Abstract
Two fundamental findings of the modern theory of wave turbulence are 1) existence of Kolmogorov-Zakharov power energy spectra (KZ-spectra) in $k$-space, \cite{zak2}, and 2) existence of ``gaps" in KZ-spectra corresponding to the resonance clustering, \cite{K06-1}. Accordingly, three wave turbulent regimes can be singled out - \emph{kinetic} (described by wave kinetic equations and KZ-spectra, in random phase approximation, \cite{ZLF92}); \emph{discrete} (described by a few dynamical systems, with coherent phases corresponding to resonance conditions, \cite{K09b}) and \emph{mesoscopic} (where kinetic and discrete evolution of the wave field coexist, \cite{zak4}). We present an explanation of freak waves appearance in capillary waves in He-II, \cite{ABKL09}, as a manifestation of discrete wave turbulent regime. Implications of these results for other wave systems are briefly discussed.
| Original language | English |
|---|---|
| Title of host publication | Geophysical Research Abstracts |
| Editors | E. Pelinovsky, C. Kharif |
| Pages | 1889-1889 |
| Number of pages | 1 |
| Volume | 12 |
| Publication status | Published - 2010 |
Fields of science
- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101003 Applied geometry
- 102025 Distributed systems
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)