Clusters, deformation, and dilation: Diagnostics for material accumulation regions

Abstract

Clusters of material at the ocean surface have been frequently observed. Such accumulations of material play an important role in a variety of applications, from biology to pollution mitigation. Identifying where clusters will form can aid in locating, for example, hotspots of biological activity or regions of high pollutant concentration. Here cluster strength is introduced as a new metric for defining clusters when all particle positions are known. To diagnose regions likely to contain clusters without the need to integrate millions of particle trajectories, we propose to use dilation, which quantifies area changes of Lagrangian patches. Material deformation is decomposed into dilation and area‐preserving stretch processes to refine previous approaches based on finite‐time Lyapunov exponents (FTLE) by splitting the FTLE into fundamental kinematic properties. The concepts are developed theoretically and illustrated in the context of a state‐of‐the‐art data‐assimilating predictive ocean model of the Gulf of Mexico. Regions of dilation less than one are shown to be much more likely (6 times more likely in the given example) to be visited by particles than those of dilation greater than one. While the relationship is nonlinear, dilation and cluster strength exhibit a fairly good correlation. In contrast, both stretch and Eulerian divergence are found to be uncorrelated with cluster strength. Thus, dilation maps can be used as guides for identifying cluster locations, while saving some of the computational cost of trajectory integrations.

Submesoscale evolution of surface drifter triads in the Gulf of Mexico

“…Strain rate and divergence play an important role in tracer patch deformation [Gawȩdzki and Vergassola, 2000;Boffetta et al, 2004;Kalda et al, 2014;Huntley et al, 2015]. Here we provide estimates of these kinematic, velocity gradient properties from the drifters.…”

“…In the present study, triplet shape metrics from in situ drifters are analyzed to further quantify tracer patch evolution, complementing prior numerical investigations on surface clustering [ Zhong and Bracco , ; Kalda et al , ; Huntley et al , ; Jacobs et al , ] and ultimately informing oil spill mitigation efforts. LaCasce and Ohlmann [] and LaCasce [] investigated triangle evolution from 30 chance triplets of drifters initially separated by ≈1 km in the Gulf of Mexico.…”

Clustering of Floating Tracer Due to Mesoscale Vortex and Submesoscale Fields

“…Ocean circulation at the scales smaller than the mesoscale is dominated by the broad range of submesoscale processes, which have been intensively studied (Berti et al, 2011(Berti et al, , 2016Haza et al, 2016;Huntley et al, 2015;Jacobs et al, 2016;McWilliams, 2016;Ohlmann et al, 2019;Schroeder et al, 2012;Zhong & Bracco, 2013). Interactions between submesoscale and mesoscale motions are essential in the formation and breakdown of coherent mesoscale vortices, but the theoretical understanding is hindered by overwhelming computational costs due to the spatial resolution requirements (Dauhajre et al, 2019).…”

“…Although it is well established that floating tracers tend to form spatially localized aggregations (Cozar et al, 2014;Law et al, 2010;McComb, 1990;Martinez et al, 2009;Maximenko et al, 2012;Okubo, 1980;Väli et al, 2018) referred to as clusters, their definitions and measures of the degree of clustering differ substantially (Huntley et al, 2015;Jacobs et al, 2016). Dynamics of floating tracers is fundamentally different from the 10.1029/2019GL086504 dynamics of passive tracers, because in the former case, the tracer density on fluid particles changes due to the experienced surface-velocity divergence, whereas in the latter case, it is materially conserved and only advected by the flow.…”

Anisotropy and Inhomogeneity in Drifter Dispersion

“…In the last few decades, as the understanding and predictability of mesoscale and large-scale flows have matured, attention has turned to the role of the submesoscale (e.g., McWilliams, 2016). It has become increasingly clear that an energetic submesoscale flow field introduces local anisotropy and inhomogeneity (e.g., Lapeyre and Klein, 2006;Capet et al, 2008;Gula et al, 2014;Shulman et al, 2015), leading to local clustering of passive tracers in a statistically dispersive ocean (D'Asaro et al, 2018;Huntley et al, 2015;Jacobs et al, 2016). Anisotropy and inhomogeneity are likely stronger at the smaller scales, where the effects of frontogenetic processes are more prominent.…”