Pokric, Filip (2024) Wave Propagation in variations of the Lorenz-96 model. Bachelor's Thesis, Mathematics.
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Abstract
The Lorenz 96 (L96) model, developed by Edward Lorenz, has been broadly researched and applied to many areas such as oceanography and climate modelling. In previous studies, travelling and stationary waves were observed in the model, for suitable forcing parameter values, as they represent stable periodic orbits born after supercritical Hopf bifurcations. In this paper, suitable modifications to the original L96 system are studied, in order to derive variations of the travelling and stationary waves. The variations of the model and the L96 model are related by a linear change of coordinates, which is presented in the form of propositions. Additionally, an analysis of eigenvalues of the Jacobian matrix evaluated at the equilibrium solution was preformed for the lowest possible dimension n = 4 in order to identify a Hopf bifurcation, which produces a stable periodic orbit seen as a travelling wave. The periodic orbit is approximated in order to examine spatial and temporal properties of the travelling waves in the variations of the model. When analysing stationary waves, the dimension n = 6 was taken. A pitchfork bifurcation of the original equilibrium produces two new equilibrium solutions, whose further supercritical Hopf bifurcations give rise to two coexisting stable periodic orbits, which can be interpreted as stationary waves. Spatial and temporal properties of the waves are examined such as wave number and period. All waves are represented using a Hovmöller diagram.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Sterk, A.E. and Jardon Kojakhmetov, H. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 16 Jul 2024 11:00 |
| Last Modified: | 16 Jul 2024 11:00 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33453 |
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