Discrete Wave Turbulence

Abstract

In this Letter we present 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 $\mathbf{k}$-space. NR-diagrams are introduced, a handy graphical presentation 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.

Presentation of NR-diagrams is improved, comparision with Feynman diagrams is added, typo corrected

References in corpus (5)

• Dynamics of nonlinear resonances in Hamiltonian systems
• Cluster Dynamics of Planetary Waves
• Laminated Wave Turbulence: Generic Algorithms III
• Cluster formation in mesoscopic systems
• Laminated Wave Turbulence: Generic Algorithms I

Cited by in corpus (1)

• Nonlinear resonances of water waves