimes for the energy spectrum at high energies and low energies, respectively, and gave an analytical explanation for the high-energy spectrum. An analytical explanation is given here for the low-energy spectrum, which corresponds to the laminar regime.