# Aggregation-Fragmentation Processes and Wave Kinetics

Source: [Aggregation-Fragmentation Processes and Wave Kinetics](<https://www.sota2.com/research/paper/68fa2c3d1e209131ce84e1b3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:17.220Z

Authors: C. Connaughton, P.L. Krapivsky

Published: 2009-09-29T18:05:24.000Z

## Abstract

There is a formal correspondence between the isotropic 3-wave kinetic equation and the rate equations for a non-linear fragmentation--aggregation process. We exploit this correspondence to study analytically the time evolution of the wave frequency power spectrum. Specifically, we analyzed a 3-wave turbulence in which the wave interaction kernel is a constant. We consider both forced and decaying turbulence. In the forced case, the scaling function diverges as $x^{-3/2}$ as expected from Kolmogorov-Zakharov theory. In the decaying case, the scaling function exhibits non-trivial, and hitherto unexpected, divergence with both algebraic and logarithmic spectral exponents which we calculate. This divergence leads to non-trivial decay laws for the total wave action and the number of primary waves. All theoretical predictions are verified with high quality numerical simulations of the 3-wave kinetic equation.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0909.5399>)

[PDF](<https://arxiv.org/pdf/0909.5399.pdf>)