Discrete Wave Turbulence

TL;DR

This paper introduces discrete wave turbulence (DWT) as a new framework distinct from classical wave turbulence, emphasizing resonance clustering and the coexistence of integrable and chaotic dynamics within clusters.

Contribution

It presents DWT as a novel research field with unique methods, including NR-diagrams for resonance clusters, expanding the understanding of nonlinear wave phenomena.

Findings

Resonance clustering characterizes DWT, differing from cluster size dependence.

NR-diagrams enable unique reconstruction of cluster dynamics.

DWT encompasses both integrable and chaotic behaviors in wave systems.

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.