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Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
Lagrangian methods continue to stand at the forefront of the analysis of time-dependent dynamical systems. Most Lagrangian methods have criteria that must be fulfilled by trajectories as they are followed throughout a given finite flow…
This paper surveys various results concerning stability for the dynamics of Lagrangian (or Hamiltonian) systems on compact manifolds. The main, positive results state, roughly, that if the configuration manifold carries a hyperbolic metric,…
We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the vorticity, in general fluid flows. These special material…
Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this…
We review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows. We consider both mathematical methods and diagnostic scalar fields, comparing their…
Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to…
We investigate the effects of bacterial activity on the mixing and transport properties of a passive scalar in time-periodic flows in experiments and in a simple model. We focus on the interactions between swimming E. coli and the…
Persistent Lagrangian transport patterns at the ocean surface are revealed from Lagrangian Coherent Structures (LCSs) computed from daily climatological surface current velocities in the northwestern Gulf of Mexico (NWGoM). The velocities…
The properties of mesoscale Lagrangian turbulence in the Adriatic Sea are studied from a drifter data set spanning 1990-1999, focusing on the role of inhomogeneity and nonstationarity. A preliminary study is performed on the dependence of…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two-…
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred…
This study presents several new observations from the study of a warm-core ring (WCR) in the Gulf of Mexico based on the ECCO2 global ocean simulation. Using Lagrangian coherent structures (LCS) techniques to investigate this flow reveals a…
We extend previous analyses of the origins of complex transport dynamics in poroelastic media to the case where the input transient signal at a boundary is generated by a multimodal spectrum. By adding harmonic and anharmonic modal…
Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a…
Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly…
Rotationally coherent Lagrangian vortices (RCLVs) are identified from satellite-derived surface geostrophic velocities in the Eastern Pacific (180$^\circ$-130$^\circ$ W) using the objective (frame-invariant) finite-time…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations of all scales ranging…