Emergence of Coherent Clusters in the Ocean
Why does material tend to congregate in long coherent clusters at the surface of the ocean when it is well known that the ocean is dispersive? Here we review some recent research that addresses this question. A standard diagnostic for discerning transport pathways in incompressible 2D flows is the finite time Lyapunov exponent (FTLE). The FTLE can be expressed as the average of two rarely evaluated Lagrangian objects: the dilation and stretch rates. The stretch rate accounts for the ability of fluid shear to change the shape of fluid blobs, and for incompressible fluids it is the FTLE. However, in the real ocean and especially at submesoscales, the horizontal divergence is not negligible. This is quantified by the dilation rate, which is identically zero in 2D incompressible flow. Our analysis demonstrates that the combination of fluid dilation and stretch enhances accumulation of buoyant material along thin clusters in an otherwise dispersing ocean.
KeywordsLyapunov exponents Clustering Dilation Stretch Singular value decomposition Deformation Mixing Transport boundaries
This work was funded in part by grant N00014-11-1-0087 from the Office of Naval Research for MURI OCEAN 3D+1 and in part by a grant from The Gulf of Mexico Research Initiative to the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment. The authors thank Karal Gregory for technical assistance in preparation of the manuscript.
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