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Wavelet Methods for Studying the Onset of Strong Plasma Turbulence

Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents (FTLE), and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations $R_{ic}$ is found to be fairly uniform across different plasma models and provides an empirical threshold for turbulence onset. The technique is illustrated through examples. First, it is applied to the Kelvin--Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, it is applied to the development of turbulence downstream of the bowshock in a magnetosphere simulation.