Statistical theory of structure formation: self-organization

TL;DR

This paper introduces a novel non-perturbative method to predict the probability distribution of self-organized shear flows, revealing strong intermittency and confirming results through numerical simulations, with implications for various stochastic systems.

Contribution

It provides the first prediction of the PDF for shear flow self-organization using a new method based on coherent structures, advancing understanding of stochastic nonlinear systems.

Findings

Strong intermittency with exponential tails in PDFs

Good agreement between predicted and simulated power spectra

High probability of supercritical states due to stochastic effects

Abstract

We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent structure is utilized for the prediction of the PDFs, revealing strong intermittency with exponential tails. Numerical simulations confirm these results. The predicted power spectra are also in a good agreement with simulation results. The results imply a significant probability of supercritical states due to stochastic perturbation in a variety of systems.