The physics of vortex merger and the effects of ambient stable stratification

Abstract

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.

Asymmetric vortex merger: mechanism and criterion

“…It also has practical significance, e.g., in the nearfield wake dynamics of an aircraft. Yet despite its elementary nature, the physical mechanisms of two-dimensional vortex merger have not been fully resolved [1,2,12].…”

“…The determination of (a/b) cr has been the focus of a number of studies, e.g., [11,10,9]. The physical mechanisms of symmetric merger have also been considered, e.g., [7,8,4,13,1,2]. In the more general interaction of two unequal size and/or strength (asymmetric) vortices, there is a greater range of flow behavior and the interaction may result in the destruction of the smaller/weaker vortex.…”

“…As in previous studies, it is useful to consider the flow structure in the co-rotating frame of reference. Figure 2 shows the instantaneous co-rotating streamlines (bold lines) indicating the inner core regions and the exchange band where fluid is advected around both vortices [7,2]. In time, all the flows result in a single vortex.…”

“…Figure 1a corresponds to symmetric vortices ( o,2 / o,1 = 1.0). Our previous analysis of symmetric merger describes the merging process in terms of four phases of development [2]. In the diffusive/deformation phase, the separation distance remains relatively constant while the cores grow by diffusion.…”

Asymmetric vortex merger: mechanism and criterion

“…The study follows from our previous work on equal vortices [2] identifying the primary physical mechanisms associated with vortex merging and develops a more generalized description and criterion for asymmetric merger. …”