A matrix-free numerical bifurcation method applied to sheared annular electroconvection

Abstract

We investigate the flow transitions in sheared annular electroconvection using matrix-free numerical bifurcation methods. In particular, we study a model that simulates a liquid crystal film in the Smectic A phase suspended between two annular electrodes, and subjected to an electric potential difference and a shear applied by rotating the inner anode at a constant rate. In this thesis, a matrix-free numerical bifurcation method is implemented to identify the transitions of the flow that result due to changes in the main nondimensional control parameter, the Rayleigh number R. This method consists of a natural continuation method by detecting fixed points of two different discrete-time dynamical systems based on numerical integration, and a linear stability analysis that identifies the local behaviour of the flow.