Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis

Jupiter's zonal jets and Great Red Spot are well known from still images. Yet the planet's atmosphere is highly unsteady, which suggests that the actual material transport barriers delineating its main features should be time-dependent. Rare video footages of Jupiter's clouds provide an opportunity to verify this expectation from optically reconstructed velocity fields. Available videos, however, provide short-time and temporally aperiodic velocity fields that defy classical dynamical systems analyses focused on asymptotic features. To this end, we use here the recent theory of geodesic transport barriers to uncover finite-time mixing barriers in the wind field extracted from a video captured by NASA's Cassini space mission. More broadly, the approach described here provides a systematic and frame-invariant way to extract dynamic coherent structures from time-resolved remote observations of unsteady continua

Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems

We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy-Green strain tensor computed from the flow map of the forced mechanical system. This approach enables the finite-time visualization of generalized stable and unstable manifolds, attractors and generalized KAM curves under arbitrary forcing, when Poincaré maps are not available. We illustrate these results by detailed visualizations of the key finite-time invariant sets of conservatively and dissipatively forced Duffing oscillator

Defining coherent vortices objectively from the vorticity

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two- and three-dimensional flows.ISSN:0022-1120ISSN:1469-764

An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different