Volume 87, Number 4, August 2009
Article Number 44001
Number of page(s) 5
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 07 September 2009
EPL, 87 (2009) 44001
DOI: 10.1209/0295-5075/87/44001

Discrete wave turbulence

E. Kartashova

RISC, J. Kepler University - Linz 4040, Austria, EU

received 12 June 2009; accepted in final form 5 August 2009; published August 2009
published online 7 September 2009

In this letter we propose discrete wave turbulence (DWT) as a counterpart of classical statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the size of clusters, i.e. it includes, but is not reduced to, the study of low-dimensional systems. Clusters with integrable and chaotic dynamics co-exist in different sub-spaces of the ${\bf k}$-space. NR-diagrams are introduced, a graphical representation of an arbitrary resonance cluster allowing to reconstruct uniquely dynamical system describing the cluster. DWT is shown to be a novel research field in nonlinear science, with its own methods, achievements and application areas.

47.10.-g - General theory in fluid dynamics.
05.45.-a - Nonlinear dynamics and chaos.
47.27.-i - Turbulent flows.

© EPLA 2009