Lectures on wave turbulence and intermittency
UNSPECIFIED (2002) Lectures on wave turbulence and intermittency. In: Conference of the NATO-Advanced-Study-Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows, CARGESE, FRANCE, JUN 21-JUL 03, 1999. Published in: NONLINEAR PDE'S IN CONDENSED MATTER AND REACTIVE FLOWS, 569 pp. 227-271.Full text not available from this repository.
In the early sixties, it was established that the stochastic initial value problem for weakly coupled wave systems has a natural asymptotic closure induced by the dispersive properties of the waves and the large separation of linear and nonlinear time scales. One is thereby led to kinetic equations for the redistribution of spectral densities via three and four wave resonances together with a nonlinear renormalization of the frequency. The kinetic equations have equilibrium solutions which are much richer than the familiar thermodynamic, Fermi-Dirac or Bose-Einstein spectra and admit in addition finite flux (Kolmogorov-Zakharov) solutions which describe the transfer of conserved densities, (e.g. energy) between sources and sinks. There is much one can learn from the kinetic equations about the behaviour of particular systems of interest including insights in connection with the phenomenon of intermittency.
What we would like to convince you is that what we call weak or wave turbulence is every bit as rich as the macho turbulence of 3D hydrodynamics at high Reynolds numbers and, moreover, is analytically more tractable. It is an excellent paradigm for the study of many body Hamiltonian systems which are driven far from equilibrium by the presence of external forcing and damping. In almost all cases, it contains within its solutions behavior which invalidates the premises on which the theory is based in some spectral range. We give some new results concerning the dynamic breakdown of the weak turbulence description and discuss the fully nonlinear and intermittent behavior which follows. These results may also be important for proving or disproving the global existence of solutions for the underlying partial differential equations.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Series Name:||NATO ADVANCED SCIENCE INSTITUTES SERIES, SERIES C, MATHEMATICAL AND PHYSICAL SCIENCES|
|Journal or Publication Title:||NONLINEAR PDE'S IN CONDENSED MATTER AND REACTIVE FLOWS|
|Editor:||Berestycki, H and Pomeau, Y|
|Number of Pages:||45|
|Page Range:||pp. 227-271|
|Title of Event:||Conference of the NATO-Advanced-Study-Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows|
|Location of Event:||CARGESE, FRANCE|
|Date(s) of Event:||JUN 21-JUL 03, 1999|
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