Coherent structures and the saturation of a nonlinear dynamo

Abstract

Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied, the kinematic stage, where a seed magnetic field undergoes exponential growth, and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, besides providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite-time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

“…The latter have been intensively studied in MHD turbulence, including their generation via flow instabilities [26], their detection [27], the role of compressibility in their dynamics [28], as well as, their effects on stochastic particle acceleration [29], and energy dissipation [30].…”

A dynamical systems perspective for a real-time response to a marine oil spill

“…[26,15]). The choice of this tool versus others mentioned above, such as for instance FTLE, is based on the advantages discussed in the literature [27,28,29,30]. These are related to its accuracy, ability to detect Lagrangian features of the true ocean state, computational 115 efficiency and programming simplicity.…”

Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets

“…However, this does not influence our results as LDs do not depend on such a parameter. Rempel et al (2013) have extended the comparison with FTLE to the context of 3-D turbulent flows. Some of the advantages found are listed next; LDs are computationally cheaper than FTLEs; on data sets the function M is less sensitive to the quality of the interpolation of the vector field.…”