M1: Instabilities across scales and statistical mechanics of multi-scale GFD systems

Principal investigators: Prof. Ingenuin Gasser (Universität Hamburg), Prof. Valerio Lucarini (Universität Hamburg), Prof. Reiner Lauterbach (Universität Hamburg)

In this subproject we will use the formalism of covariant Lyapunov vectors to investigate the dynamics of simplified multi-scale geophysical fluid systems, in order to gain a fundamentally new understanding of their instabilities and of their statistical mechanics. This will allow for greatly improving our understanding of the link between the micro-mesoscopic and macroscopic properties of turbulent geophysical flows. Asymptotic methods will be used for clarifying the emergence of different regimes of motions and of the corresponding instabilities.

Reports from the scientific front

Multi-scale instabilities and energy transfers

(By Sebastian Schubert)

Since September 2016, I work as a Post-Doctoral Researcher for the TRR. Previously, I was working as part of the DFG funded project MERCI after finishing my PhD at the International Max-Planch Research School at the Max-Planck-Institute for Meteorology in Hamburg.

My research is mainly focused on the various applications of dynamical system theory to geophysical models of simple to intermediate complexity. In particular, I have applied the theory of Covariant Lyapunov Vectors to a quasi-geostrophic two layer model and studied the connection between the unstable and stable directions to their baroclinic and barotropic energy conversions (Schubert & Lucarini, 2015). This type of analysis also allowed it to illuminate some features of simple blocking like patterns (Schubert & Lucarini, 2016).

For the project M1, I will study the properties of multi-scale instabilities using CLVs. The presence of multi-scale features usually impedes efforts to make good predictions. I will investigate the connection between multi-scale instabilities and energy transfers between atmosphere and ocean using firstly a rather simple quasi geostrophic model of the atmosphere and ocean (MAOOAM). Secondly, my interest lies in exploring the multi-scale properties of linear instabilities in a primitive equation model (PUMA). With these investigations using new tools from dynamical system theory, we expect to foster the understanding of multi-scale processes that are slow evolving and are usually “hidden” behind the faster dynamics.

Lyapunov vectors and the geophysical flow

(by Florian Noethen)

Since August 2016 I am a Ph.D. student at Universität Hamburg. Specifically, I am a member of the research group differential equations and dynamical systems at the department of mathematics. Under supervision of Professor Reiner Lauterbach, Professor Ingenuin Gasser and Professor Valerio Lucarini, together with Dr. Sebastian Schubert, I work on the subproject M1: Instabilities across scales and statistical mechanics of multi-scale GFD systems.

In particular, my forthcoming research is based on the numerics of covariant Lyapunov vectors. These vectors identify directions of asymptotic growth rates to small linear perturbations of orbits in a dynamical system. The theory of covariant Lyapunov vectors provides an extension to the stability analysis of equilibria and to Floquet theory. Hence, they can be used to investigate the stability of more complex objects in, for example, geophysical flows.

Furthermore, I am to investigate the dynamics of a low-dimensional model of the Gulf Stream in the context of bifurcation analysis. With the use of local and global properties such as temperature, specific weight and ocean salinity, we hope to better understand the effects of melting of glaciers related to global warming on the Gulf Stream within the scope of a small model.

Before the project, I studied mathematics at Universität Hamburg and wrote my master's thesis on the dynamics of coupled cell systems this year.

I am happy for the opportunity to gain new experience through this project and to contribute to this research.