Asymmetric vortex merger: mechanism and criterion

Abstract

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 Regeneration of the Lofoten Vortex through Vertical Alignment

“…Due to the complexity of the process, investigations of vortex mergers have mostly been conducted in theoretical settings. Some theoretical works consider asymmetric vortex pairs (Brandt et al, 2010;Melander et al, 1987;Ozugurlu et al, 2008) or symmetric vortex interactions with external influences (Brandt and Nomura, 2007;Carton et al, 2002;Dritschel, 2002;Carton, 2008, 2010). However, most works consider interactions of identical vortices in an isolated, quiet environment (Carton, 1992;Griffiths and Hopfinger, 1987;Melander et al, 1988;Sutyrin and Yushina, 1989;Velasco Fuentes and Velázquez Muñoz, 2003;von Hardenberg et al, 2000;Waugh, 1992).…”

“…A more realistic scenario is where the vortices differ in size and strength, which is also the case in the Lofoten basin. In addition to complete merger events, as described above, the merger process can then also be partially completed, and other processes, such as partial straining out and complete straining out, can occur (Brandt et al, 2010;Dritschel, 1995;Dritschel and Waugh, 1992;. In a partial merger, parts of the vorticity of the weaker vortex is absorbed by the stronger vortex .…”

Short-wave instabilities on a vortex pair of unequal strength circulation ratio

“…This relaxation process, leading towards the quasi-steady state, has been described in detail for equal strength vortex pairs by Le Dizès and Verga [19] for corotating vortices, and [15] for counter-rotating vortices. More recently, [18,20] have considered the case of jKj -1. Following the standard approach for stability analysis of vortex pairs [16], a frozen snapshot of the flow when the vortices have adapted to each other, serves as a basis for the second stage of the technique (linear stability analysis).…”