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

Principal investigators: Prof. Ingenuin Gasser (Universität Hamburg), Prof. Valerio Lucarini (University of Reading/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.

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Progress on CLVs in PUMA

We would like to understand the multiscale behaviour that is observable in the atmosphere using a spectral primitive equations model.

Sebastian Schubert, former Postdoc in M1

I am Sebastian Schubert and I am a postdoc in sub project M1 “Instabilities across scales and statistical mechanics of multi-scale GFD systems”.

We would like to understand the multi-scale behaviour that is observable in the atmosphere using a spectral primitive equations models. For this, we use PUMA, a spectral primitive equation model, that is the dynamical core of PLASIM (Planet Simulator). For this purpose, we are studying instability of linear Progress on CLVs in PUMA years. Our results show that there is convergence towards a rate function which describes the behavior of large fluctuations. Nevertheless, we did not find a growth dependent variation of the rate function. This means in order to find discriminating perturbations in a generalized framework which develop on chaotic backgrounds.

For this, we make use of the splitting of tangent linear space into a covariant Lyapunov basis as described by Osedelecs theorem. Recently, we have studied the existence of a large fluctuation theorem for the Lyapunov exponents. The investigation is difficult because the computational effort only allows “short” time series of about 25 years. Our results show that there is convergence towards a rate function which describes the behavior of large fluctuations. Nevertheless, we did not find a growth dependent variation of the rate function. This means in order to find discriminating properties that are growth dependent we really have to study the scale dependency of the CLVs. As a first step, we are investigating the fastest growing instabilities in comparison to their presence in the actual non-linear background state. We see a clear detachment of the scales present in the first CLVs after going to a resolution of T85 (128x256, 1.39° at the equator). Our objective is now to expand this analysis to leading linear instabilities (the CLVs) and see if there are trends of the dominating waves towards larger scales.

Multi-scale instabilities and energy transfers

We expect to foster the understanding of multi-scale processes that are slow evolving and are usually ‘hidden’ behind the faster dynamics.

Sebastian Schubert, former Postdoc in M1

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.