Dynamics and deformation of a vortex during pairing under the influence of external shear

In general, a given vortex in a real flow may interact with other nearby vortices as well as large-scale background flows such as shear. To better understand the behavior of the vortices in such flows, the dynamics and interactions of a pair of two-dimensional like-signed viscous vortices having a circulation ratio Λ = Γ₁/Γ₂ = (a²₁/a²₂)(ω₁/ω₂) under the influence of a linear background shear having vorticity ω₂, of strength ζ = ω_S/ω₂, with finite viscosity, are investigated numerically. The main flow regimes, pairing and separation, are identified and briefly discussed; this work focuses on vortex-dominated pairings, in which the shear is observed to primarily aid or hinder the onset of detrainment, which precipitates the main convective interaction that results in a single final vortex. During such pairings, the vortices revolve with varying peak-peak distance b, such that the strain rate each vortex induces on the other varies in time, while the orientation of this vortex-induces strain rate relative to that of the background shear also varies. This results in a periodic deformation effect. The nature of this effect is examined and discussed. The subsequent pairing outcomes are then outlined and characterized in terms of key parameters.