Point vortex dynamics: A classical mathematics playground

The Dynamics of Point-Vortex Data Assimilation

Reverse mathematics: the playground of logic

The general enterprise of calibrating the strength of classical mathematical theorems in terms of the axioms (typically of set existence) needed to prove them was begun by Harvey Friedman in [1971] (see also [1967]). His goals were both philosophical and foundational. What existence assumptions are really needed to develop classical mathematics and what other axioms and methods suffice to carry...

Dynamics-Informed Data Assimilation in a Point-Vortex Model

Fast and accurate numerical models are critical for the tracking, prediction, and control of fluid flows. Traditional grid-based modelling techniques, though highly accurate, are often too slow for these purposes. So-called reduced-order models—which track abstract flow structures, rather than the details of fluid velocities at every point—are much faster, but the inherent coarseness of their m...

Point vortex dynamics within a background vorticity patch

Recent experiments and simulations have observed that the interaction of strong vortices with a low vorticity background can strongly affect the dynamics of both vortices and background. This paper considers an idealized model of this interaction. The background is treated as a patch of uniform vorticity with a nearly circular shape. The strong vortices are treated as point vortices, and their ...

Dynamics of vortices and drift waves: a point vortex model

The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a dipole, splitting and merging of two like-circulation vortices, and chaos. The analytical and numerical results of this model have been found to predict under ...