Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity

Abstract

Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to detect them and gain information about their tracks, their lifetimes and their shapes. We present a Lagrangian descriptor based on the modulus of vorticity to construct an eddy tracking tool. In our approach we denote an eddy as a rotating region in the flow possessing an eddy core corresponding to a local maximum of the Lagrangian descriptor and enclosed by pieces of manifolds of distinguished hyperbolic trajectories (eddy boundary). We test the performance of the eddy tracking tool based on this Lagrangian descriptor using an convection flow of four eddies, a synthetic vortex street and a velocity field of the western Baltic Sea. The results for eddy lifetime and eddy shape are compared to the results obtained with the Okubo-Weiss parameter, the modulus of vorticity and an eddy tracking tool used in oceanography. We show that the vorticity-based Lagrangian descriptor estimates lifetimes closer to the analytical results than any other method. Furthermore we demonstrate that eddy tracking based on this descriptor is robust with respect to certain types of noise, which makes it a suitable method for eddy detection in velocity fields obtained from observation.

A Persistent Deep Anticyclonic Vortex in the Rockall Trough Sustained by Anticyclonic Vortices Shed From the Slope Current and Wintertime Convection

“…The OW parameter is widely used as an eddy detection method and is applicable to defining vortices in both altimetry and model output data sets (e.g., Chelton et al, 2011; Gula et al, 2016a; Isern‐Fontanet et al, 2006). The OW parameter is taken as a quantification of strain versus vorticity and equal to , where s n is the normal strain component, s s the shear strain component, and ζ is the relative vorticity of the two‐dimensional field ( u and v the zonal and meridional components), with s n = ∂u / ∂x − ∂v / ∂y , s s = ∂v / ∂x + ∂u / ∂y and ζ = ∂v / ∂x − ∂u / ∂y (Gula et al, 2016a; Isern‐Fontanet et al, 2006; Petersen et al, 2013; Vortmeyer‐Kley et al, 2016). Within eddy cores, vorticity amplitude manifests itself as a local maximum, thus outweighing the strain component, underlining eddy cores by characteristic negative OW parameter (Vortmeyer‐Kley et al, 2016).…”

“…The OW parameter is taken as a quantification of strain versus vorticity and equal to s 2 n þ s 2 s − ζ 2 , where s n is the normal strain component, s s the shear strain component, and ζ is the relative vorticity of the two-dimensional field (u and v the zonal and meridional components), with s n = ∂u/∂x−∂v/∂y, s s = ∂v/∂x+∂u/∂y and ζ = ∂v/∂x − ∂u/∂y (Gula et al, 2016a;Isern-Fontanet et al, 2006;Petersen et al, 2013;Vortmeyer-Kley et al, 2016). Within eddy cores, vorticity amplitude manifests itself as a local maximum, thus outweighing the strain component, underlining eddy cores by characteristic negative OW parameter (Vortmeyer-Kley et al, 2016). Following and , we impose OW < 0 criterion, thus allowing to define vortices of various sizes.…”

Eddies: Fluid Dynamical Niches or Transporters?–A Case Study in the Western Baltic Sea

“…The search for eddies relies on the concept of Lagrangian descriptors developed to identify certain points in the flow which can be linked to the eddy core and the boundaries of regions around these points which can be linked to the eddy shape. We refer to Mancho et al (2013) for details on Lagrangian descriptors in general and to Vortmeyer-Kley et al (2016) for details on M V and the implementation of the specific eddy detection tool used in this study. Here, we will only provide a brief outline.…”

“…This quantity M V is related to the vorticity, i.e., a measure of the strength of rotation a fluid particle experiences along its path for a finite time interval 2 • τ (mathematical details cf. Vortmeyer-Kley et al, 2016 and. Fluid particles that stay in regions of strong rotation collect large values of this measure.…”

“…In order to generate the velocity fields to conduct the eddy tracking, we rely on the output of a numerical model of the Western Baltic Sea. The model settings are similar to Gräwe et al (2015) and Vortmeyer-Kley et al (2016). Figure 1 shows the area of study.…”