Lagrangian Rotating Contracting Structures

Abstract

We identify materially defined regions in unsteady two-dimensional flows that combine finite-time contraction with elevated accumulated intrinsic rotation along trajectories, which we term \emph{Lagrangian rotating contracting structures} (LRCS). These regions are detected using existing objective diagnostics -- the Lagrangian-averaged vorticity deviation (LAVD) together with direct tests of material contraction -- without relying on the geometry of LAVD level sets. In strongly deforming flows, LAVD maxima need not correspond to vortical regions or be enclosed by regular level sets, rendering geometry-based identification unreliable. Nevertheless, regions exhibiting inward spiraling motion and contraction can be extracted by combining LAVD with a contraction criterion. Applications to atmospheric and oceanic flows show that such behavior arises both in twisted LAVD fields generated at submesoscales and in mesoscale flows where it is enhanced by inertial effects, with finite-time contraction providing the dynamical constraint that isolates materially organized regions with elevated intrinsic rotation.