Aggregation-Fragmentation Processes and Wave Kinetics

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.

4 pages, 5 figures

References in corpus (3)

• Shattering Transitions in Collision-Induced Fragmentation
• Numerical Solutions of the Isotropic 3-Wave Kinetic Equation
• Dynamical Scaling and the Finite Capacity Anomaly in 3-Wave Turbulence

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