Aggregation-fragmentation processes and decaying three-wave turbulence

We use a formal correspondence between the isotropic three-wave kinetic equation and the rate equations for a nonlinear fragmentation-aggregation process to study the wave frequency power spectrum of decaying three-wave turbulence in the infinite capacity regime. We show that the transient spectral exponent is lambda + 1, where lambda is the degree of homogeneity of the wave interaction kernel and derive a formula for the decay amplitude. When lambda = 0 the transient exponent coincides with the thermodynamic equilibrium exponent leading to logarithmic corrections to scaling which we calculate explicitly for the case of constant interaction kernel.