Exact and quasi-resonances in discrete water-wave turbulence

TL;DR

This paper investigates the structure and abundance of exact and quasi-resonances in discrete water-wave turbulence, revealing their vast numbers and potential influence on energy transport, with implications for other mesoscopic systems.

Contribution

It provides a detailed analysis of discrete resonances in water-wave turbulence and introduces a general approach applicable to various mesoscopic systems.

Findings

Hundreds of millions of exact 4-wave resonances in small spectral domains.

Angle transport can influence scale energy transport.

Restrictions for the onset of quasi-resonances are identified.

Abstract

The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy transport is taken into account. It is also shown that angle transport can contribute inexplicitly to scale transport. Restrictions for quasi-resonances to start are written out. The general approach can be applied directly to mesoscopic systems encountered in condensed matter (quantum dots), medical physics, etc.