Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Abstract

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.PACS numbers: 05.45.Ac, 45.20.Jj, 47.27.ed, 47.52.+j Keywords: Lagrangian coherent structures, coherent Lagrangian eddies, inertial particles, finite-size and buoyancy effects, oceanic mesoscale eddies, drifting buoys, Sargassum Satellite-tracked drifting buoy trajectories and satellite-derived algal distributions are commonly used in oceanography to infer Lagrangian aspects of the surface ocean circulation. At the same time, dynamical systems techniques applied to surface ocean velocities inferred from satellite altimetry reveal persistent coherent Lagrangian eddies. Paradoxically, buoys and algae display dissipative-looking patterns in contrast to the conservative-looking coherent Lagrangian eddies. Here we show that the dissipative patterns are due to inertial effects superimposed on the conservative fluid patterns produced by coherent Lagrangian eddies.

Lagrangian based methods for coherent structure detection

“…Examples of work on this topic include a study of coherent structures from the inertial equations of motion as applied to a hurricane 66 and jellyfish predation, 62 and investigations of inertial particle transport near elliptic structures motivated by the behavior of drifters near large scale eddies. 8 Another active research area is the application of coherent structure detection to diffusion-advection-reaction systems. By calculating the FTLE field for an ensemble of runs and comparing the results to the asymptotic states of chemical reactions, it has been shown that there is a strong correlation between regions of high FTLE and dynamically different reaction fates.…”

Inertia Influences Pelagic Sargassum Advection and Distribution

“…However, here we find the effective radius of the rafts is on the order of 90 cm. While Sargassum observations have been seen as qualitatively consistent with the theory governing inertial particles (Beron‐Vera et al, ), no validation for effective radius of Sargassum aggregations has previously been reported.…”

“…We considered the influence of inertia using the theory for a spherical particle (Maxey & Riley, ) as applied to large‐scale ocean flow by Beron‐Vera et al (). Inertia is a function of radius ( r ), latitude, and the ratio of the density of ambient seawater ( ρ ) to the particle density ( ρ P ).…”

Generalized Lagrangian coherent structures

“…Coherence of co-evolving variables may be different, and LCSs are not guaranteed to reveal it. The need for methods that can capture coherence of something other than fluid trajectories have urged researchers to extend the concept of LCSs to some chemical and bio-physical applications by using a modified velocity field in (1) [32,33,34,35,36,111,112,113,114]. In the next section we present a unified notation of generalized LCSs that naturally incorporate these prior developments and are readily applicable to other co-evolving variables not considered in prior literature.…”

“…Thus, GLCSs are again required. There has been some work attempting to extend simple LCSs to capture their behavior [111,112,113], but more work remains to be done. A particular complicating factor for inertial particle dynamics is the fact that the Basset history force makes their evolution nonlocal in time, in that the force on an inertial particle at an instant depends on its entire previous history.…”