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The chaotic nature of ocean motion is a major challenge that hinders the discovery of spatio-temporal current routes that govern the transport of material. Certain material, such as oil spills, pose significant environmental threats and these are enhanced by the fact that they evolve in a chaotic sea, in a way which still nowadays is far from being systematically anticipated. Recently such an oil spill event has affected the Mediterranean coast of several Middle Eastern countries. No accidents were reported for these spills previous to their arrival at the coast, and therefore there was no hint of their origin. Modelling such an event, in which uncertainties are increased due to the lack of information on where and when the spills was produced, stretches available technologies to their limits, and requires the use of novel ideas that help to understand the essential features of oil and tar transport by ocean currents. In this regard Lagrangian Coherent Structures enable us to find order within ocean chaos and provide powerful insights into chaotic events and their relationships over different locations and times like the one addressed. Using the observed locations of the oil impacting the coast at specific times, we seek to determine its original location and the time it was released in the open ocean. We have determined both using a combination of earlier satellite observations and computational modelling of the time evolution. The observed agreement between modeled cases and satellite observations highlights the power of these ideas.

▪ Abstract  Chaotic advection and, more generally, ideas from dynamical systems, have been fruitfully applied to a diverse, and varied, collection of mixing and transport problems arising in engineering applications over the past 20 years. Indeed, the “dynamical systems approach” was developed, and tested, to the point where it can now be considered a standard tool for understanding mixing and transport issues in many disciplines. This success for engineering-type flows motivated an effort to apply this approach to transport and mixing problems in geophysical flows. However, there are fundamental difficulties arising in this endeavor that must be properly understood and overcome. Central to this approach is that the starting point for analysis is a velocity field (i.e., the “dynamical system”). In many engineering applications this can be obtained sufficiently accurately, either analytically or computationally, so that it describes particle trajectories for the actual flow. However, in geophysical flows (and we concentrate here almost exclusively on oceanographic flows), the wide range of dynamically significant time and length scales makes the justification of any velocity field, in the sense of reproducing particle trajectories for the actual flow, a much more difficult matter. Nevertheless, the case for this approach is compelling due to the advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.), which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. This has been pursued in recent years through a combination of laboratory studies, kinematic models, and dynamically consistent models that have all been compared with observational data. During the course of these studies it has become apparent that a new type of dynamical system is necessary to consider in these studies (i.e., a finite time, aperiodically time-dependent velocity field defined as a data set), which requires the development of new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. In this article we review a number of the key developments to date in this young, but rapidly developing, area at the interface between geophysical fluid dynamics and applied and computational mathematics. We also describe the wealth of new directions for research that this approach unlocks.

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

Recently, new steps have been taken for the development of operational applications in coastal areas which require very high resolutions both in modeling and remote sensing products. In this context, this work describes a complete monitoring of an oil spill: we discuss the performance of high resolution hydrodynamic models in the area of Gran Canaria and their ability for describing the evolution of a real-time event of a diesel fuel spill, well-documented by port authorities and tracked with very high resolution remote sensing products. Complementary information supplied by different sources enhances the description of the event and supports their validation.

The present two-part paper provides a Lagrangian perspective of the final southern warming in 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. Part I focuses on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on a selected isentropic surface in the middle stratosphere. Part II discusses the three-dimensional evolution of the selected sudden warming event. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor as a tool. In this Part I we work in the idealized framework of a kinematic model that allows for an understanding of the contributing elements of the flow in late September during the splitting. We introduce a definition of kinematic SPV boundary based on a criterion for binning parcels inside and outside the vortex according to their values of the Lagrangian descriptor and associated PDF. This definition is justified by using arguments that go beyond heuristic considerations based on the potential vorticity. Next, we turn to the filamentation processes along this kinematic boundary, and the role of Lagrangian structures in the SPV splitting. We determine a criterion for splitting based on the structure of the evolving unstable and unstable manifolds.

This two-part paper aims to provide a Lagrangian perspective of the final southern warming in spring of 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor that is applied to reanalysis data. Part I presents our methodology and focuses by means of a kinematic model, on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on an isentropic surface in the middle stratosphere. The present Part II discusses the three dimensional evolution of the flow during the selected event. For this, we apply the definition of vortex boundary developed in Part I for guidance in the selection of trajectories to illuminate the evolving flow structures, and invoke a criterion that allows to justify why at an isentropic level a pinched vortex will split in later times. Lagrangian structures identified include surfaces that are several kilometers deep, and which a particle trajectory analysis confirms as barriers to the flow. The role of Lagrangian structures in determining the fate of particles during the SPV splitting is discussed.

In this paper we briefly review the main issues associated with mixing at the microscale and introduce the papers comprising the Theme Issue.In this paper we briefly review the main issues associated with mixing at the microscale and introduce the papers comprising the Theme Issue.