Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets

Abstract

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. Finite-time coherent sets are determined by assembling gridded Lagrangian trajectories into a grid-to-grid transition matrix and computing dominant singular vectors of this matrix. We introduce a new combination of transfer operator based coherent set techniques with an overlapping window scheme, which enables ring size to vary over time, and follow an Agulhas ring's west-north-westward pathway across the southern Atlantic Ocean for over more than 2 years. We describe the evolution of the ring during this long journey and draw relationships between various dynamical and physical quantities associated with the ring and its decay. The advantage of the transfer operator method is that mass loss from rings is explicitly minimised over moderate periods of time using Lagrangian trajectory information. Our overlapping window approach readily accommodates the decay of rings over longer timespans during which part of the fluid is expelled from the structure. The ring boundary obtained by our method can then be used to explicitly study ring decay in both Eulerian and Lagrangian senses.

Agulhas Ring Transport Efficiency From Combined Satellite Altimetry and Argo Profiles

“…Interactions with such topographic features are not surprising given that the vertical extent of the eddies inferred from the profiles of density anomalies was deeper than 1,500 m. The loss of volume induced by such interactions is consistent with results by Frenger et al () who showed that bottom interactions are one of the most important processes to dissipate mesoscale energy in the Southern Ocean. Between the two ridges the eddies showed reduced volume losses (<0.5 × 10 13 m 3 ), as observed in Froyland et al () and Wang et al (). Other studies (Doglioli et al, ; van Sebille et al, ) have reported larger volume losses.…”

“…The ∼0.5 × 10 13 m 3 of water advected by eddy B12 west of 30°W corresponds to ∼33% of the initial volume of the eddy after the Mid‐Atlantic Ridge, and to ∼12.5% of the initial combined volume of eddies AN1 and AS2 east of the Walvis Ridge. These percentages are lower than those found by Froyland et al () and Wang et al (), but the difference can be mostly explained by the depth variation in eddy volume, which was not considered in those studies.…”

“…In recent years, these estimates have been further refined with the emergence of Lagrangian techniques capable of detecting coherent mesoscale eddies (Haller & Beron‐Vera, , ). Compared with traditional Eulerian eddy detection (e.g., Chaigneau et al, ; Chelton et al, ; Nencioli et al, ), studies based on these novel techniques can identify eddies capable of transporting water within their core with no noticeable leakage (Froyland et al, ; Wang et al, , ). Thus, these Lagrangian studies can provide more accurate estimates of the associated eddy transport.…”

Meridional and Zonal Wavenumber Dependence in Potential Vorticity Flux in Rossby Waves

“…This occurs at y =ŷ, which is the solution to sin y = −cy (33) which lies in the domain y ∈ (0, π). Equation (33) is transcendental and requires numerical evaluation.…”

“…The formulas to be given from this point onwards assume that −1 < c < 0 (corresponding to β > 0), in which case the Rossby wave travels as in Figure 1. Having determinedŷ which satisfies (33), it is necessary to define the function…”