The smooth ponomarenko dynamo
File(s)
Author(s)
Wynne, James
Type
Thesis
Abstract
In this work, we study a class of continuous generalisations of the kinematic Ponomarenko Dynamo, in an annulus with perfectly conducting boundary conditions.\par
We first consider the fundamentals of dynamo theory, deriving the governing equations and a general numerical code to find the growth rates for all modes and magnetic Reynolds numbers $R$. We concentrate on three types of flow fields: (a) flows which approximate the discontinuous Ponomarenko dynamo, (b) full solutions of the Navier Stokes driven by an axial pressure gradient and moving boundaries, and (c) flows where both the axial and azimuthal velocity components are powers of the cylindrical radius. Good agreement is found between the numerical results and the known asymptotic theory for large $R$. The smallest $R$-values permitting dynamo action are found, along with the values which gives rise to the fastest growing mode.
We first consider the fundamentals of dynamo theory, deriving the governing equations and a general numerical code to find the growth rates for all modes and magnetic Reynolds numbers $R$. We concentrate on three types of flow fields: (a) flows which approximate the discontinuous Ponomarenko dynamo, (b) full solutions of the Navier Stokes driven by an axial pressure gradient and moving boundaries, and (c) flows where both the axial and azimuthal velocity components are powers of the cylindrical radius. Good agreement is found between the numerical results and the known asymptotic theory for large $R$. The smallest $R$-values permitting dynamo action are found, along with the values which gives rise to the fastest growing mode.
Version
Open Access
Date Issued
2016-12
Date Awarded
2017-06
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Mestel, Jonathan
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)