Axisymmetric Rayleigh-Benard convection
This thesis considers axisymmetric Rayleigh-Benard convection in an infinite horizontal layer of fluid heated from below major emphasis is placed on a study of the effect of rotation of the layer, where both the stationary and overstable cases are analysed. In Chapter 2, a numerical solution of the linearised equations which govern the non-rotating fluid with rigid boundaries, is presented. In Chapter 3, the non-rotating layer is perturbed by making the elevation of the lower plane a small slowly varying function .1 of the radial coordinate. The modified amplitude equation is found and at the central axis the matching with a local solution in terms of Bessel functions is carried out. In Chapter 4, the effect of rotation is incorporated and the numerical scheme of Chapter 2, is modified to solve the appropriate linearised equations. In Chapter 5, the non-linear amplitude equation is derived for the rotating layer with rigid boundaries in the case when the system is subject to the exchange of stabilities. The matching process with a solution in terms of Bessel functions near the axis of rotation is described in Chapter 6, and is shown to lead to the possibility of'phase-winding' effects associated with variations in the wavelength of convection. 2. In Chapter 7, it is shown that when the rotating layer is subject to overstability a pair of amplitude equations governs the motion away from the axis of rotation. Again one of the main interests lies in how the solution matches with that valid in the neighbourhood of the axis.