Quantifying Transport by Coherent Lagrangian Vortices

Ocean mesoscale turbulence contributes significantly to the transport of heat and other tracers in the ocean. Mesoscale transport is most commonly quantified via an Eulerian Reynolds flux formulation, in which the eddy transport is defined as the correlation between fluctuating velocity and tracer fields, a difficulty quantity to observe in the ocean. Some recent studies, however, have attempted to estimate mesoscale transport by tracking the motion of a discrete number of coherent mesoscale eddies, assuming these eddies are material structures which trap fluid inside and transport it over long distances. Such a method only works if the eddies being tracked are truly materially coherent, i.e. if they are objective Lagrangian coherent structures. Most common eddy tracking techniques used in oceanography are neither objective nor Lagrangian, and thus the material coherence of the identified structures is unknown.

In this study, we employ recently developed tools from dynamical systems theory to make a comprehensive census of coherent Lagrangian mesoscale eddies over a wide sector in the East Pacific. Our eddy identification method is based on an objective dynamic polar decomposition of the deformation gradient developed by Haller et al. (2016). We compute the deformation gradient by advecting a dense mesh of over 8 million Lagrangian particles by satellite-altimetry-derived surface geostrophic velocities. Advection is performed for contiguous 30, 90, and 270 day intervals over the entire 25-year satellite record. This is the largest-scale Lagrangian eddy census performed to date, with 41875 30-day eddies and 1182 90-day eddies identified. The statistics of Lagrangian eddy size and propagation speed are broadly similar to previous eddy tracking results based on sea-surface height anomalies (e.g. Chelton et al. 2011). However, the material nature of our Lagrangian eddies enables a precise quantification of their role in transport. We define a "coherent diffusivity" diagnostic based on the relative meridional dispersion of Lagrangian particles contained within material eddies and show that the the transport due to these structures accounts for less than 1% of the total turbulent meridional transport. We conclude that most of the ocean "eddy flux" is due to incoherent transport, rather than the bulk translation of coherent structures. Implications for the parameterization of eddy fluxes are discussed.