Date of Award

Spring 2015

Document Type

Restricted Thesis

Terms of Use

© 2015 Peter J. Weck. All rights reserved. Access to this work is restricted to users within the Swarthmore College network and may only be used for non-commercial, educational, and research purposes. Sharing with users outside of the Swarthmore College network is expressly prohibited. For all other uses, including reproduction and distribution, please contact the copyright holder.

Degree Name

Bachelor of Arts

Department

Physics & Astronomy Department

First Advisor

Michael R. Brown

Abstract

At the heart of turbulence physics is the idea that some flows can be made sense of only statistically, and that once we adopt a statistical perspective, universalities and symmetries begin to emerge from the chaos. Usually such statistical characteristics are identified using frequency spectra, or probability distributions describing the size of fluctuations in the system across different time scales. However, the inherently probabilistic component to the study of turbulence also makes it amenable to more elaborate statistical measures of information and complexity. While more difficult to interpret than frequency spectra, such metrics provide a promising new way to look at turbulence, especially turbulence in plasmas where the electromagnetic character of flows contributes additional structure. In this thesis, statistical metrics known as permutation entropy and Jensen-Shannon complexity will be applied to datasets describing turbulent fluctuations in several laboratory and astrophysical plasmas. These metrics decompose a time series generated by discrete measurements of some physical parameter into ordinal patterns, similarly to how Fourier analysis decomposes a waveform into sinusoidal modes. By studying ordinal dynamics, or patterns in the relative sizes of successive values in a time series, essential information about the statistical nature of the fluctuations can be obtained. Measures of complexity and entropy based on ordinal patterns have been used to study plasma turbulence before [1, 2], although the work presented here and in [3] represents the first application of these methods to astrophysical plasma turbulence or plasma turbulence in a device like the Swarthmore Spheromak Experiment. The results highlight important differences between the various turbulent plasmas studied, and demonstrate the potential usefulness of these metrics in identifying time scales of physical interest and characterizing the effectiveness of laboratory plasma sources as models for astrophysical sources. Several practical conclusions, connected to the effects of insufficient statistics on these metrics, the appropriate choice of parameters, and even issues of terminology in turbulence physics, are also made. On the whole, permutation entropy and Jensen-Shannon complexity constitute promising new tools for the statistical study of turbulent fluctuations.

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