Dynamical cascade generation as basic mechanism of Benjamin-Feir instability

TL;DR

This paper introduces a new model for energy cascades caused by Benjamin-Feir instability, explaining how direct and inverse cascades form and stabilize wave systems, with applications to laboratory and future experiments.

Contribution

It presents a discretized energy cascade model specific to Benjamin-Feir instability, detailing conditions for cascade emergence and stabilization, advancing understanding of wave dynamics.

Findings

Conditions for direct and inverse cascade appearance

Criteria for wave system stabilization

Application to laboratory and planned experiments

Abstract

A novel model of discretized energy cascade generated by Benjamin-Feir instability is presented. Conditions for appearance of direct and inverse cascades are given explicitly, as well as conditions for stabilization of the wave system due to cascade termination. These results can be used directly for explanation of available results of laboratory experiments and as basic forecast scenarios for planned experiments, depending on the frequency of an initially excited mode and steepness of its amplitude.