A ROW OF COUNTER-ROTATING VORTICES

In 1967, Stuart [J. Fluid Mech. 29, 417 (1967)] found an exact nonlinear solution of the inviscid, incompressible two-dimensional Navier-Stokes equations, representing an infinite row of identical vortices which are now known as Stuart vortices. In this Brief Communication, the corresponding result for an infinite row of counter-rotating vortices, i.e., a row of vortices of alternating sign, is presented. While for Stuart's solution, the streamfunction satisfied Liouville's equation, the streamfunction presented here satisfies the sinh-Gordon equation [Solitons: An Introduction (Cambridge U.P., London, 1989)]. The connection with Stuart's solution is discussed.