Structure and stability of the finite-area von Karman street

By using a recently developed numerical method, we explore in detail the equilibria for a Karman street of uniform, large-area vortices. We construct a reliable implementation of an energy argument to find superharmonic instabilities. This leads us to organize flows into families with fixed impulse $I$, and to construct diagrams of the flow energy $E$ and horizontal spacing $L$. Families of large-$I$ streets exhibit a turning point in $L$, and terminate with ``cat's eyes'' vortices (as also suggested by previous investigators). However, for low-$I$ streets, the solution families display a multitude of turning points (leading to multiple possible streets, for given $L)$, and terminate with teardrop-shaped vortices. This is radically different from previous suggestions in the literature. These two qualitatively different limiting states are connected by a special street, whereby vortices from opposite rows touch, such that each vortex exhibits three corners. Furthermore, by following the family of $I$ = 0 streets to small $L$, we access a large, hitherto unexplored regime, involving streets with $L$ much smaller than previously believed possible. For each solution family, our stability approach also reveals a single superharmonic bifurcation, leading to new vortex streets, which exhibit lower symmetry.