Stabilized Kuramoto-Sivashinsky equation: A useful model for secondary instabilities and related dynamics of experimental one-dimensional cellular flows

TL;DR

This paper uses numerical simulations of the stabilized Kuramoto-Sivashinsky equation to model secondary instabilities and complex dynamics in one-dimensional cellular flows, providing insights relevant to experimental observations.

Contribution

It introduces a detailed numerical analysis of the stabilized Kuramoto-Sivashinsky equation focusing on secondary instabilities in one-dimensional cellular patterns, bridging theory and experiment.

Findings

Identification of secondary instabilities in cellular solutions

Comparison of destabilization scenarios with experimental data

Insights into transition to disorder in pattern-forming systems

Abstract

We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of secondary instabilities or transition toward disorder. We compare some of these collective behaviors to those observed in experiments. In particular, destabilization scenarios of bifurcated states are studied in a spatially semi-extended situation, which is common in realistic patterns, but has been barely explored so far.