Different approaches are discussed of variational principles characterizing coherent vortex structures in two-dimensional flows. Turbulent flows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realizing an extremal value of the energy or a minimum of enstruphy. On the other hand the small scales take care of the in...

We study semi-infinite and bi-infinite scalar feed-forward networks. We find that the temporal dynamics of these systems is closely linked to the spatial dynamics of an associated interval map and show how this interval map may be used to describe stationary interfaces. Beyond stationary structures, we show that the onset of instabilities in finite networks is intimately related to the emergenc...

Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great F...

Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they con...

Turbulence and chaos play a fundamental role in stellar convective zones through the transport of particles, energy and momentum, and in fast dynamos, through the stretching, twisting and folding of magnetic flux tubes. A particularly revealing way to describe turbulent motions is through the analysis of Lagrangian coherent structures (LCS), which are material lines or surfaces that act as tran...

Two methods for the identification of coherent structures in fluid flows are studied for possible combination in a hybrid method providing deeper insight and greater efficiency. One method uses wavelet transforms to partition the field into coherent and incoherent portions using a thresholding of the wavelet coefficients. The other method is based on the stability analysis of trajectories throu...

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asymptotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved quantities leads naturally to localized and coherent structures. If the phase space is compact, the final equilibrium state is governed by entropy maximization a...