arXiv subjects

David Ian Pontin

Publications and source records attributed to David Ian Pontin.

3 recordsLinked to original sources

arXiv2021

Topological Constraints in the Reconnection of Vortex Braids

We study the relaxation of a topologically non-trivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field -- characterized by braided vorticity field lines -- determines the dynamics, particularly the asymptotic behaviour under vortex reconnection in an evolution at high Reynolds numbers 25,000. Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process the existence of regions of positive and negative kinetic helicity imposes a lower bound for the kinetic energy. For the enstrophy we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments.

physics.flu-dyn↗

arXiv2017

Quantifying the Tangling of Trajectories Using the Topological Entropy

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional magnetic fields, which are periodic in one direction. This method is based on measuring the length of a material line in the flow. Depending on the nature of the flow, the fluid can be mixed very efficiently which causes the line to stretch. Here we study a method that adaptively increases the resolution at locations along the line where folds lead to high curvature. This reduces the computational cost greatly which allows us to study unprecedented parameter regimes. We demonstrate how this efficient implementation allows the computation of the variation of the finite-time topological entropy in the mapping. This measure quantifies spatial variations of the braiding efficiency, important in many practical applications.

physics.plasm-ph↗

arXiv2017

Effects of Fieldline Topology on Energy Propagation in the Corona

We study the effect of photospheric footpoint motions on magnetic field structures containing magnetic nulls. The footpoint motions are prescribed on the photospheric boundary as a velocity field which entangles the magnetic field. We investigate the propagation of the injected energy, the conversion of energy, emergence of current layers and other consequences of the non-trivial magnetic field topology in this situation. These boundary motions lead initially to an increase in magnetic and kinetic energy. Following this, the energy input from the photosphere is partially dissipated and partially transported out of the domain through the Poynting flux. The presence of separatrix layers and magnetic null-points fundamentally alters the propagation behavior of disturbances from the photosphere into the corona. Depending on the field line topology close to the photosphere, the energy is either trapped or free to propagate into the corona.

astro-ph.SR↗