The merging of two co-rotating vortices: a numerical study

Abstract

The merging of two-dimensional co-rotating vortices is analysed through direct numerical simulations at large Reynolds numbers. It is shown how the Reynolds number affects each of the three phases that characterise this phenomenon. In the first phase, we examine the merging onset and focus on its definition. During the second rapid phase, the contributions of various flow regions upon the dynamics of a vortex are quantitatively studied. These regions are respectively the companion vortex, the filaments and an intermediate zone between vortices and filaments. The third phase is interpreted in terms of an advection diffusion process. Finally the final profile and circulation of the merged vortex is determined: the two thirds of the total circulation of the two initial vortices is contained in the newly formed vortex.

Dynamics and Instabilities of Vortex Pairs

“…At sufficiently high Reynolds numbers, the vortex is surrounded by fine concentric filaments (right column in Figure 9). Josserand & Rossi (2007) studied the different merging phases over a wide range of Reynolds numbers and deduced that various parts of the flow field contribute to the rapid approach during the convective stage of merging. They found that approximately 30% of the total circulation orbits the central merged vortex during the final stage.…”

“…The net result is that this vortex will move toward the other vortex; essentially both vortices rapidly move toward each other. There has been some debate, in a number of papers, as to whether the filaments are responsible for the merger (e.g., Velasco Fuentes 2005; Brandt & Nomura 2007, 2010Josserand & Rossi 2007). One issue with such discussion is that the answer depends on the definition of the term filament, which could, for example, be taken to mean the tip all the way to the root (right next to the vortex cores) or could be just the thin filament within the outer region.…”

“…(b) Direct numerical simulation at Re = 10,000. Panel b adapted with permission fromJosserand & Rossi (2007), copyright Elsevier Masson SAS. From these curves, it is possible to distinguish four distinct stages in the merging process.…”

Direct numerical simulation of helical vortices

“…In the pure two-dimensional case (L = ∞), it is known that two identical vortices rotate around each other for a period of time proportional to Reynolds number (Josserand and Rossi, 2007). Eventually, their mutual distance suddenly decreases and, after some rapid oscillations, vanishes, indicating that the vortices have merged.…”

The dynamics of barotropic vortex merging

“…Various fluid processes have been shown to be characterized by well-defined and coherent vortex interactions ranging from minute fluid vortex eddies to large-scale circulations (e.g., Yasuda, 1995;Ferreira and Schubert, 1997;Lansky et al, 1997;Cerretelli and Williamson, 2003;Josser and Rossi, 2007;Rodríguez-Marroyo et al, 2011;Yamazaki and Itoh, 2013;Luo et al, 2014;Tallapragada and Kieu, 2014). For specific mesoscale circulations in the atmosphere, vortex mergers are often connected to swift changes in development of tropical disturbances, which have significant impacts on the formation and subsequent track and intensity changes of tropical cyclones (Lander and Holland, 1993;Simpson et al, 1997;Ferreira and Schubert, 1997;Kieu and Zhang, 2009;Yu et al, 2010;Jang and Chun, 2015).…”