Vortex Dipole Evolution in Viscoelastic Media: Effects of Asymmetry, Coupling, and Transverse Shear Waves

TL;DR

This study investigates how vortex dipoles evolve in viscoelastic media, highlighting the effects of asymmetry, coupling strength, and transverse shear waves on vortex dynamics and interactions.

Contribution

It introduces numerical simulations of vortex dipoles in viscoelastic fluids, revealing how viscoelasticity and asymmetry influence vortex motion and wave interactions.

Findings

Symmetric dipoles exhibit sustained translation with speed decreasing as separation increases.

Asymmetric dipoles induce rotational motion due to imbalance in vortex properties.

Transverse shear waves significantly affect vortex interactions in strongly coupled regimes.

Abstract

The dynamics of a Lamb-Oseen vortex dipole in a viscoelastic fluid are investigated, with emphasis on asymmetry, coupling strength, and transverse shear waves relevant to strongly coupled dusty plasmas. Dusty plasmas provide a natural realization of strongly coupled VE behavior, where transverse shear modes dominate in the incompressible limit. Numerical simulations are carried out using the incompressible generalized hydrodynamic model for both symmetric and asymmetric dipoles, with variations in vortex core size, circulation strength, and separation distance. In the symmetric case, dipoles exhibit sustained translational motion, with propagation speed decreasing as the initial separation distance increases, consistent with inviscid predictions. In contrast, asymmetric configurations-arising from unequal core radii or circulation strengths-lead to rotational motion due to imbalance in induced velocities, with the weaker vortex orbiting the stronger one. Viscoelasticity introduces transverse shear waves whose strength and propagation speed increase with coupling. In weakly coupled regimes, their influence is minor, while in moderately coupled regimes they modify propagation and induce deformation. In strongly coupled regimes, transverse shear waves significantly enhance vortex-vortex interaction, accelerating strain-induced deformation and leading to rapid dissipation of the weaker vortex. The evolution also satisfies the conservation theorem, where the contributions from convective, radiative, and dissipative processes dynamically compensate each other, maintaining global balance throughout the dynamics. These results provide insight into wave-vortex coupling in complex fluids, with implications for transport processes and structure formation in strongly coupled plasmas and other viscoelastic media.