This TRR 181 seminar will be held by Mallory Carlu (University of Aberdeen) on
Probing multiscale chaoticity
at Universität Hamburg on June 14th at 10 am, Bundesstr. 53, Room 22/23 (ground floor).
In this seminar, I will unravel some mechanisms at the core of multiscale chaoticity, namely the interplay between chaotic subsystems featuring different amplitudes and time scales, through the prism of Lyapunov analysis (Lyapunov Exponents, LEs, and Covariant Lyapunov Vectors, CLVs). To this purpose, I will make use of a modified version of the two-layer Lorenz 96 model, featuring external forcing in the fast variables to render them chaotic by their own (i.e without the need of being coupled to the slow variables). I will highlight the emergence of a group of CLVs, associated to a band of LEs centered around 0, that have a significant projection on the slow subspace. The number of such CLVs is greater than the number of slow variables, thus hinting at a non-trivial mechanism of transfer in the tangent space dynamics and therefore might give more insight in the long term dynamics of the system. Some scaling arguments will be presented and I will show that this so-called central band emerges as a mixing of slow and fast modes. These results will be compared with a master-slave setup where slow variables remain untouched by the fast ones and I will show how this limit can be attained with the regular setup, playing only with the scale separation factor. I will also present some insights on the geometrical structure of these CLVs and show that those belonging to the central band are highly delocalized, thus fitting to the concept of Hydrodynamic Lyapunov Modes (HLMs). Finally the diversity of directions spanned by CLVs will be discussed, through the use of angles between individual vectors and Ensemble dimension.