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The simulation and analysis of vortex dynamics in nearly-inviscid 2D and layerwise-2D flows. (English) Zbl 0927.76079

Vincent, Alain (ed.), Numerical methods in fluid mechanics. Providence, RI: AMS, American Mathematical Society. CRM Proc. Lect. Notes. 16, 33-52 (1998).
Summary: These notes review recent advances in the simulation and analysis of vorticity-dominated flows, ranging from idealised two-dimensional (2D) flows to more realistic layerwise-2D (stratified, rotating three-dimensional (3D)) flows. A numerical method capable of efficiently simulating this broad range of flows is contour surgery (CS), an extension and refinement of contour dynamics. CS is particularly suited to ultra-high Reynolds number flows (nearly-inviscid flows), a domain presently far out of the reach of both conventional numerical methods and of other Lagrangian “vortex methods”.
The latest CS method is described and illustrated. Fast algorithms, making use of a Lagrangian or vortex-based multipole expansion, are outlined for vortex dynamics on the infinite plane and on the surface of a sphere. A novel, versatile analysis tool is described that allows one to automatically track and diagnose arbitrarily complex vortes structures, defined as finite amorphous regions of fluid, as they move through the fluid and collide with one another. Applied to 2D turbulence, this tool reveals that vortex collisions involve minimally three close vortices, two of like sign and one of opposite sign, as in the “collapse” of three singular point vortices. These notes conclude with a discussion of future research, first in 3D quasi-geostrophic vortex dynamics, were a new instability is changing long-held views, and second in incorporating viscosity, which had been thought to be impossible.
For the entire collection see [Zbl 0898.00021].

MSC:

76M23 Vortex methods applied to problems in fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
76V05 Reaction effects in flows
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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