The merging of a pair of symmetric, horizontally oriented vortices in unstratified and stably stratified viscous fluid is investigated. Two-dimensional numerical simulations are performed for a range of flow conditions. The merging process is resolved into four phases of development and key underlying physics are identified. In particular, the deformation of the vortices, explained in terms of the interaction of vorticity gradient, ∇ω, and rate of strain, S, leads to a tilt in ω contours in the vicinity of the center of rotation (a hyperbolic point). In the diffusive/deformation phase, diffusion of the vortices establishes the interaction between ∇ω and mutually induced S. During the convective/deformation phase, induced flow by filaments and, in stratified flow, baroclinically generated vorticity (BV), advects the vortices thereby modifying S, which, in general, may enhance or hinder the development of the tilt. The tilting and diffusion of ω near the center hyperbolic point causes ω from the core region to enter the exchange band where it is entrained. In the convective/entrainment phase, the vortex cores are thereby eroded and ultimately entrained into the exchange band, whose induced flow becomes dominant and transforms the flow into a single vortex. The critical aspect ratio, associated with the start of the convective/entrainment phase, is found to be the same for both the unstratified and stratified flows. In the final diffusive/axisymmetrization phase, the flow evolves towards axisymmetry by diffusion. In general, the effects of stratification depend on the ratio of the diffusive time scale (growth of cores) to the turnover time (establishment of BV), i.e. the Reynolds number. A crossover Reynolds number is found, above which convective merging is accelerated with respect to unstratified flow and below which it is delayed.

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.

Results of numerical simulations provide further insight on the physical mechanisms associated with symmetric vortex merger. The relative contributions of filament and exchange band fluid to the reduction in the vortex separation are determined and the latter is found to be dominant. A key underlying process is the interaction of strain rate and vorticity gradient near the center of rotation, through which a tilt in the vorticity contours is established. This leads to the entrainment of core fluid into the exchange band, which is transformed into a single vortex.

The merging of two unequal co-rotating vortices in a viscous fluid is investigated. Two-dimensional numerical simulations of initially equal sized Lamb-Oseen vortices with differing relative strengths are performed. Results show how the disparity in deformation rates between the vortices alters the interaction. Key physical mechanisms associated with vortex merging are identified. A merging criterion is formulated in terms of the relative timing of core detrainment and destruction. A critical strain parameter is defined to characterize the establishment of core detrainment. This parameter is shown to be directly related to the critical aspect ratio in the case of symmetric merger.

The merging of two unequal co-rotating vortices in a viscous fluid is investigated. Two-dimensional numerical simulations of initially equal sized Lamb-Oseen vortices with differing relative strengths are performed. Results show how the disparity in deformation rates between the vortices alters the interaction. Key physical mechanisms associated with vortex merging are identified. A merging criterion is formulated in terms of the relative timing of core detrainment and destruction. A critical strain parameter is defined to characterize the establishment of core detrainment. This parameter is shown to be directly related to the critical aspect ratio in the case of symmetric merger.