Amplitude-phase Synchronization in Intermittent Turbulence and Spatiotemporal Chaos

The solar-terrestrial environment provides a natural laboratory for observing intermittent turbulence [1]. The degree of non-Gaussianity (intermittency) in a turbulence can be quantified by calculating the normalized fourth-order structure function, also known as kurtosis. Recently, a phase coherence surrogate technique for characterizing phase synchronization was developed for space plasmas [2]. The link between non-Gaussianity and phase synchronization in intermittent turbulence was established by Koga et al. [3] using magnetic field data upstream and downstream of the Earth’s bow shock. The analysis of dynamical systems modelled by partial differential equations (PDEs) serves as a bridge between chaos theory and both plasma and fluid dynamics. Such systems may exhibit a wealth of regimes, which include temporal chaos (TC) and spatiotemporal chaos (STC) [6]. In PDEs, we refer to temporal chaos whenever the patterns generated vary chaotically in time, but spatial coherence is preserved. In spatiotemporal chaos, the dynamics is chaotic in time and irregular in space. At the onset of STC, there is on-off spatiotemporal intermittency which consists of random switchings between TC and STC [6]. In this paper we analyze synchronization due to multiscale interactions in observations of intermittent turbulence and numerical simulations of spatiotemporal intermittency. First, we apply kurtosis and phase coherence index to measure the degree of amplitude-phase synchronization of intermittent magnetic field turbulence observed in the solar wind. Next, we use a model of nonlinear waves to measure the degree of amplitude-phase synchronization by computing the power-phase spectral entropy, respectively, at the onset of spatiotemporal intermittency. Our results indicate that the duality of amplitude-phase synchronization may be the origin of intermittency in fully-developed turbulence in the solar-terrestrial environment. 1. INTERMITTENT MAGNETIC FIELD TURBULENCE