Coherent structures

In order to develop more quantitative measures of coherent structures that would have comparative value over a range of experiments, it is essential that such measures be independent of the observer. It is only through such a general framework that theories with a fundamental predictive value can be developed. The triple decomposition phi = bar-phi + phi(c) + phi(r) (where bar-phi is the mean, phi(c) is the coherent part, and phi(r) is the random part of any turbulent field phi) serves this purpose. The equations of motion for the mean and coherent flow fields, based on the triple decomposition, are presented and modeling methods for the time-averaged and phase-averaged Reynolds stress are discussed

Coherent structures in an electron beam

The formation and evolution of coherent structures in a low-energy electron beam produced in a Malmberg-Penning trap is investigated by means of CCD diagnostics. The electrons are emitted from a thermionic cathode and their energy is controlled by an acceleration grid. By varying the spatial distribution of the energy of emitted electrons, different space charge effects are observed, as, e. g., a sharp or a gradual transition to a space charge dominated regime. The variation of the coherent structures along the beam is studied by varying the electron density or/and the value of the confined magnetic field. The observed processes are interpreted using a tridimensional particle-in-cell code which solves the Vlasov-Poisson system in zeroth order drift approximation.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Lagrangian coherent structures in nonlinear dynamos

Turbulence and chaos play a fundamental role in stellar convective zones through the transportof 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 transport barriers in the fluid. We report the detection of Lagrangian coherent structures in helical MHD dynamo simulations with scale separation. In an ABC--flow, two dynamo regimes, a propagating coherent mean--field regime and an intermittent regime, are identified as the magnetic diffusivity is varied. The sharp contrast between the chaotic tangle of attracting and repelling LCS in both regimes permits a unique analysis of the impact of the magnetic field on the velocity field. In a second example, LCS reveal the link between the level of chaotic mixing of the velocity field and the saturation of a large--scale dynamo when the magnetic field exceeds the equipartition value

Coherent structures in a turbulent environment

A systematic method is proposed for the determination of the statistical properties of a field consisting of a coherent structure interacting with turbulent linear waves. The explicit expression of the generating functional of the correlations is obtained, performing the functional integration on a neighbourhood in the function space around the soliton. The results show that the non-gaussian fluctuations observed in the tokamak plasma edge can be explained by the intermittent formation of nonlinear coherent structures.Comment: Revtex 21 pages includes 6 EPS figure

Localization and Coherence in Nonintegrable Systems

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic 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 and the final coherent structures are stable lumps. In systems where the phase space is not compact, the coherent structures can be collapses represented in phase space by a heteroclinic connection to infinity.Comment: 41 pages, 15 figure

Lagrangian Coherent Structures: A Climatological Look

A relatively new area at the crossroads of fluid and nonlinear dynamics are objects known as Lagrangian Coherent Structures (LCSs). LCSs are mathematically classified to differentiate parts of fluid flows. They, themselves, are the most influential parts of fluids. These objects have the most influence on the fluids around them and they allow for a sense of hierarchy in an otherwise busy environment of endless variables and trajectories. While all particles of fluids have the same dynamics on an individual basis, areas of fluid are not created equal and to be able to detect which parts will be the most important to look at allows for easier, but just as accurate, prediction of fluid movement. Recent applications include cleanup operations during the BP Deepwater Horizon oil spill, pollutant transfer in oceanic basins, and the analysis of polar storm activity. This thesis explores LCSs from the discrete mathematics to the future climatological impacts using virtual fluid simulations and LCS detection tools to facilitate analysis as well as diving into a case study with real and unapproximated oceanic data in the days following the Fukushima Daiichi nuclear power plant disaster

Low-dimensional dynamical system model for observed coherent structures in ocean satellite data

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one obtained from the experimental data. We apply the procedure to analyze coherent structures in an oceanic setting, the ones arising from instabilities of the Algerian current, in the western Mediterranean Sea. Data are from satellite altimetry providing Sea Surface Height, and the model is a two-layer quasigeostrophic system. A four-dimensional dynamical system is obtained that correctly describe the observed coherent structures (moving eddies). Finally, a bifurcation analysis is performed on the reduced model.Comment: 23 pages, 7 figure