Demonstration of the refined three-dimensional structure of mesoscale eddies and computational error estimates via Lagrangian analysis

Abstract

In previous studies, Lagrangian analyses were used to assess large-scale ocean circulation, and the Lagrangian coherent structure could also reveal the evolution of the two-dimensional structure of the mesoscale eddies. However, few studies have demonstrated the three-dimensional structure of the mesoscale eddies via Lagrangian analysis. Compared with previous studies, which investigated the eddy structure via a Eulerian view, we used a Lagrangian view to provide a different perspective to study the eddy structure. An idealized cyclonic mesoscale eddy is built up over a seamount, and it presents downwelling inside the eddy and upwelling alongside the eddy formed within a closed circulation system. This structure is difficult to display via a Eulerian analysis. However, the trajectories of particles can well demonstrate the full cycle: the fluid sank and rotated inside the eddies, converged to the upwelling zone of the bottom layer and returned to the surface through upwelling. We also applied a Lagrangian analysis to a realistic simulation. As a significant phenomenon in the South China Sea, the dipole structure of the anticyclonic eddy (AE)/cyclonic eddy (CE) pair off of central Vietnam has been well studied but mainly at the sea surface. With a Lagrangian analysis, we illustrate the three-dimensional structure of the eddy pair: the fluid sank (rose) and rotated inside the AE (CE). More importantly, the trajectories of the particles suggested that there was no fluid exchange between the two eddies since the strong boundary jet separates them from each other. All the conclusions above have been verified and are supported by the computational error estimate. With a selected time step and integral period, the computational errors always present small values, although they increase with strong divergent and vertical diffusive flow.