Viscous vortex crystals
Michele Dolce, Martin Donati
TL;DR
This paper analyzes the behavior of vortex crystals in 2D incompressible flows, focusing on their stability and evolution before vortex merging occurs, using symmetry and stability analysis of Navier-Stokes solutions.
Contribution
It introduces a detailed analysis of vortex crystal solutions in 2D Navier-Stokes equations, highlighting stability properties and solution control up to sub-diffusive times.
Findings
Description of vortex crystal solutions and their symmetries
Control of solutions up to sub-diffusive time scales
Insights into vortex merging onset
Abstract
We study the solution to the two-dimensional incompressible Navier-Stokes equations arising from a sum of Dirac masses in a particular co-rotating configuration. This configuration consists of a polygonal vortex crystal with or without a central vortex. By exploiting the symmetries and stability properties of the system, we describe and control the solution up to sub-diffusive time scales, prior to the expected onset of vortex merging.
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Taxonomy
TopicsNavier-Stokes equation solutions · Fluid Dynamics and Turbulent Flows · Nonlinear Dynamics and Pattern Formation