Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation
arxiv(2024)
摘要
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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