UC San Diego

Two-dimensional vortex interactions and merging in fluid flows have long been a subjectof significant research interest, with particular focus on clarifying their role in the inverse energy cascade of two-dimensional turbulence. Previous research has generally taken one of two forms: detailed study of the interaction of two vortices in isolation, or macroscopic study of a field of many vortices. Bridging the gap between these has been difficult, due to the complexity of the two-vortex, i.e., vortex pair, interaction and its varied outcomes when the vortices are unequal. In order to rectify this, this research considers in detail the interaction of two unequal co-rotating vortices in viscous fluid, and develops a method to quantitatively assess their outcomes. This enables a simple characterization of interaction outcomes in terms of certain key parameters. Using this, the case of a vortex pair interacting in linear shear which serves as a simple model of the background flow generated by a field of many vortices, is then studied. Collectively, this work establishes a method for studying the influence of background flow on interacting vortices.

For the present research, numerical simulations are performed of vortex pairs having arange of vortex strength ratios in background flow having a linear shear velocity profile having a range of strengths, for finite Reynolds number. A method is introduced to monitor the flow development continuously, enabling the quantitative assessment of interaction outcomes in terms of an enhancement factor, ε, and a merging efficiency. η, which compare the circulations at the start and end of the convective interaction. The variation of these outcomes is found to be well-characterized by a mutuality parameter, a quantity directly related to the vortices’ enstrophy ratio. The presence of shear is then found to produce two distinct flow regimes: separation, in which the vortices move apart continuously, and hendition, in which they interact to form a single vortex similar to, and similarly characterized as in, the isolated-pair case. However, the presence of shear is observed to alter the timing of key physical interaction processes, which may in some cases significantly alter the ultimate outcome. Taken together, these findings imply a general framework for two-dimensional co-rotating vortex interactions that can be incorporated into turbulence models.