.M ech.(2006)L02002 ournal of Statistical Mechanics: An IOP and SISSA journalJ Theory and Experiment LETTER Sandpile behaviour in discrete

doi:10.1088/1742-5468/2006/02/L02002 Abstract. I construct a sandpile model for the evolution of the energy spectrum of water waves in finite basins. This model takes into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the wave action spectrum takes a critical ω−10 shape where the nonlinear resonance broadening overcomes the effect of the Fourier grid spacing. The energy cascade in this case takes the form of rare weak avalanches on the critical slope background. For larger forcing, this regime is replaced by a continuous cascade and a Zakharov–Filonenko ω−8 wave action spectrum. For intermediate forcing levels, both scalings will be relevant, ω−10 at small frequencies and ω−8 at large frequencies, with a transitional region in between, characterized by strong avalanches