Berlin 2015 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 60: Poster - complex systems and data analysis
DY 60.6: Poster
Thursday, March 19, 2015, 16:00–18:00, Poster A
Markovian approximation and perturbation theory of transport processes in geophysical flows — Naoya Fujiwara1, Kathrin Kirchen2,3, Jonathan F. Donges3,4, •Reik V. Donner3, Jürgen Kurths3,5, and Kazuyuki Aihara1 — 1University of Tokyo, Japan — 2University of Bonn, Germany — 3Potsdam Institute for Climate Impact Research, Germany — 4Stockholm Resilience Centre, Sweden — 5Humboldt University, Berlin, Germany
We propose a Markov chain-based framework for analyzing passive transport in geophysical flows. For this purpose, the available space is coarse-grained, and transition probabilities between different boxes are estimated. The stochastic transition matrix becomes time-dependent if the underlying flow exhibits changes with time. In order to analytically treat this case, we introduce a first-order perturbation theory that allows evaluating the corresponding changes in terms of the largest eigenvalue and associated eigenvector of the perturbed transition matrix. Specifically, three different problem classes are studied that are potentially relevant for geophysical applications: point-wise absorption of particles, absorption in the presence of a constant input of particles, and changes in the steady state in the case of mass conservation. For some simple 2D flow model exhibiting Lagrangian turbulence, we demonstrate numerically that the absorption rates provided by first-order perturbation theory describe the actual dynamics of the system very well.