Abstract
Lagrangian coherent sets are known to crucially determine transport and mixing processes in non-autonomous flows. Prominent examples include vortices and jets in geophysical fluid flows. Coherent sets can be identified computationally by a probabilistic transfer-operator-based approach within a set-oriented numerical framework. Here, we study sudden changes in flow patterns that correspond to bifurcations of coherent sets. Significant changes in the spectral properties of a numerical transfer operator are heuristically related to critical events in the phase space of a time-dependent system. The transfer operator approach is applied to different example systems of increasing complexity. In particular, we study the 2002 splitting event of the Antarctic polar vortex.
Highlights
Characterizing and predicting the occurrence of sudden changes in the dynamics of complex systems—typified in this context by geophysical flow patterns—is crucial in understanding and controlling such critical events, which may have serious environmental consequences
There, almost-invariant sets were built around a global stationary state, whose bifurcation yielded the qualitative change of the underlying flow patterns
As the second singular vectors are known to represent the polar vortex flow pattern during the split [23], we focus on the behavior of the corresponding singular value σ2t for final times between 18 September and 4 October 2002 (Figure 11)
Summary
Characterizing and predicting the occurrence of sudden changes in the dynamics of complex systems—typified in this context by geophysical flow patterns—is crucial in understanding and controlling such critical events, which may have serious environmental consequences. Within a set-oriented numerical framework [14], this infinite-dimensional operator can be approximated by the transition matrix of a finitestate Markov chain, and the sign structures of left and right singular vectors to singular values close to 1 are systematically used to yield initial and final time-robust coherent patterns [7,8,12] We note that this is fundamentally different from the singular value decomposition methods often used in atmospheric sciences There, almost-invariant sets were built around a global stationary state, whose bifurcation yielded the qualitative change of the underlying flow patterns All of these previous works dealt with autonomous systems, and only very recently has a transfer-operator-based computational approach for studying changes in non-autonomous flow structures been proposed [23].
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