2002/10/07 by Peter R. Kramer, Joseph A. Biello, Kramer, Peter R. +4 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Photonic Systems #Strong Light-Matter Interactions #Tropical and Extratropical Cyclones Research #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0210007
10 pages, to appear "Proceedings of the Fourth International Converence on Dynamical Systems and Differential Equations"
arxiv created 2002/10/07 · openalex publication_date 2002/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss interesting dynamics of the energy transfer process starting from a large-scale excitation. This failure is traced to an enforcement of the exact resonance condition, whereas mathematically the resonance should be broadened due to the energy transfer happening on large but finite time scales. By allowing for the broadened resonance, a modified three-wave kinetic equation is derived for the FPU model. This kinetic equation produces some correct scaling predictions about the statistical dynamics of the FPU model, but does not model accurately the detailed evolution of the energy spectrum. The reason for the failure seems not to be one of the previously clarified reasons for breakdown in the weak turbulence theory.