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

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.