Abstract
This paper focuses on the wave inverse cascade instability analysis with self-regulating feedback control for a fixed external potential field and a highly localized finite-amplitude initial pulse. The wave inverse cascade instability analysis is carried out by solving the corresponding two-dimensional generalized nonlinear Schrödinger equation. The wave field firstly suffers from the modulation instability, followed by collapse into turbulence containing the shortest-wavelength modes in the system. This is followed by inverse cascade of the shortest wavelength modes back to the longer-wavelength ones, until a statistical stationary turbulent state is reached. It is found that the inverse cascade is limited to the shorter-wavelength modes with the wavenumber
$\left |k\right |\geq 100$
. This shows that the viscous damping
$p_i$
acts like a control switch to the inverse cascade, and the feedback control can also regulate the intensity of the inverse cascade mode.
Funder
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)