Characterization of the interactions of two unequal co-rotating vortices

Abstract

The interactions and merging of two unequal co-rotating vortices in a viscous fluid are investigated. Two-dimensional numerical simulations of initially equal-sized vortices with differing relative strengths are performed. In the case of equal-strength vortices, i.e. symmetric vortex pairs (Brandt & Nomura, J. Fluid Mech., vol. 592, 2007, pp. 413–446), the mutually induced strain deforms and tilts the vortices, which leads to a core detrainment process. The weakened vortices are mutually entrained and rapidly move towards each other as they intertwine and destruct. The flow thereby develops into a single compound vortex. With unequal strengths, i.e. asymmetric pairs, the disparity of the vortices alters the interaction. Merger may result from reciprocal but unequal entrainment, which yields a compound vortex; however other outcomes are possible. The various interactions are classified based on the relative timing of core detrainment and core destruction of the vortices. Through scaling analysis and simulation results, a critical strain rate parameter which characterizes the establishment of core detrainment is identified and determined. The onset of merging is associated with the achievement of the critical strain rate by ‘both’ vortices, and a merging criterion is thereby developed. In the case of symmetric pairs, the critical strain rate parameter is shown to be related to the critical aspect ratio. In contrast with symmetric merger, which is in essence a flow transformation, asymmetric merger may result in the domination of the stronger vortex because of the unequal deformation rates. If the disparity of the vortex strengths is sufficiently large, the critical strain rate is not attained by the stronger vortex before destruction of the weaker vortex, and the vortices do not merge.