Clusters, Deformation, and Dilation: Diagnostics for Material Accumulation Regions
Journal Article - Open Access
Naval Research Laboratory Stennis Space Center United States
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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.
- Physical and Dynamic Oceanography