Anomalous Scaling on a Spatiotemporally Chaotic Attractor

TL;DR

This paper investigates the anomalous scaling behavior in a spatiotemporally chaotic attractor within the Nikolaevskiy model, revealing discrepancies with initial theories and showing that higher-order corrections restore expected scaling laws.

Contribution

It demonstrates that higher-order corrections are necessary to accurately describe the scaling behavior in the Nikolaevskiy model's chaotic attractor.

Findings

Unexpected scaling behavior of long-wave modes

Discrepancies between numerical results and initial asymptotic theory

Higher-order corrections recover the predicted scaling laws

Abstract

The Nikolaevskiy model for pattern formation with continuous symmetry exhibits spatiotemporal chaos with strong scale separation. Extensive numerical investigations of the chaotic attractor reveal unexpected scaling behavior of the long-wave modes. Surprisingly, the computed amplitude and correlation time scalings are found to differ from the values obtained by asymptotically consistent multiple-scale analysis. However, when higher-order corrections are added to the leading-order theory of Matthews and Cox, the anomalous scaling is recovered.