Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos

TL;DR

This paper develops an effective hydrodynamic theory for spatio-temporal chaos in the Kuramoto-Sivashinsky equation, highlighting the role of space-time defects and stochasticity in system stability.

Contribution

It introduces a novel stochastic equation in the KPZ universality class that models the chaotic dynamics of the KS system through a coarse-graining approach.

Findings

Effective theory parameters are computed approximately.

Stability is mediated by space-time defects with stochastic behavior.

The approach may apply to other spatio-temporal chaos problems.

Abstract

Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS) equation is investigated analytically and numerically. An effective stochastic equation belonging to the KPZ universality class is constructed by incorporating the chaotic dynamics of the small KS system in a coarse-graining procedure. The bare parameters of the effective theory are computed approximately. Stability of the system is shown to be mediated by space-time defects that are accompanied by stochasticity. The method of analysis and the mechanism of stability may be relevant to a class of STC problems.