Volume_47_1_(2026)_71_81

Self-Similar Vortex Patches: Expansion Rate and Angular Velocity

Marco Cecchini

Abstract. We study the time evolution of an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks, close to a three point self-similarly expanding configurations in the point vortex model. We show that the centers of mass of these patches follow a self-similarly expanding trajectory and, for the first time, compute their angular velocity, while also refining the accuracy of the expansion rate, extending the work of Samuel Zbarsky. As a corollary, we obtain a stability result for self-similarly expanding configurations of three point vortices.

Rend. Mat. Appl. (7) 47 (2026) 71-81;  pdf