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Session S15 - Mathematics of Planet Earth

Thursday, July 15, 19:00 ~ 19:25 UTC-3

On the Lorenz '96 model and some generalization

Hans Engler

Georgetown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In 1996, the meteorologist and mathematician Edward Lorenz introduced a system of ordinary differential equations that describes a scalar quantity evolving on a circular array of sites, undergoing forcing, dissipation, and rotation invariant advection. Essentially, this is simplified weather on a one-dimensional planet. Lorenz constructed the system as a test problem for numerical weather prediction. Since then, the system has also found use as a test case in data assimilation. Mathematically, this is a dynamical system with a sparse quadratic nonlinear term that preserves energy, and it shares these properties with several other truncated models in geophysics and fluid dynamics. The system has a single bifurcation parameter (rescaled forcing), leading to multiple bifurcations, and it exhibits chaotic behavior for large forcing.

In this talk, after introducing the model and some of its properties and phenomena, the main characteristics of the advection term in the model will be identified and used to describe and classify possible generalizations of the system. A graphical method to study the bifurcation behavior of constant solutions for the general class of models will be introduced, and it will be shown how to compute normal forms of all these systems analytically. Problems with site-dependent forcing, dissipation, or advection will also be considered.

Joint work with John Kerin, Georgetown University.

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