Coherent sets in dynamical systems are regions in phase space that optimally “carry mass” with them under the system's evolution, so that these regions experience minimal leakage. The dominant tool for determining coherent sets is the transfer operator, which provides a complete description of Lagrangian mass transport. In this work, we combine existing transfer operator methods with a windowing scheme to study the spatial and temporal evolution of a so-called Agulhas ring: a large anticyclonic mesoscale eddy playing a key role in inter-ocean exchange of climate-relevant properties. Our focus is on ring decay over time and the windowing scheme enables us to study how the most coherent region (our estimate of the ring) varies in position and size over a period of more than two years. We compare the eddy-like structure and its spatio-temporal changes as revealed by our method and by a classical Eulerian approach.
The altimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support from CNES (http://www.aviso.oceanobs.com/duacs/). G.F. and C.H. were partially supported by the 2011/12 Go8/DAAD Australia/Germany Joint Research Co-Operation Scheme. G.F. was also supported by an ARC Future Fellowship. E.v.S. was supported by the ARC via Grant DE130101336. V.R. acknowledges support from MICINN and FEDER through the ESCOLA project (CTM2012-39025-C02-01) while finishing this paper.
I. INTRODUCTION II. TRACKING THE EVOLUTION OF COHERENT SETS A. A pair of coherent sets B. Computing a sequence of coherent sets via overlapping time windows III. OCEAN SURFACE FLOW AND LAGRANGIAN CALCULATIONS A. Time-dependent surface flow derived from satellite B. Selection of initial domain, trajectory integration, and transition matrix calculation IV. INVESTIGATION OF THE PATHWAY OF AN AGULHAS RING A. Boundaries, pathways, and comparison with other ring diagnostics B. Decay C. Discussion and conclusions
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