Resonant duet modeling approach for the spectral analysis of strongly nonlinear wave turbulent signal

In the prior work [Wonjung Lee, Phys. Rev. E, 98(2):022137, 2018], the author proposed one probabilistic model for the purpose of facilitating the analysis and processing of rapidly varying random signal generated from the wave turbulence prototype. The present paper is devoted to the rigorous derivation and systematic generalization of this existing non-Markov model, and in order to achieve this goal, use is made of the resonant duet modeling framework. By this we mean the reduced-order modeling technique, which proceeds via carefully constructing a macrovariable in resonance with the target system variable and statistically projecting the true complex dynamical system onto the linear space spanned by this couple of variables. One theoretical merit of such an attempt is the emergence of the bivariate diffusion model which is almost Markovian and whose marginalization provides a principled way to obtaining a non-Markovian model for the single variable. As for the practical advantage of the methodology, the formalism proves useful for performing an accurate spectral analysis of the four-wave system of turbulence.

Keywords

strong wave turbulence, non-Markovian turbulent signal, reduced-order model approach for spectral analysis, four-wave resonances, resonant duet model

2010 Mathematics Subject Classification

60G15, 82B31

Full Text (PDF format)

Received 28 December 2022

Received revised 6 July 2023

Accepted 15 September 2023

Published 12 July 2024