Wavelet Methods for Studying the Onset of Strong Plasma Turbulence
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Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. 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 (Pearson correlation coefficient of > 0.9) 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 Ric is found to be fairly uniform across different plasma models and provides an empirical threshold for turbulence onset. The utility of this 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, the wavelet diagnostic is applied to the development of turbulence downstream of the bowshock in a global magnetosphere simulation. Finally, the wavelet technique is also shown to be useful as a de-noising method for particle simulations.
Fig6 description: In fluid turbulence, there exists a parameter called Reynolds number that describes the degree of turbulence. No one has been able to find an equivalent parameter in plasma turbulence. The question we asked was whether we can come up with a parameter that can be used to signal the onset of turbulence. We were able to show, using an iterative wavelet technique that decomposes the signal into coherent and incoherent components, that the onset of turbulence occurs when the ratio of incoherent to coherent components becomes about 0.1. We are now exploring the universality of this result.
Fig15 description: This movie shows the simulation of the impact of a discontinuity in the solar wind as it reaches and interacts with the Earth's magnetosphere. One of the unsolved problems in physics is the identification of a quantity that measures the dissipation in a collisionless plasma. We recently used an iterative wavelet decomposition technique to address this problem. We were able to demonstrate that the coherent wavelet component is highly correlated with the formation of coherent structures like current sheets and wavefronts (the left panel) whereas the incoherent wavelet component is associated with plasma heating. Our further analysis and the details of how regions of large incoherent component appear in this movie are strongly suggestive of the interpretation of the incoherent wavelet component as a proxy for plasma dissipation.
Click here to read the full paper
Please also enjoy some short movies that help support points throughout the paper.
Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. 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 (Pearson correlation coefficient of > 0.9) 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 Ric is found to be fairly uniform across different plasma models and provides an empirical threshold for turbulence onset. The utility of this 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, the wavelet diagnostic is applied to the development of turbulence downstream of the bowshock in a global magnetosphere simulation. Finally, the wavelet technique is also shown to be useful as a de-noising method for particle simulations.
Fig6 description: In fluid turbulence, there exists a parameter called Reynolds number that describes the degree of turbulence. No one has been able to find an equivalent parameter in plasma turbulence. The question we asked was whether we can come up with a parameter that can be used to signal the onset of turbulence. We were able to show, using an iterative wavelet technique that decomposes the signal into coherent and incoherent components, that the onset of turbulence occurs when the ratio of incoherent to coherent components becomes about 0.1. We are now exploring the universality of this result.
Fig15 description: This movie shows the simulation of the impact of a discontinuity in the solar wind as it reaches and interacts with the Earth's magnetosphere. One of the unsolved problems in physics is the identification of a quantity that measures the dissipation in a collisionless plasma. We recently used an iterative wavelet decomposition technique to address this problem. We were able to demonstrate that the coherent wavelet component is highly correlated with the formation of coherent structures like current sheets and wavefronts (the left panel) whereas the incoherent wavelet component is associated with plasma heating. Our further analysis and the details of how regions of large incoherent component appear in this movie are strongly suggestive of the interpretation of the incoherent wavelet component as a proxy for plasma dissipation.
Click here to read the full paper
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