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.

• Received 19 October 2009

DOI:https://doi.org/10.1103/PhysRevE.81.035303