A numerical method involving isolated sources located outside the flow
domain is used to compute potential flows in two dimensions involving
the nonlinear water-wave boundary condition. The method is tested on
Stokes waves, and then used on steady streaming flows about submerged
cylinders. The circular cylinder with and without circulation is discu
ssed for a range of submergences and Froude numbers. Emphasis is place
d on the special choices of circulation for which the net vertical for
ce is small and the amplitude of downstream waves is reduced.