Bell, Nicholas Kiran (2018) Wave turbulence in rotating and non-rotating magnetohydrodynamics. PhD thesis, University of Warwick.

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Abstract

In this thesis Magnetohydrodynamics (MHD) is considered within the framework of wave turbulence (WT). I open with an introduction to MHD and turbulence theory before providing the fundamental theory for WT - including a worked example of the main steps in a WT derivation.

In non-rotating MHD, the system exhibits Alfveén waves. A WT theory for Alfv´en waves is well known and results in a prediction for the wave action spectrum in a steady state, n(kꞱ) - kꞱ−3 ? . In the first part of this thesis, the evolution of the spectrum preceding the formation of the steady state is studied. It is postulated that the evolution of the spectrum proceeds as a three step process. In the first stage, the spectrum forms a front which propagates from small to large wave numbers. In the second stage there is a reflected wave from large to small wavenumbers which leaves the KZ spectrum in its wake.

The first stage of the development of the KZ spectrum is studied here first. This stage is understood to occur via self-similar solutions of the kinetic equation. In infinite capacity systems such as MHD, the self-similarity is of the second kind. In this case, the similarity can not be fixed by conservation laws as for the first kind, but is instead found from the solution of an eigenvalue solution. The problem is reformulated into a nonlinear eigenvalue problem which is investigated analytically and numerically.

Next the second stage is investigated. Again the solution is expected to be self-similar in nature. However now the similarity is fixed neither by conservation laws or by solving a nonlinear eigenvalue problem. Instead they are determined by imposed asymptotics at one end of the similarity interval. These solutions are studied numerically by devising a numerical method to find the correct form of the spectrum at this stage.

The final part of this thesis concerns rotating MHD turbulence. First the theory is introduced including the weak and strong turbulence predictions. These are then compared with numerical simulations of the governing equations. Finally the kinetic equation is examined to discuss coupling of waves.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Magnetohydrodynamics, Magnetohydrodynamic waves, Turbulence
Official Date:	September 2018
Dates:	Date Event September 2018 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Nazarenko, Sergey
Format of File:	pdf
Extent:	ix, 100 leaves : charts
Language:	eng

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