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arXiv · 2404.08530

Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation

Francesco Vercesi·Susie Poirier·Anna Minguzzi·Léonie Canet
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Abstract

We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation.

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Francesco Vercesi, Susie Poirier, Anna Minguzzi, Léonie Canet. 2024-04-12. Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation. https://doi.org/10.1103/physreve.109.064149

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