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The skeleton of plasma turbulence : applications of nonlinear dynamical systems theory to a subcritical plasma turbulence model
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Smith, Oliver Joel (2023) The skeleton of plasma turbulence : applications of nonlinear dynamical systems theory to a subcritical plasma turbulence model. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3965283~S15
Abstract
The formation of localised travelling structures in plasma turbulence is investigated through the application of dynamical systems methods novel to plasma physics contexts. These methods involve studying a plasma model by identifying model solutions known as relative periodic orbits (RPOs). RPOs are a generalisation of periodic solutions which allow for symmetries, and collectively form a ‘skeleton’ in phase space representing the set of solutions the system can approach and move between. Locating and categorising these RPOs and their overall structure in parameter space gives a new framework through which plasma turbulence can be analysed, allowing complex fully nonlinear structures to be identified and isolated, and the structure of turbulence to be better understood. This RPO-based approach has been applied in neutral fluid systems and has aided the understanding of similar bursty behaviour in contexts such as pipe flow [Pringle et al., Phil. Trans. R. Soc. A 367, 457 (2009)] and Couette flow [Viswanath, D., J. Fluid Mech. 580, 339 (2007)].
A pseudospectral code was developed for a simple plasma model known as the plasma interchange model. The ‘edge of chaos’ (EOC) – a manifold separating the basins of attraction of the equilibrium and turbulence - is located through a bisection method, and is found to contain attractor RPOs with similar characteristics to structures seen in turbulence. An implementation of the Newton-Krylov-Hookstep algorithm is used to extend the manifold of RPOs beyond the EOC, where travellingwave-like RPOs are identified, some of which are stable, providing an intuitive explanation as to why such structures appear in plasma turbulence at high shear. Quasi-travelling waves with oscillatory structure are also identified, and found to generate spatially periodic zonal structures. It is demonstrated that RPO-based methods are a powerful tool for identifying coherent structures in plasmas and understanding their impact on turbulence.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QC Physics | ||||
Library of Congress Subject Headings (LCSH): | Plasma turbulence, Nonlinear systems, Energy transfer | ||||
Official Date: | January 2023 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Physics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | McMillan, Ben F. | ||||
Format of File: | |||||
Extent: | xi, 118 pages : illustrations, charts | ||||
Language: | eng |
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