期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1999
卷号：96
期号：25
页码：14216-14221
DOI：10.1073/pnas.96.25.14216
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed--the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)--depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date--over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.
