Double-periodic arrays of vortices

Analytical solutions to the sinh-Poisson equation are discussed. This equation plays a role in the theory of vortex dynamics [Mallier and Maslowe, Phys. Fluids A 5, 1074 (1993)] and in the discussion of the most probable states of inviscid two-dimensional flows in fluids and plasmas [Montgomery and Joyce, Phys. Fluids 17, 1139 (1974)]. We present a family of double-periodic solutions on a rectangular grid. In limiting cases these solutions reproduce Mallier-Maslowe vortex streets and arrays of Greenhill's point vortices. (C) 2000 American Institute of Physics. [S1070- 6631(00)00912-0].