Vercesi Francesco, Poirier Susie, Minguzzi Anna, Canet Léonie
Université Grenoble Alpes, CNRS, <a href="https://ror.org/02mc6qk71">LPMMC</a>, 38000 Grenoble, France.
<a href="https://ror.org/055khg266">Institut Universitaire de France</a>, 5 rue Descartes, 75005 Paris, France.
Phys Rev E. 2024 Jun;109(6-1):064149. doi: 10.1103/PhysRevE.109.064149.
We consider the one-dimensional deterministic complex Ginzburg-Landau equation in the regime of phase turbulence, where the order parameter displays a defect-free chaotic phase dynamics, which maps to the Kuramoto-Sivashinsky equation, characterized by negative viscosity and a modulational instability at linear level. In this regime, the dynamical behavior of the large wavelength modes is captured by the Kardar-Parisi-Zhang (KPZ) universality class, determining their universal scaling and their statistical properties. These modes exhibit the characteristic KPZ superdiffusive scaling with the dynamical critical exponent z=3/2. We present numerical evidence of the existence of an additional scale-invariant regime, with the dynamical exponent z=1, emerging at scales which are intermediate between the microscopic ones, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new scaling regime belongs to the universality class corresponding to the inviscid limit of the KPZ equation.
我们考虑一维确定性复金兹堡 - 朗道方程在相湍流 regime 下的情况，其中序参量呈现无缺陷的混沌相动力学，它映射到库拉托莫 - 西瓦辛斯基方程，其特征为负粘性和线性水平的调制不稳定性。在这个 regime 中，大波长模式的动力学行为由 Kardar - Parisi - Zhang（KPZ）普适类描述，确定了它们的普适标度和统计性质。这些模式表现出具有动力学临界指数 z = 3/2 的特征性 KPZ 超扩散标度。我们给出了数值证据，证明存在一个额外的尺度不变 regime，其动力学指数 z = 1，出现在调制不稳定性固有的微观尺度和宏观尺度之间的中间尺度上。我们认为这个新的标度 regime 属于对应于 KPZ 方程无粘极限的普适类。
