Instability, coalescence and fission of finite-area vortex structures

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract andfuse(or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortexfinite-areasystem corresponding to a von Kármán street of point vortices. Here the critical parameter isb/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At\[ b/a = 0.281 \]the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m= 2), triangular (m= 3), etc. surface modes owing to mutual interactions. Atb/a= 0 the measured growth rate is smaller than that for the corresponding von Kármán system and atb/a= 0·6 the measured growth rate is larger. Atb/a= 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.