Use this URL to cite or link to this record in EThOS:
Title: The smooth Ponomarenko Dynamo
Author: Wynne, James
ISNI:       0000 0004 6421 071X
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
Availability of Full Text:
Access from EThOS:
Access from Institution:
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.
Supervisor: Mestel, Jonathan Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral