  The stability of periodic arrays of Mallier-Maslowe or Kelvin-Stuart vortices
is discussed. We derive with the energy-Casimir stability method the nonlinear
stability of this solution in the inviscid case as a function of the solution
parameters and of the domain size. We exhibit the maximum size of the domain
for which the vortex street is stable. By adapting a numerical time-stepping
code, we calculate the linear stability of the Mallier-Maslowe solution in the
presence of viscosity and compensating forcing. Finally, the results are
discussed and compared to a recent experiment in fluids performed by Tabeling
et al.~[Europhysics Letters {\bf 3}, 459 (1987)]. Electromagnetically driven
counter-rotating vortices are unstable above a critical electric current, and
give way to co-rotating vortices. The importance of the friction at the bottom
of the experimental apparatus is also discussed.
