On the Effects of Vortex Core Modeling for Isolated and Paired Vortex Systems

Analytical models of unequal-strength vortex pairs are essential tools in the study of slender filament dynamics in engineering applications. However, these models typically assume an identical core size and structure for each vortex, despite physical examples demonstrating that distinct core properties can strongly affect the dynamics of the vortex pair. This paper investigates how vortices with distinct cores influence the self-induced motion of isolated filaments and the dynamics of interacting vortex pairs. Specifically, we revisit the Klein–Majda (K–M) model for single- and double-vortex systems, which includes the effects of the viscous vortex core and balances local self-induction asymptotically with higher-order self-stretching and interaction effects. However, the K–M model does not incorporate distinct core properties and asymmetries in the initial perturbation of vortex filaments. We suggest a model amendment to incorporate distinct vortex features in the double-vortex case. Our results demonstrate that differences in vortex core size, core velocity profiles, and initial perturbation amplitudes and wavelengths can significantly alter the evolution of interacting vortices at the leading order, challenging assumptions that are commonly made in asymptotic vortex models.