Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation

TL;DR

This paper studies how pure additive noise influences the long-term behavior of the noisy Kuramoto-Sivashinsky equation, revealing noise-induced state transitions, intermittency, and universality classes through numerical and analytical methods.

Contribution

It demonstrates that degenerate noise causes state transitions and intermittency in the KS equation, establishing universality with the noisy Burgers equation via critical exponents.

Findings

Noise induces multiple state transitions including intermittency.

Critical exponents characterize the noise-induced transitions.

KS and noisy Burgers equations share the same universality class.

Abstract

We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both the KS and the noisy Burgers equation belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.