Analytical solutions for von Karman streets of hollow vortices

New analytical solutions are presented for steadily translating von Karman vortex streets made up of two infinite rows of hollow vortices. First, the solution for a single row of hollow vortices due to Baker ["Structure of a linear array of hollow vortices of finite cross-section," J. Fluid Mech. 74, 469 (1976)] is rederived, in a modified form, and using a new mathematical approach. This approach is then generalized to find relative equilibria for both unstaggered and staggered double hollow vortex streets. The method employs a combination of free streamline theory and conformal mapping ideas. The staggered hollow vortex streets are compared with analogous numerical solutions for double streets of vortex patches due to Saffman and Schatzman ["Properties of a vortex street of finite vortices," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 2, 285 (1981)] and several common features are found. In particular, within the two different inviscid vortex models, the same street aspect ratio of approximately 0.34-0.36 is found to have special significance for the equilibria. (C) 2011 American Institute of Physics. [doi:10.1063/1.3665102]