​Dynamics of the Lorenz-96 model

The atmosphere is a very complex and chaotic system, due to the many different factors that influence its behaviour. This thesis is dedicated to the study of the 1996 model of Edward Lorenz, a test model particularly constructed to study fundamental questions regarding the predictability of the atmosphere. The model describes waves in the atmosphere by taking values of a meteorological quantity in a certain number of equal sectors of a circle of constant latitude on the earth. Although the Lorenz-96 model does not describe the atmosphere realistically, it is --- due to its simplicity --- still a widely used model nowadays, even for applications outside the geophysical field.

The objectives of this work have been to unravel the dynamical structure of the Lorenz-96 model, which has not been investigated systematically before. To achieve this, we explored the symmetry of the model and analysed the bifurcations of the stable attractors using both analytical and numerical means. A clear overview of the transition of the stable trivial equilibrium via different bifurcations (namely Hopf, double-Hopf and pitchfork bifurcations) into one or more stable periodic orbits is obtained for any dimension. We also provide a coherent overview of the spatiotemporal properties and routes to chaos of the resulting waves. It turns out that both qualitative and quantitative aspects of the dynamics depend on the dimension. Our results enhance the understanding of the dynamics of the Lorenz-96 model and can be used to select the most appropriate parameter values in particular applications.

Dissertation: http://hdl.handle.net/11370/c67926eb-c8ef-4b9a-a48a-6e965f7d2262