title: Aggregation-fragmentation processes and decaying three-wave turbulence.
abstract: 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.
authors.affiliation: Mathematics Institute and Centre for Complexity Science, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom. connaughtonc@gmail.com
authors.forename: Colm
authors.initials: C
authors.lastname: Connaughton
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky