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.
Connaughton
Colm
C
Mathematics Institute and Centre for Complexity Science, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom. connaughtonc@gmail.com
Krapivsky
P L
PL