Characterization of coherent structures in three-dimensional flows using the finite-size Lyapunov exponent

TL;DR

This paper uses the finite size Lyapunov exponent (FSLE) to identify and analyze three-dimensional Lagrangian coherent structures in turbulent flows, revealing differences between wall-bounded and oceanic flows in their structure and mixing properties.

Contribution

It introduces a method to locate 3D coherent structures using FSLE ridges in different turbulent flow regimes, highlighting their geometric and dynamical differences.

Findings

FSLE ridges differ significantly between channel and oceanic flows.

Horizontal stirring dominates in oceanic flows, forming quasi-vertical FSLE ridges.

Vertical motions are suppressed in oceanic flows due to rotation and stratification.

Abstract

In this paper we use the finite size Lyapunov Exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3d) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. Three-dimensional FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by numerical solution of the primitive equations where two-dimensional turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3d character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2d turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3d character of the FSLE ridges shows.